Search results for: Tikhonov regularization method

Authors: Ranadhir Roy

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Inverse problems arise in medical (molecular) imaging. These problems are characterized by large in three dimensions, and by the diffusion equation which models the physical phenomena within the media. The inverse problems are posed as a nonlinear optimization where the unknown parameters are found by minimizing the difference between the predicted data and the measured data. To obtain a unique and stable solution to an ill-posed inverse problem, a priori information must be used. Mathematical conditions to obtain stable solutions are established in Tikhonov’s regularization method, where the a priori information is introduced via a stabilizing functional, which may be designed to incorporate some relevant information of an inverse problem. Effective determination of the Tikhonov regularization parameter requires knowledge of the true solution, or in the case of optical imaging, the true image. Yet, in, clinically-based imaging, true image is not known. To alleviate these difficulties we have applied the penalty/modified barrier function (PMBF) method instead of Tikhonov regularization technique to make the inverse problems well-posed. Unlike the Tikhonov regularization method, the constrained optimization technique, which is based on simple bounds of the optical parameter properties of the tissue, can easily be implemented in the PMBF method. Imposing the constraints on the optical properties of the tissue explicitly restricts solution sets and can restore uniqueness. Like the Tikhonov regularization method, the PMBF method limits the size of the condition number of the Hessian matrix of the given objective function. The accuracy and the rapid convergence of the PMBF method require a good initial guess of the Lagrange multipliers. To obtain the initial guess of the multipliers, we use a least square unconstrained minimization problem. Three-dimensional images of fluorescence absorption coefficients and lifetimes were reconstructed from contact and noncontact experimentally measured data.

Keywords: constrained minimization, ill-conditioned inverse problems, Tikhonov regularization method, penalty modified barrier function method

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Authors: Fethi Soltani, Adel Almarashi, Idir Mechai

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Tikhonov regularization and reproducing kernels are the most popular approaches to solve ill-posed problems in computational mathematics and applications. And the Fourier multiplier operators are an essential tool to extend some known linear transforms in Euclidean Fourier analysis, as: Weierstrass transform, Poisson integral, Hilbert transform, Riesz transforms, Bochner-Riesz mean operators, partial Fourier integral, Riesz potential, Bessel potential, etc. Using the theory of reproducing kernels, we construct a simple and efficient representations for some class of Fourier multiplier operators Tm on the Paley-Wiener space Hh. In addition, we give an error estimate formula for the approximation and obtain some convergence results as the parameters and the independent variables approaches zero. Furthermore, using numerical quadrature integration rules to compute single and multiple integrals, we give numerical examples and we write explicitly the extremal function and the corresponding Fourier multiplier operators.

Keywords: fourier multiplier operators, Gauss-Kronrod method of integration, Paley-Wiener space, Tikhonov regularization

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Authors: Arka Roy, Chandra Prakash Dubey

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Inverse problem generally used for recovering hidden information from outside available data. Vertical component of gravity field we will be going to use for underneath density structure calculation. Ill-posing nature is main obstacle for any inverse problem. Linear regularization using Tikhonov formulation are used for appropriate choice of SVD and GSVD components. For real time data handle, signal to noise ratios should have to be less for reliable solution. In our study, 2D and 3D synthetic model with rectangular grid are used for gravity field calculation and its corresponding inversion for density reconstruction. Fine grid also we have considered to hold any irregular structure. Keeping in mind of algebraic ambiguity factor number of observation point should be more than that of number of data point. Picard plot is represented here for choosing appropriate or main controlling Eigenvalues for a regularized solution. Another important study is depth resolution plot (DRP). DRP are generally used for studying how the inversion is influenced by regularizing or discretizing. Our further study involves real time gravity data inversion of Vredeforte Dome South Africa. We apply our method to this data. The results include density structure is in good agreement with known formation in that region, which puts an additional support of our method.

Keywords: depth resolution plot, gravity inversion, Picard plot, SVD, Tikhonov formulation

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Authors: L. Raczynski, P. Moskal, P. Kowalski, W. Wislicki, T. Bednarski, P. Bialas, E. Czerwinski, A. Gajos, L. Kaplon, A. Kochanowski, G. Korcyl, J. Kowal, T. Kozik, W. Krzemien, E. Kubicz, Sz. Niedzwiecki, M. Palka, Z. Rudy, O. Rundel, P. Salabura, N.G. Sharma, M. Silarski, A. Slomski, J. Smyrski, A. Strzelecki, A. Wieczorek, M. Zielinski, N. Zon

