Search results for: tikhonov regularization

Authors: Gabrielle Robertson, Matthew Downs, Joseph Dagher

Abstract:

Iron deposition in the brain has been linked with a host of neurological disorders such as Alzheimer’s, Parkinson’s, and Multiple Sclerosis. While some treatment options exist, there are no objective measurement tools that allow for the monitoring of iron levels in the brain in vivo. An emerging Magnetic Resonance Imaging (MRI) method has been recently proposed to deduce iron concentration through quantitative measurement of magnetic susceptibility. This is a multi-step process that involves repeated modeling of physical processes via approximate numerical solutions. For example, the last two steps of this Quantitative Susceptibility Mapping (QSM) method involve I) mapping magnetic field into magnetic susceptibility and II) mapping magnetic susceptibility into iron concentration. Process I involves solving an ill-posed inverse problem by using regularization via injection of prior belief. The end result from Process II highly depends on the model used to describe the molecular content of each voxel (type of iron, water fraction, etc.) Due to these factors, the accuracy and repeatability of QSM have been an active area of research in the MRI and medical imaging community. This work aims to estimate iron concentration in the brain via a single step. A synthetic numerical model of the human head was created by automatically and manually segmenting the human head on a high-resolution grid (640x640x640, 0.4mm³) yielding detailed structures such as microvasculature and subcortical regions as well as bone, soft tissue, Cerebral Spinal Fluid, sinuses, arteries, and eyes. Each segmented region was then assigned tissue properties such as relaxation rates, proton density, electromagnetic tissue properties and iron concentration. These tissue property values were randomly selected from a Probability Distribution Function derived from a thorough literature review. In addition to having unique tissue property values, different synthetic head realizations also possess unique structural geometry created by morphing the boundary regions of different areas within normal physical constraints. This model of the human brain is then used to create synthetic MRI measurements. This is repeated thousands of times, for different head shapes, volume, tissue properties and noise realizations. Collectively, this constitutes a training-set that is similar to in vivo data, but larger than datasets available from clinical measurements. This 3D convolutional U-Net neural network architecture was used to train data-driven Deep Learning models to solve for iron concentrations from raw MRI measurements. The performance was then tested on both synthetic data not used in training as well as real in vivo data. Results showed that the model trained on synthetic MRI measurements is able to directly learn iron concentrations in areas of interest more effectively than other existing QSM reconstruction methods. For comparison, models trained on random geometric shapes (as proposed in the Deep QSM method) are less effective than models trained on realistic synthetic head models. Such an accurate method for the quantitative measurement of iron deposits in the brain would be of important value in clinical studies aiming to understand the role of iron in neurological disease.

Keywords: magnetic resonance imaging, MRI, iron deposition, machine learning, quantitative susceptibility mapping

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Authors: Hyohun Kim, Dongwha Shin, Yeonseok Kim, Ji-Su Ahn, Kensuke Nakamura, Dongeun Choi, Byung-Woo Hong

Abstract:

Artefacts are commonly encountered in the imaging process of clinical computed tomography (CT) where the artefact refers to any systematic discrepancy between the reconstructed observation and the true attenuation coefficient of the object. It is known that CT images are inherently more prone to artefacts due to its image formation process where a large number of independent detectors are involved, and they are assumed to yield consistent measurements. There are a number of different artefact types including noise, beam hardening, scatter, pseudo-enhancement, motion, helical, ring, and metal artefacts, which cause serious difficulties in reading images. Thus, it is desired to remove nuisance factors from the degraded image leaving the fundamental intrinsic information that can provide better interpretation of the anatomical and pathological characteristics. However, it is considered as a difficult task due to the high dimensionality and variability of data to be recovered, which naturally motivates the use of machine learning techniques. We propose an image restoration algorithm based on the deep neural network framework where the denoising auto-encoders are stacked building multiple layers. The denoising auto-encoder is a variant of a classical auto-encoder that takes an input data and maps it to a hidden representation through a deterministic mapping using a non-linear activation function. The latent representation is then mapped back into a reconstruction the size of which is the same as the size of the input data. The reconstruction error can be measured by the traditional squared error assuming the residual follows a normal distribution. In addition to the designed loss function, an effective regularization scheme using residual-driven dropout determined based on the gradient at each layer. The optimal weights are computed by the classical stochastic gradient descent algorithm combined with the back-propagation algorithm. In our algorithm, we initially decompose an input image into its intrinsic representation and the nuisance factors including artefacts based on the classical Total Variation problem that can be efficiently optimized by the convex optimization algorithm such as primal-dual method. The intrinsic forms of the input images are provided to the deep denosing auto-encoders with their original forms in the training phase. In the testing phase, a given image is first decomposed into the intrinsic form and then provided to the trained network to obtain its reconstruction. We apply our algorithm to the restoration of the corrupted CT images by the artefacts. It is shown that our algorithm improves the readability and enhances the anatomical and pathological properties of the object. The quantitative evaluation is performed in terms of the PSNR, and the qualitative evaluation provides significant improvement in reading images despite degrading artefacts. The experimental results indicate the potential of our algorithm as a prior solution to the image interpretation tasks in a variety of medical imaging applications. This work was supported by the MISP(Ministry of Science and ICT), Korea, under the National Program for Excellence in SW (20170001000011001) supervised by the IITP(Institute for Information and Communications Technology Promotion).

Keywords: auto-encoder neural network, CT image artefact, deep learning, intrinsic image representation, noise reduction, total variation

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