Analysis and Synthesis Prior Greedy Algorithms for Non-linear Sparse Recovery

In this work we address the problem of recovering sparse solutions to non linear inverse problems. We look at two variants of the basic problem, the synthesis prior problem when the solution is sparse and the analysis prior problem where the solution is cosparse in some linear basis. For the first problem, we propose non linear variants of the Orthogonal Matching Pursuit (OMP) and CoSamp algorithms; for the second problem we propose a non linear variant of the Greedy Analysis Pursuit (GAP) algorithm. We empirically test the success rates of our algorithms on exponential and logarithmic functions. We model speckle denoising as a non linear sparse recovery problem and apply our technique to solve it. Results show that our method outperforms state of the art methods in ultrasound speckle denoising

Адаптивний метод фільтрації УЗД-зображення на основі анізотропної дифузії

Запропоновано адаптивний фільтр спекл-шуму на основі використання анізотропної дифузії, що використовує локальну статистику для визначення примежових ділянок об’єктів на зображенні та змінює глибину фільтрації, відповідно до отриманих даних.Предложен адаптивный фильтр спекл-шума с использованием анизотропной дифузии, который использует локальную статистику для определения приконтурных областей и изменяет глубину фильтрации, согласно полученным данным.An adaptive filter for despeckling based on anisotropic diffusion is developed. Filter uses local statistics for defining edge areas and changes the depth of filtering according to these information

Mean of Median Absolute Derivation Technique for Speckle Noise Variance Estimation in Computerised Tomography Images

The accurate estimation of noise variance in an image is the first important stage in image filtering using adaptive filters. In this paper, a new technique for the estimation of speckle noise present in Computerised Tomography (CT) lung image was developed. The development of mean of median absolute derivation technique based on the estimated mean of speckle noise present in CT images is presented. From the result of the simulations, the new technique gave a reasonably accurate estimate of variance of speckle noise present in CT Images. Ten samples of 85x73 CT images corrupted by speckle noise level ranging from 10% to 30% where used as test images. Also, the new technique gave the lowest average speckle noise variance estimation error of 2.53% compared to 12.53% for the Median of Median Absolute Derivative Technique, 18.18% for the Transfer function technique and 37.14% for the Mode of Variance Technique. The simulation software used in the paper is Matrix Laboratory (MATLAB2012).http://dx.doi.org/10.4314/njt.v34i2.2

A robust detail preserving anisotropic diffusion for speckle reduction in ultrasound images

<p>Abstract</p> <p>Background</p> <p>Speckles in ultrasound imaging affect image quality and can make the post-processing difficult. Speckle reduction technologies have been employed for removing speckles for some time. One of the effective speckle reduction technologies is anisotropic diffusion. Anisotropic diffusion technology can remove the speckles effectively while preserving the edges of the image and thus has drawn great attention from image processing scientists. However, the proposed methods in the past have different disadvantages, such as being sensitive to the number of iterations or low capability of preserving the details of the ultrasound images. Thus a detail preserved anisotropic diffusion speckle reduction with less sensitive to the number of iterations is needed. This paper aims to develop this kind of technologies.</p> <p>Results</p> <p>In this paper, we propose a robust detail preserving anisotropic diffusion filter (RDPAD) for speckle reduction. In order to get robust diffusion, the proposed method integrates Tukey error norm function into the detail preserving anisotropic diffusion filter (DPAD) developed recently. The proposed method could prohibit over-diffusion and thus is less sensitive to the number of iterations</p> <p>Conclusions</p> <p>The proposed anisotropic diffusion can preserve the important structure information of the original image while reducing speckles. It is also less sensitive to the number of iterations. Experimental results on real ultrasound images show the effectiveness of the proposed anisotropic diffusion filter.</p

Automated reduction the speckle noise of the panoramic ultrasound images of Muscles and Tendons

Peer reviewedPublisher PD

Removing multiplicative noise by Douglas-Rachford splitting methods

Multiplicative noise appears in various image processing applications, e.g., in synthetic aperture radar (SAR), ultrasound imaging or in connection with blur in electronic microscopy, single particle emission computed tomography (SPECT) and positron emission tomography (PET). In this paper, we consider a variational restoration model consisting of the I-divergence as data fitting term and the total variation semi-norm or nonlocal means as regularizer. Although the I-divergence is the typical data fitting term when dealing with Poisson noise we substantiate why it is also appropriate for cleaning Gamma noise. We propose to compute the minimizer of our restoration functional by applying Douglas-Rachford splitting techniques, resp. alternating split Bregman methods, combined with an efficient algorithm to solve the involved nonlinear systems of equations. We prove the Q-linear convergence of the latter algorithm. Finally, we demonstrate the performance of our whole scheme by numerical examples. It appears that the nonlocal means approach leads to very good qualitative results

Anisotropic Diffusion Filter with Memory based on Speckle Statistics for Ultrasound Images

Ultrasound imaging exhibits considerable difficulties for medical visual inspection and for the development of automatic analysis methods due to speckle, which negatively affects the perception of tissue boundaries and the performance of automatic segmentation methods. With the aim of alleviating the effect of speckle, many filtering techniques are usually considered as a preprocessing step prior to automatic analysis methods or visual inspection. Most of the state-of-the-art filters try to reduce the speckle effect without considering its relevance for the characterization of tissue nature. However, the speckle phenomenon is the inherent response of echo signals in tissues and can provide important features for clinical purposes. This loss of information is even magnified due to the iterative process of some speckle filters, e.g., diffusion filters, which tend to produce over-filtering because of the progressive loss of relevant information for diagnostic purposes during the diffusion process. In this work, we propose an anisotropic diffusion filter with a probabilistic-driven memory mechanism to overcome the over-filtering problem by following a tissue selective philosophy. Specifically, we formulate the memory mechanism as a delay differential equation for the diffusion tensor whose behavior depends on the statistics of the tissues, by accelerating the diffusion process in meaningless regions and including the memory effect in regions where relevant details should be preserved. Results both in synthetic and real US images support the inclusion of the probabilistic memory mechanism for maintaining clinical relevant structures, which are removed by the state-of-the-art filters