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The J-PET scanner, which allows for single bed imaging of the whole human body, is currently under development at the Jagiellonian University. The J-PET detector improves the TOF resolution due to the use of fast plastic scintillators. Since registration of the waveform of signals with duration times of few nanoseconds is not feasible, a novel front-end electronics allowing for sampling in a voltage domain at four thresholds was developed. To take fully advantage of these fast signals a novel scheme of recovery of the waveform of the signal, based on ideas from the Tikhonov regularization (TR) and Compressive Sensing methods, is presented. The prior distribution of sparse representation is evaluated based on the linear transformation of the training set of waveform of the signals by using the Principal Component Analysis (PCA) decomposition. Beside the advantage of including the additional information from training signals, a further benefit of the TR approach is that the problem of signal recovery has an optimal solution which can be determined explicitly. Moreover, from the Bayes theory the properties of regularized solution, especially its covariance matrix, may be easily derived. This step is crucial to introduce and prove the formula for calculations of the signal recovery error. It has been proven that an average recovery error is approximately inversely proportional to the number of samples at voltage levels. The method is tested using signals registered by means of the single detection module of the J-PET detector built out from the 30 cm long BC-420 plastic scintillator strip. It is demonstrated that the experimental and theoretical functions describing the recovery errors in the J-PET scenario are largely consistent. The specificity and limitations of the signal recovery method in this application are discussed. It is shown that the PCA basis offers high level of information compression and an accurate recovery with just eight samples, from four voltage levels, for each signal waveform. Moreover, it is demonstrated that using the recovered waveform of the signals, instead of samples at four voltage levels alone, improves the spatial resolution of the hit position reconstruction. The experiment shows that spatial resolution evaluated based on information from four voltage levels, without a recovery of the waveform of the signal, is equal to 1.05 cm. After the application of an information from four voltage levels to the recovery of the signal waveform, the spatial resolution is improved to 0.94 cm. Moreover, the obtained result is only slightly worse than the one evaluated using the original raw-signal. The spatial resolution calculated under these conditions is equal to 0.93 cm. It is very important information since, limiting the number of threshold levels in the electronic devices to four, leads to significant reduction of the overall cost of the scanner. The developed recovery scheme is general and may be incorporated in any other investigation where a prior knowledge about the signals of interest may be utilized.

Keywords: plastic scintillators, positron emission tomography, statistical analysis, tikhonov regularization

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Authors: Hamed Kalhori, Lin Ye

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In this study, an inverse method was developed to reconstruct the magnitude and duration of impact forces exerted to a rectangular carbon fibre-epoxy composite honeycomb sandwich panel. The dynamic signals captured by Piezoelectric (PZT) sensors installed on the panel remotely from the impact locations were utilized to reconstruct the impact force generated by an instrumented hammer through an extended deconvolution approach. Two discretized forms of convolution integral are considered; the traditional one with an explicit transfer function and the modified one without an explicit transfer function. Deconvolution, usually applied to reconstruct the time history (e.g. magnitude) of a stochastic force at a defined location, is extended to identify both the location and magnitude of the impact force among a number of potential impact locations. It is assumed that a number of impact forces are simultaneously exerted to all potential locations, but the magnitude of all forces except one is zero, implicating that the impact occurs only at one location. The extended deconvolution is then applied to determine the magnitude as well as location (among the potential ones), incorporating the linear superposition of responses resulted from impact at each potential location. The problem can be categorized into under-determined (the number of sensors is less than that of impact locations), even-determined (the number of sensors equals that of impact locations), or over-determined (the number of sensors is greater than that of impact locations) cases. For an under-determined case, it comprises three potential impact locations and one PZT sensor for the rectangular carbon fibre-epoxy composite honeycomb sandwich panel. Assessments are conducted to evaluate the factors affecting the precision of the reconstructed force. Truncated Singular Value Decomposition (TSVD) and the Tikhonov regularization are independently chosen to regularize the problem to find the most suitable method for this system. The selection of optimal value of the regularization parameter is investigated through L-curve and Generalized Cross Validation (GCV) methods. In addition, the effect of different width of signal windows on the reconstructed force is examined. It is observed that the impact force generated by the instrumented impact hammer is sensitive to the impact locations of the structure, having a shape from a simple half-sine to a complicated one. The accuracy of the reconstructed impact force is evaluated using the correlation co-efficient between the reconstructed force and the actual one. Based on this criterion, it is concluded that the forces reconstructed by using the extended deconvolution without an explicit transfer function together with Tikhonov regularization match well with the actual forces in terms of magnitude and duration.

Keywords: honeycomb composite panel, deconvolution, impact localization, force reconstruction

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Authors: Benedict Barnes, Anthony Y. Aidoo

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A Divergence Regularization Method (DRM) is used to regularize the ill-posed Helmholtz equation where the boundary deflection is inhomogeneous in a Hilbert space H. The DRM incorporates a positive integer scaler which homogenizes the inhomogeneous boundary deflection in Cauchy problem of the Helmholtz equation. This ensures the existence, as well as, uniqueness of solution for the equation. The DRM restores all the three conditions of well-posedness in the sense of Hadamard.

