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Showing 3 results for Entropy
Modeling of the Maximum Entropy Problem as an Optimal Control Problem and its Application to Pdf Estimation of Electricity Price
M. E. Haji Abadi, H. Rajabi Mashhadi,
Volume 9, Issue 3 (9-2013)
Abstract
In this paper, the continuous optimal control theory is used to model and solve the maximum entropy problem for a continuous random variable. The maximum entropy principle provides a method to obtain least-biased probability density function (Pdf) estimation. In this paper, to find a closed form solution for the maximum entropy problem with any number of moment constraints, the entropy is considered as a functional measure and the moment constraints are considered as the state equations. Therefore, the Pdf estimation problem can be reformulated as the optimal control problem. Finally, the proposed method is applied to estimate the Pdf of the hourly electricity prices of New England and Ontario electricity markets. Obtained results show the efficiency of the proposed method.
Shearlet-Based Adaptive Noise Reduction in CT Images
M. Petrov,
Volume 17, Issue 1 (3-2021)
Abstract
The noise in reconstructed slices of X-ray Computed Tomography (CT) is of unknown distribution, non-stationary, oriented and difficult to distinguish from main structural information. This requires the development of special post-processing methods based on the local statistical evaluation of the noise component. This paper presents an adaptive method of reducing noise in CT images employing the shearlet domain in order to obtain such an estimate. The algorithm for statistical noise assessment takes into account the distribution of signal energy in different scales and directions. The method efficiently uses the strong targeted sensitivity of shearlet systems in order to reflect more accurately the anisotropic information in the image. Because of the complex characteristics of the noise in these images, the threshold constant is determined by means of the relative entropy change criterion. The comparative analysis, which has been conducted, shows that the proposed method achieves higher values for the Peak Signal-to-Noise Ratio (PSNR), as well as lower values for the Mean Squared Error (MSE), in comparison with the other methods considered. For the MATLAB’S Shepp Logan Phantom test image, the numerical value of this superiority is on average more than 23% for the first quantitative measure, and 37% for the second. Its efficiency, which is greater than that of the wavelet-based method, is confirmed by the results obtained – the edges have been preserved during noise reduction in real CT images.

Left Ventricular Entropy as a Measure of Wall Motion Abnormalities in Echocardiography Images
Neda Gorji Kandi, Hamid Behnam, Ali Hosseinsabet,
Volume 20, Issue 2 (6-2024)
Abstract
Cardiovascular diseases (CVD) are today a major cause of death globally that is diagnosed by measurement and quantification of left ventricle (LV) wall motion (WM) abnormality of the heart. The aim of this study was to assess the utility of left ventricular (LV) entropy, a novel measure of disease derived from two-dimensional (2D) echocardiography images that assesses the probability distribution of pixel intensities in the LV. The purpose of this research is to develop the method of LV entropy to predict heart diseases. In this algorithm, a frame is usually chosen as the reference frame to extract the region of interest (ROI) around LV and then it is mapped to all images in a cardiac cycle. Then Shannon Entropy transform was applied to calculate the distribution of pixel intensities across the LV so we obtained entropy curves and compared them. The main idea is to find a motion estimation accuracy. The results obtained by our method are quantitatively evaluated to those obtained by an experienced echocardiographer visually on 22 normal cases and 19 myocardial infarction (MI) cases in apical four-chamber (A4C) view. The entropy of diastole in MI cases was 0.50 (0.29-0.58) while in normal cases was 0.75 (0.64-1.13). The entropy of systole in MI cases was 0.64 (0.26-1.04) while in normal cases was 0.81 (0.63-1.26). The percent change of entropy for diastole and systole between normal and MI cases are 33.3% and 20.2%. The results indicate that the LV entropy curves of MI cases have less changes than normal cases.
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© 2022 by the authors. Licensee IUST, Tehran, Iran. This is an open access journal distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) license.