Search results for: fast Fourier algorithms

Authors: Reza Nematirad, Anil Pahwa, Balasubramaniam Natarajan

Abstract:

Time series data consist of successive data points collected over a period of time. Accurate prediction of future values is essential for informed decision-making in several real-world applications, including electricity load demand forecasting, lifetime estimation of industrial machinery, traffic planning, weather prediction, and the stock market. Due to their critical relevance and wide application, there has been considerable interest in time series forecasting in recent years. However, the proliferation of sensors and IoT devices, real-time monitoring systems, and high-frequency trading data introduce significant intricate temporal variations, rapid changes, noise, and non-linearities, making time series forecasting more challenging. Classical methods such as Autoregressive integrated moving average (ARIMA) and Exponential Smoothing aim to extract pre-defined temporal variations, such as trends and seasonality. While these methods are effective for capturing well-defined seasonal patterns and trends, they often struggle with more complex, non-linear patterns present in real-world time series data. In recent years, deep learning has made significant contributions to time series forecasting. Recurrent Neural Networks (RNNs) and their variants, such as Long short-term memory (LSTMs) and Gated Recurrent Units (GRUs), have been widely adopted for modeling sequential data. However, they often suffer from the locality, making it difficult to capture local trends and rapid fluctuations. Convolutional Neural Networks (CNNs), particularly Temporal Convolutional Networks (TCNs), leverage convolutional layers to capture temporal dependencies by applying convolutional filters along the temporal dimension. Despite their advantages, TCNs struggle with capturing relationships between distant time points due to the locality of one-dimensional convolution kernels. Transformers have revolutionized time series forecasting with their powerful attention mechanisms, effectively capturing long-term dependencies and relationships between distant time points. However, the attention mechanism may struggle to discern dependencies directly from scattered time points due to intricate temporal patterns. Lastly, Multi-Layer Perceptrons (MLPs) have also been employed, with models like N-BEATS and LightTS demonstrating success. Despite this, MLPs often face high volatility and computational complexity challenges in long-horizon forecasting. To address intricate temporal variations in time series data, this study introduces Times2D, a novel framework that parallelly integrates 2D spectrogram and derivative heatmap techniques. The spectrogram focuses on the frequency domain, capturing periodicity, while the derivative patterns emphasize the time domain, highlighting sharp fluctuations and turning points. This 2D transformation enables the utilization of powerful computer vision techniques to capture various intricate temporal variations. To evaluate the performance of Times2D, extensive experiments were conducted on standard time series datasets and compared with various state-of-the-art algorithms, including DLinear (2023), TimesNet (2023), Non-stationary Transformer (2022), PatchTST (2023), N-HiTS (2023), Crossformer (2023), MICN (2023), LightTS (2022), FEDformer (2022), FiLM (2022), SCINet (2022a), Autoformer (2021), and Informer (2021) under the same modeling conditions. The initial results demonstrated that Times2D achieves consistent state-of-the-art performance in both short-term and long-term forecasting tasks. Furthermore, the generality of the Times2D framework allows it to be applied to various tasks such as time series imputation, clustering, classification, and anomaly detection, offering potential benefits in any domain that involves sequential data analysis.

Keywords: derivative patterns, spectrogram, time series forecasting, times2D, 2D representation

Procedia PDF Downloads 44

Authors: Guilherme Giacomini, Ana Luiza Menegatti Pavan, Allan Felipe Fattori Alves, Marcela de Oliveira, Fernando Antonio Bacchim Neto, José Ricardo de Arruda Miranda, Seizo Yamashita, Diana Rodrigues de Pina

Abstract:

The maxillary sinus (MS), part of the paranasal sinus complex, is one of the most enigmatic structures in modern humans. The literature has suggested that MSs function as olfaction accessories, to heat or humidify inspired air, for thermoregulation, to impart resonance to the voice and others. Thus, the real function of the MS is still uncertain. Furthermore, the MS anatomy is complex and varies from person to person. Many diseases may affect the development process of sinuses. The incidence of rhinosinusitis and other pathoses in the MS is comparatively high, so, volume analysis has clinical value. Providing volume values for MS could be helpful in evaluating the presence of any abnormality and could be used for treatment planning and evaluation of the outcome. The computed tomography (CT) has allowed a more exact assessment of this structure, which enables a quantitative analysis. However, this is not always possible in the clinical routine, and if possible, it involves much effort and/or time. Therefore, it is necessary to have a convenient, robust, and practical tool correlated with the MS volume, allowing clinical applicability. Nowadays, the available methods for MS segmentation are manual or semi-automatic. Additionally, manual methods present inter and intraindividual variability. Thus, the aim of this study was to develop an automatic tool to quantity the MS volume in CT scans of paranasal sinuses. This study was developed with ethical approval from the authors’ institutions and national review panels. The research involved 30 retrospective exams of University Hospital, Botucatu Medical School, São Paulo State University, Brazil. The tool for automatic MS quantification, developed in Matlab®, uses a hybrid method, combining different image processing techniques. For MS detection, the algorithm uses a Support Vector Machine (SVM), by features such as pixel value, spatial distribution, shape and others. The detected pixels are used as seed point for a region growing (RG) segmentation. Then, morphological operators are applied to reduce false-positive pixels, improving the segmentation accuracy. These steps are applied in all slices of CT exam, obtaining the MS volume. To evaluate the accuracy of the developed tool, the automatic method was compared with manual segmentation realized by an experienced radiologist. For comparison, we used Bland-Altman statistics, linear regression, and Jaccard similarity coefficient. From the statistical analyses for the comparison between both methods, the linear regression showed a strong association and low dispersion between variables. The Bland–Altman analyses showed no significant differences between the analyzed methods. The Jaccard similarity coefficient was > 0.90 in all exams. In conclusion, the developed tool to quantify MS volume proved to be robust, fast, and efficient, when compared with manual segmentation. Furthermore, it avoids the intra and inter-observer variations caused by manual and semi-automatic methods. As future work, the tool will be applied in clinical practice. Thus, it may be useful in the diagnosis and treatment determination of MS diseases. Providing volume values for MS could be helpful in evaluating the presence of any abnormality and could be used for treatment planning and evaluation of the outcome. The computed tomography (CT) has allowed a more exact assessment of this structure which enables a quantitative analysis. However, this is not always possible in the clinical routine, and if possible, it involves much effort and/or time. Therefore, it is necessary to have a convenient, robust and practical tool correlated with the MS volume, allowing clinical applicability. Nowadays, the available methods for MS segmentation are manual or semi-automatic. Additionally, manual methods present inter and intraindividual variability. Thus, the aim of this study was to develop an automatic tool to quantity the MS volume in CT scans of paranasal sinuses. This study was developed with ethical approval from the authors’ institutions and national review panels. The research involved 30 retrospective exams of University Hospital, Botucatu Medical School, São Paulo State University, Brazil. The tool for automatic MS quantification, developed in Matlab®, uses a hybrid method, combining different image processing techniques. For MS detection, the algorithm uses a Support Vector Machine (SVM), by features such as pixel value, spatial distribution, shape and others. The detected pixels are used as seed point for a region growing (RG) segmentation. Then, morphological operators are applied to reduce false-positive pixels, improving the segmentation accuracy. These steps are applied in all slices of CT exam, obtaining the MS volume. To evaluate the accuracy of the developed tool, the automatic method was compared with manual segmentation realized by an experienced radiologist. For comparison, we used Bland-Altman statistics, linear regression and Jaccard similarity coefficient. From the statistical analyses for the comparison between both methods, the linear regression showed a strong association and low dispersion between variables. The Bland–Altman analyses showed no significant differences between the analyzed methods. The Jaccard similarity coefficient was > 0.90 in all exams. In conclusion, the developed tool to automatically quantify MS volume proved to be robust, fast and efficient, when compared with manual segmentation. Furthermore, it avoids the intra and inter-observer variations caused by manual and semi-automatic methods. As future work, the tool will be applied in clinical practice. Thus, it may be useful in the diagnosis and treatment determination of MS diseases.

Keywords: maxillary sinus, support vector machine, region growing, volume quantification

Procedia PDF Downloads 504