Keywords: divergence regularization method, Helmholtz equation, ill-posed inhomogeneous Cauchy boundary conditions

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Authors: Ömer Aktaş, Olga A. Suvorova, Oleg Tretyakov

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The boundary value problem on non-canonical and arbitrary shaped contour is solved with a numerically effective method called Analytical Regularization Method (ARM) to calculate propagation parameters. As a result of regularization, the equation of first kind is reduced to the infinite system of the linear algebraic equations of the second kind in the space of L2. This equation can be solved numerically for desired accuracy by using truncation method. The parameters as cut-off wavenumber and cut-off frequency are used in waveguide evolutionary equations of electromagnetic theory in time-domain to illustrate the real-valued TM fields with lossy and lossless media.

Keywords: analytical regularization method, electromagnetic theory evolutionary equations of time-domain, TM Field

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Authors: Tahir Nawaz Cheema, Dumitru Baleanu, Ali Raza

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In this research work, we design intelligent computing through Bayesian Regularization artificial neural networks (BRANNs) introduced to solve the mathematical modeling of infectious diseases (Covid-19). The dynamical transmission is due to the interaction of people and its mathematical representation based on the system's nonlinear differential equations. The generation of the dataset of the Covid-19 model is exploited by the power of the explicit Runge Kutta method for different countries of the world like India, Pakistan, Italy, and many more. The generated dataset is approximately used for training, testing, and validation processes for every frequent update in Bayesian Regularization backpropagation for numerical behavior of the dynamics of the Covid-19 model. The performance and effectiveness of designed methodology BRANNs are checked through mean squared error, error histograms, numerical solutions, absolute error, and regression analysis.

Keywords: mathematical models, beysian regularization, bayesian-regularization backpropagation networks, regression analysis, numerical computing

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Authors: Bry X., Trottier C., Mortier F., Cornu G., Verron T.

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We address component-based regularization of a Multivariate Generalized Linear Model (MGLM). A set of random responses Y is assumed to depend, through a GLM, on a set X of explanatory variables, as well as on a set T of additional covariates. X is partitioned into R conceptually homogeneous blocks X1, ... , XR , viewed as explanatory themes. Variables in each Xr are assumed many and redundant. Thus, Generalised Linear Regression (GLR) demands regularization with respect to each Xr. By contrast, variables in T are assumed selected so as to demand no regularization. Regularization is performed searching each Xr for an appropriate number of orthogonal components that both contribute to model Y and capture relevant structural information in Xr. We propose a very general criterion to measure structural relevance (SR) of a component in a block, and show how to take SR into account within a Fisher-scoring-type algorithm in order to estimate the model. We show how to deal with mixed-type explanatory variables. The method, named THEME-SCGLR, is tested on simulated data.

Keywords: Component-Model, Fisher Scoring Algorithm, GLM, PLS Regression, SCGLR, SEER, THEME

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Authors: Christine Böckmann, Julia Rosemann

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We present an inversion algorithm that is used in the European Aerosol Lidar Network for the inversion of data collected with multi-wavelength Raman lidar. These instruments measure backscatter coefficients at 355, 532, and 1064 nm, and extinction coefficients at 355 and 532 nm. The algorithm is based on manually controlled inversion of optical data which allows for detailed sensitivity studies and thus provides us with comparably high quality of the derived data products. The algorithm allows us to derive particle effective radius, volume, surface-area concentration with comparably high confidence. The retrieval of the real and imaginary parts of the complex refractive index still is a challenge in view of the accuracy required for these parameters in climate change studies in which light-absorption needs to be known with high accuracy. Single-scattering albedo (SSA) can be computed from the retrieve microphysical parameters and allows us to categorize aerosols into high and low absorbing aerosols. From mathematical point of view the algorithm is based on the concept of using truncated singular value decomposition as regularization method. This method was adapted to work for the retrieval of the particle size distribution function (PSD) and is called hybrid regularization technique since it is using a triple of regularization parameters. The inversion of an ill-posed problem, such as the retrieval of the PSD, is always a challenging task because very small measurement errors will be amplified most often hugely during the solution process unless an appropriate regularization method is used. Even using a regularization method is difficult since appropriate regularization parameters have to be determined. Therefore, in a next stage of our work we decided to use two regularization techniques in parallel for comparison purpose. The second method is an iterative regularization method based on Pade iteration. Here, the number of iteration steps serves as the regularization parameter. We successfully developed a semi-automated software for spherical particles which is able to run even on a parallel processor machine. From a mathematical point of view, it is also very important (as selection criteria for an appropriate regularization method) to investigate the degree of ill-posedness of the problem which we found is a moderate ill-posedness. We computed the optical data from mono-modal logarithmic PSD and investigated particles of spherical shape in our simulations. We considered particle radii as large as 6 nm which does not only cover the size range of particles in the fine-mode fraction of naturally occurring PSD but also covers a part of the coarse-mode fraction of PSD. We considered errors of 15% in the simulation studies. For the SSA, 100% of all cases achieve relative errors below 12%. In more detail, 87% of all cases for 355 nm and 88% of all cases for 532 nm are well below 6%. With respect to the absolute error for non- and weak-absorbing particles with real parts 1.5 and 1.6 in all modes the accuracy limit +/- 0.03 is achieved. In sum, 70% of all cases stay below +/-0.03 which is sufficient for climate change studies.

Keywords: aerosol particles, inverse problem, microphysical particle properties, regularization

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Authors: Yanping Liao, Congcong He, Ruigang Zhao

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The application of magnetocardiography signals to detect cardiac electrical function is a new technology developed in recent years. The magnetocardiography signal is detected with Superconducting Quantum Interference Devices (SQUID) and has considerable advantages over electrocardiography (ECG). It is difficult to extract Magnetocardiography (MCG) signal which is buried in the noise, which is a critical issue to be resolved in cardiac monitoring system and MCG applications. In order to remove the severe background noise, the Total Variation (TV) regularization method is proposed to denoise MCG signal. The approach transforms the denoising problem into a minimization optimization problem and the Majorization-minimization algorithm is applied to iteratively solve the minimization problem. However, traditional TV regularization method tends to cause step effect and lacks constraint adaptability. In this paper, an improved TV regularization method for denoising MCG signal is proposed to improve the denoising precision. The improvement of this method is mainly divided into three parts. First, high-order TV is applied to reduce the step effect, and the corresponding second derivative matrix is used to substitute the first order. Then, the positions of the non-zero elements in the second order derivative matrix are determined based on the peak positions that are detected by the detection window. Finally, adaptive constraint parameters are defined to eliminate noises and preserve signal peak characteristics. Theoretical analysis and experimental results show that this algorithm can effectively improve the output signal-to-noise ratio and has superior performance.

Keywords: constraint parameters, derivative matrix, magnetocardiography, regular term, total variation

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Authors: Ramazan I. Kadiev, Arcady Ponosov

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Mathematical models of gene regulatory networks can in many cases be described by ordinary differential equations with switching nonlinearities, where the initial value problem is ill-posed. Several regularization methods are known in the case of deterministic networks, but the presence of stochastic noise leads to several technical difficulties. In the presentation, it is proposed to apply the methods of the stochastic singular perturbation theory going back to Yu. Kabanov and Yu. Pergamentshchikov. This approach is used to regularize the above ill-posed problem, which, e.g., makes it possible to design stable numerical schemes. Several examples are provided in the presentation, which support the efficiency of the suggested analysis. The method can also be of interest in other fields of biomathematics, where differential equations contain switchings, e.g., in neural field models.

Keywords: ill-posed problems, singular perturbation analysis, stochastic differential equations, switching nonlinearities

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Authors: Teng Li, Kamran Mohseni

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This paper presents an inviscid regularization technique for the incompressible two-phase flow simulations. This technique is known as observable method due to the understanding of observability that any feature smaller than the actual resolution (physical or numerical), i.e., the size of wire in hotwire anemometry or the grid size in numerical simulations, is not able to be captured or observed. Differ from most regularization techniques that applies on the numerical discretization, the observable method is employed at PDE level during the derivation of equations. Difficulties in the simulation and analysis of realistic fluid flow often result from discontinuities (or near-discontinuities) in the calculated fluid properties or state. Accurately capturing these discontinuities is especially crucial when simulating flows involving shocks, turbulence or sharp interfaces. Over the past several years, the properties of this new regularization technique have been investigated that show the capability of simultaneously regularizing shocks and turbulence. The observable method has been performed on the direct numerical simulations of shocks and turbulence where the discontinuities are successfully regularized and flow features are well captured. In the current paper, the observable method will be extended to two-phase interfacial flows. Multiphase flows share the similar features with shocks and turbulence that is the nonlinear irregularity caused by the nonlinear terms in the governing equations, namely, Euler equations. In the direct numerical simulation of two-phase flows, the interfaces are usually treated as the smooth transition of the properties from one fluid phase to the other. However, in high Reynolds number or low viscosity flows, the nonlinear terms will generate smaller scales which will sharpen the interface, causing discontinuities. Many numerical methods for two-phase flows fail at high Reynolds number case while some others depend on the numerical diffusion from spatial discretization. The observable method regularizes this nonlinear mechanism by filtering the convective terms and this process is inviscid. The filtering effect is controlled by an observable scale which is usually about a grid length. Single rising bubble and Rayleigh-Taylor instability are studied, in particular, to examine the performance of the observable method. A pseudo-spectral method is used for spatial discretization which will not introduce numerical diffusion, and a Total Variation Diminishing (TVD) Runge Kutta method is applied for time integration. The observable incompressible Euler equations are solved for these two problems. In rising bubble problem, the terminal velocity and shape of the bubble are particularly examined and compared with experiments and other numerical results. In the Rayleigh-Taylor instability, the shape of the interface are studied for different observable scale and the spike and bubble velocities, as well as positions (under a proper observable scale), are compared with other simulation results. The results indicate that this regularization technique can potentially regularize the sharp interface in the two-phase flow simulations

Keywords: Euler equations, incompressible flow simulation, inviscid regularization technique, two-phase flow

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Authors: Teng Li, Kamran Mohseni

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This paper presents an inviscid regularization technique that is capable of regularizing the shocks and sharp interfaces simultaneously in the shock-interface interaction simulations. The direct numerical simulation of flows involving shocks has been investigated for many years and a lot of numerical methods were developed to capture the shocks. However, most of these methods rely on the numerical dissipation to regularize the shocks. Moreover, in high Reynolds number flows, the nonlinear terms in hyperbolic Partial Differential Equations (PDE) dominates, constantly generating small scale features. This makes direct numerical simulation of shocks even harder. The same difficulty happens in two-phase flow with sharp interfaces where the nonlinear terms in the governing equations keep sharpening the interfaces to discontinuities. The main idea of the proposed technique is to average out the small scales that is below the resolution (observable scale) of the computational grid by filtering the convective velocity in the nonlinear terms in the governing PDE. This technique is named “observable method” and it results in a set of hyperbolic equations called observable equations, namely, observable Navier-Stokes or Euler equations. The observable method has been applied to the flow simulations involving shocks, turbulence, and two-phase flows, and the results are promising. In the current paper, the observable method is examined on the performance of regularizing shocks and interfaces at the same time in shock-interface interaction problems. Bubble-shock interactions and Richtmyer-Meshkov instability are particularly chosen to be studied. Observable Euler equations will be numerically solved with pseudo-spectral discretization in space and third order Total Variation Diminishing (TVD) Runge Kutta method in time. Results are presented and compared with existing publications. The interface acceleration and deformation and shock reflection are particularly examined.

Keywords: compressible flow simulation, inviscid regularization, Richtmyer-Meshkov instability, shock-bubble interactions.

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Authors: Ouafa Amira, Jiangshe Zhang

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Clustering is an unsupervised machine learning technique; its aim is to extract the data structures, in which similar data objects are grouped in the same cluster, whereas dissimilar objects are grouped in different clusters. Clustering methods are widely utilized in different fields, such as: image processing, computer vision , and pattern recognition, etc. Fuzzy c-means clustering (fcm) is one of the most well known fuzzy clustering methods. It is based on solving an optimization problem, in which a minimization of a given cost function has been studied. This minimization aims to decrease the dissimilarity inside clusters, where the dissimilarity here is measured by the distances between data objects and cluster centers. The degree of belonging of a data point in a cluster is measured by a membership function which is included in the interval [0, 1]. In fcm clustering, the membership degree is constrained with the condition that the sum of a data object’s memberships in all clusters must be equal to one. This constraint can cause several problems, specially when our data objects are included in a noisy space. Regularization approach took a part in fuzzy c-means clustering technique. This process introduces an additional information in order to solve an ill-posed optimization problem. In this study, we focus on regularization by relative entropy approach, where in our optimization problem we aim to minimize the dissimilarity inside clusters. Finding an appropriate membership degree to each data object is our objective, because an appropriate membership degree leads to an accurate clustering result. Our clustering results in synthetic data sets, gaussian based data sets, and real world data sets show that our proposed model achieves a good accuracy.

Keywords: clustering, fuzzy c-means, regularization, relative entropy

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Authors: Arcady Ponosov., Ramazan Kadiev

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The work studies the global moment stability of solutions of systems of nonlinear differential Itô equations with delays. A modified regularization method (W-method) for the analysis of various types of stability of such systems, based on the choice of the auxiliaryequations and applications of the theory of positive invertible matrices, is proposed and justified. Development of this method for deterministic functional differential equations is due to N.V. Azbelev and his students. Sufficient conditions for the moment stability of solutions in terms of the coefficients for sufficiently general as well as specific classes of Itô equations are given.

Keywords: asymptotic stability, delay equations, operator methods, stochastic noise

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Authors: Aghbalou Nihad, Charki Abderafi, Saida Rahali, Reklaoui Kamal

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Maximize the benefit from the wind energy potential is the most interest of the wind power stakeholders. As a result, the wind tower size is radically increasing. Nevertheless, choosing an appropriate wind turbine for a selected site require an accurate estimate of vertical wind profile. It is also imperative from cost and maintenance strategy point of view. Then, installing tall towers or even more expensive devices such as LIDAR or SODAR raises the costs of a wind power project. Various models were developed coming within this framework. However, they suffer from complexity, generalization and lacks accuracy. In this work, we aim to investigate the ability of neural network trained using the Bayesian Regularization technique to estimate wind speed profile up to height of 100 m based on knowledge of wind speed lower heights. Results show that the proposed approach can achieve satisfactory predictions and proof the suitability of the proposed method for generating wind speed profile and probability distributions based on knowledge of wind speed at lower heights.

Keywords: bayesian regularization, neural network, wind shear, accuracy

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Authors: Paola Causin, Andrea Aspri, Alessandro Benfenati

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Diffuse Optical Tomography (DOT) is an emergent medical imaging technique which employs NIR light to estimate the spatial distribution of optical coefficients in biological tissues for diagnostic purposes, in a noninvasive and non-ionizing manner. DOT reconstruction is a severely ill-conditioned problem due to prevalent scattering of light in the tissue. In this contribution, we present our research in adopting hybrid knowledgedriven/data-driven approaches which exploit the existence of well assessed physical models and build upon them neural networks integrating the availability of data. Namely, since in this context regularization procedures are mandatory to obtain a reasonable reconstruction [1], we explore the use of neural networks as tools to include prior information on the solution. 2. Materials and Methods The idea underlying our approach is to leverage neural networks to solve PDE-constrained inverse problems of the form 𝒒 ∗ = 𝒂𝒓𝒈 𝒎𝒊𝒏𝒒 𝐃(𝒚, 𝒚̃), (1) where D is a loss function which typically contains a discrepancy measure (or data fidelity) term plus other possible ad-hoc designed terms enforcing specific constraints. In the context of inverse problems like (1), one seeks the optimal set of physical parameters q, given the set of observations y. Moreover, 𝑦̃ is the computable approximation of y, which may be as well obtained from a neural network but also in a classic way via the resolution of a PDE with given input coefficients (forward problem, Fig.1 box ). Due to the severe ill conditioning of the reconstruction problem, we adopt a two-fold approach: i) we restrict the solutions (optical coefficients) to lie in a lower-dimensional subspace generated by auto-decoder type networks. This procedure forms priors of the solution (Fig.1 box ); ii) we use regularization procedures of type 𝒒̂ ∗ = 𝒂𝒓𝒈𝒎𝒊𝒏𝒒 𝐃(𝒚, 𝒚̃)+ 𝑹(𝒒), where 𝑹(𝒒) is a regularization functional depending on regularization parameters which can be fixed a-priori or learned via a neural network in a data-driven modality. To further improve the generalizability of the proposed framework, we also infuse physics knowledge via soft penalty constraints (Fig.1 box ) in the overall optimization procedure (Fig.1 box ). 3. Discussion and Conclusion DOT reconstruction is severely hindered by ill-conditioning. The combined use of data-driven and knowledgedriven elements is beneficial and allows to obtain improved results, especially with a restricted dataset and in presence of variable sources of noise.

Keywords: inverse problem in tomography, deep learning, diffuse optical tomography, regularization

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Authors: Stylianos Kampakis

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This paper presents a new algorithm for neural networks called “Input Dropout with Aggressive Re-weighting” (IDAR) aimed specifically at datasets with many useless features. IDAR combines two techniques (dropout of input neurons and aggressive re weighting) in order to eliminate the influence of noisy features. The technique can be seen as a generalization of dropout. The algorithm is tested on two different benchmark data sets: a noisy version of the iris dataset and the MADELON data set. Its performance is compared against three other popular techniques for dealing with useless features: L2 regularization, LASSO and random forests. The results demonstrate that IDAR can be an effective technique for handling data sets with many useless features.

Keywords: neural networks, feature selection, regularization, aggressive reweighting

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Authors: Attaullah Khawaja, Amna Shabbir

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Channel inversion is one of the simplest techniques for multiuser downlink systems with single-antenna users. In this paper regularized channel inversion under equal power constraint in the multiuser multiple input multiple output (MU-MIMO) broadcast channels has been considered. Sum capacity with plain channel inversion also known as Zero Forcing Beam Forming (ZFBF) and optimum sum capacity using Dirty Paper Coding (DPC) has also been investigated. Analysis and simulations show that regularization enhances the system performance and empower linear growth in Sum Capacity and specially work well at low signal to noise ratio (SNRs) regime.

Keywords: broadcast channel, channel inversion, multiple antenna multiple-user wireless, multiple-input multiple-output (MIMO), regularization, dirty paper coding (DPC), sum capacity

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Authors: Mohammad Zavid Parvez, Manoranjan Paul

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A seizure prediction method is proposed by extracting global features using phase correlation between adjacent epochs for detecting relative changes and local features using fluctuation/deviation within an epoch for determining fine changes of different EEG signals. A classifier and a regularization technique are applied for the reduction of false alarms and improvement of the overall prediction accuracy. The experiments show that the proposed method outperforms the state-of-the-art methods and provides high prediction accuracy (i.e., 97.70%) with low false alarm using EEG signals in different brain locations from a benchmark data set.

Keywords: Epilepsy, seizure, phase correlation, fluctuation, deviation.

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Authors: Salihah Alghamdi, Surajit Ray

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Space-time data can be observed over irregularly shaped manifolds, which might have complex boundaries or interior gaps. Most of the existing methods do not consider the shape of the data, and as a result, it is difficult to model irregularly shaped data accommodating the complex domain. We used a method that can deal with space-time data that are distributed over non-planner shaped regions. The method is based on partial differential equations and finite element analysis. The model can be estimated using a penalized least squares approach with a regularization term that controls the over-fitting. The model is regularized using two roughness penalties, which consider the spatial and temporal regularities separately. The integrated square of the second derivative of the basis function is used as temporal penalty. While the spatial penalty consists of the integrated square of Laplace operator, which is integrated exclusively over the domain of interest that is determined using finite element technique. In this paper, we applied a spatio-temporal regression model with partial differential equations regularization (ST-PDE) approach to analyze a remote sensing data measuring the greenness of vegetation, measure by an index called enhanced vegetation index (EVI). The EVI data consist of measurements that take values between -1 and 1 reflecting the level of greenness of some region over a period of time. We applied (ST-PDE) approach to irregular shaped region of the EVI data. The approach efficiently accommodates the irregular shaped regions taking into account the complex boundaries rather than smoothing across the boundaries. Furthermore, the approach succeeds in capturing the temporal variation in the data.

Keywords: irregularly shaped domain, partial differential equations, finite element analysis, complex boundray

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Authors: Christoph Linse, Thomas Martinetz

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Recent findings have shown that Neural Networks generalize also in over-parametrized regimes with zero training error. This is surprising, since it is completely against traditional machine learning wisdom. In our empirical study we fortify these findings in the domain of fine-grained image classification. We show that very large Convolutional Neural Networks with millions of weights do learn with only a handful of training samples and without image augmentation, explicit regularization or pretraining. We train the architectures ResNet018, ResNet101 and VGG19 on subsets of the difficult benchmark datasets Caltech101, CUB_200_2011, FGVCAircraft, Flowers102 and StanfordCars with 100 classes and more, perform a comprehensive comparative study and draw implications for the practical application of CNNs. Finally, we show that VGG19 with 140 million weights learns to distinguish airplanes and motorbikes with up to 95% accuracy using only 20 training samples per class.

Keywords: convolutional neural networks, fine-grained image classification, generalization, image recognition, over-parameterized, small data sets

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Authors: Bolatbek Rysbaiuly, Aliya S. Azhibekova

Abstract:

Problems concerning the interpretation of the well testing results belong to the class of inverse problems of subsurface hydromechanics. The distinctive feature of such problems is that additional information is depending on the capabilities of oilfield experiments. Another factor that should not be overlooked is the existence of errors in the test data. To determine reservoir properties, some inverse problems for parabolic equations were investigated. An approach to solving the inverse problems based on the method of regularization is proposed.

Keywords: iterative approach, inverse problem, parabolic equation, reservoir properties

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Authors: Kefaya Qaddoum

Abstract:

Most of greenhouse growers desire a determined amount of yields in order to accurately meet market requirements. The purpose of this paper is to model a simple but often satisfactory supervised classification method. The original naive Bayes have a serious weakness, which is producing redundant predictors. In this paper, utilized regularization technique was used to obtain a computationally efficient classifier based on naive Bayes. The suggested construction, utilized L1-penalty, is capable of clearing redundant predictors, where a modification of the LARS algorithm is devised to solve this problem, making this method applicable to a wide range of data. In the experimental section, a study conducted to examine the effect of redundant and irrelevant predictors, and test the method on WSG data set for tomato yields, where there are many more predictors than data, and the urge need to predict weekly yield is the goal of this approach. Finally, the modified approach is compared with several naive Bayes variants and other classification algorithms (SVM and kNN), and is shown to be fairly good.

Keywords: tomato yield prediction, naive Bayes, redundancy, WSG

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Authors: Rachida Ouysse

Abstract:

This paper proposes a constrained principal components (CnPC) estimator for efficient estimation of large-dimensional factor models when errors are cross sectionally correlated and the number of cross-sections (N) may be larger than the number of observations (T). Although principal components (PC) method is consistent for any path of the panel dimensions, it is inefficient as the errors are treated to be homoskedastic and uncorrelated. The new CnPC exploits the assumption of bounded cross-sectional dependence, which defines Chamberlain and Rothschild’s (1983) approximate factor structure, as an explicit constraint and solves a constrained PC problem. The CnPC method is computationally equivalent to the PC method applied to a regularized form of the data covariance matrix. Unlike maximum likelihood type methods, the CnPC method does not require inverting a large covariance matrix and thus is valid for panels with N ≥ T. The paper derives a convergence rate and an asymptotic normality result for the CnPC estimators of the common factors. We provide feasible estimators and show in a simulation study that they are more accurate than the PC estimator, especially for panels with N larger than T, and the generalized PC type estimators, especially for panels with N almost as large as T.

Keywords: high dimensionality, unknown factors, principal components, cross-sectional correlation, shrinkage regression, regularization, pseudo-out-of-sample forecasting

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Authors: Ulrich Wake, Eniman Syamsuddin

Abstract:

The model for camera model identificaiton is trained using pretrained model ResNet43 and ResNet50. The dataset consists of 500 photos of each phone. Dataset is divided into 1280 photos for training, 320 photos for validation and 400 photos for testing. The model is trained using One Cycle Policy Method and tested using Test-Time Augmentation. Furthermore, the model is trained for 50 epoch using regularization such as drop out and early stopping. The result is 90% accuracy for validation set and above 85% for Test-Time Augmentation using ResNet50. Every model is also trained by slightly updating the pretrained model’s weights

Keywords: ​ One Cycle Policy, ResNet34, ResNet50, Test-Time Agumentation

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Authors: Bowei Yuan, Shi Li, Liuyang Song, Huaqing Wang, Lingli Cui

Abstract:

Convolutional neural networks (CNN) have received extensive attention in the field of fault diagnosis. Many fault diagnosis methods use CNN for fault type identification. However, when the amount of raw data collected by sensors is massive, the neural network needs to perform a time-consuming classification task. In this paper, a mechanical fault diagnosis method based on vibration signal down-sampling and the improved one-dimensional convolutional neural network is proposed. Through the robust principal component analysis, the low-rank feature matrix of a large amount of raw data can be separated, and then down-sampling is realized to reduce the subsequent calculation amount. In the improved one-dimensional CNN, a smaller convolution kernel is used to reduce the number of parameters and computational complexity, and regularization is introduced before the fully connected layer to prevent overfitting. In addition, the multi-connected layers can better generalize classification results without cumbersome parameter adjustments. The effectiveness of the method is verified by monitoring the signal of the centrifugal pump test bench, and the average test accuracy is above 98%. When compared with the traditional deep belief network (DBN) and support vector machine (SVM) methods, this method has better performance.

Keywords: fault diagnosis, vibration signal down-sampling, 1D-CNN

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Authors: Ali Pour Yazdanpanah, Farideh Foroozandeh Shahraki, Emma Regentova

Abstract:

The reconstruction from sparse-view projections is one of important problems in computed tomography (CT) limited by the availability or feasibility of obtaining of a large number of projections. Traditionally, convex regularizers have been exploited to improve the reconstruction quality in sparse-view CT, and the convex constraint in those problems leads to an easy optimization process. However, convex regularizers often result in a biased approximation and inaccurate reconstruction in CT problems. Here, we present a nonconvex, Lipschitz continuous and non-smooth regularization model. The CT reconstruction is formulated as a nonconvex constrained L1 − L2 minimization problem and solved through a difference of convex algorithm and alternating direction of multiplier method which generates a better result than L0 or L1 regularizers in the CT reconstruction. We compare our method with previously reported high performance methods which use convex regularizers such as TV, wavelet, curvelet, and curvelet+TV (CTV) on the test phantom images. The results show that there are benefits in using the nonconvex regularizer in the sparse-view CT reconstruction.

Keywords: computed tomography, non-convex, sparse-view reconstruction, L1-L2 minimization, difference of convex functions

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Authors: N. Dahraoui, M. Boulakroune, D. Benatia

Abstract:

In this paper, the improvement by deconvolution of the depth resolution in Secondary Ion Mass Spectrometry (SIMS) analysis is considered. Indeed, we have developed a new Tikhonov-Miller deconvolution algorithm where a priori model of the solution is included. This is a denoisy and pre-deconvoluted signal obtained from: firstly, by the application of wavelet shrinkage algorithm, secondly by the introduction of the obtained denoisy signal in an iterative deconvolution algorithm. In particular, we have focused the light on the effect of the iterations number on the evolution of the deconvoluted signals. The SIMS profiles are multilayers of Boron in Silicon matrix.

Keywords: DRF, in-depth resolution, multiresolution deconvolution, SIMS, wavelet shrinkage

Procedia PDF Downloads 418