Multiplicative Noise Removal Using L1 Fidelity on Frame Coefficients

We address the denoising of images contaminated with multiplicative noise, e.g. speckle noise. Classical ways to solve such problems are filtering, statistical (Bayesian) methods, variational methods, and methods that convert the multiplicative noise into additive noise (using a logarithmic function), shrinkage of the coefficients of the log-image data in a wavelet basis or in a frame, and transform back the result using an exponential function. We propose a method composed of several stages: we use the log-image data and apply a reasonable under-optimal hard-thresholding on its curvelet transform; then we apply a variational method where we minimize a specialized criterion composed of an $\ell^1$ data-fitting to the thresholded coefficients and a Total Variation regularization (TV) term in the image domain; the restored image is an exponential of the obtained minimizer, weighted in a way that the mean of the original image is preserved. Our restored images combine the advantages of shrinkage and variational methods and avoid their main drawbacks. For the minimization stage, we propose a properly adapted fast minimization scheme based on Douglas-Rachford splitting. The existence of a minimizer of our specialized criterion being proven, we demonstrate the convergence of the minimization scheme. The obtained numerical results outperform the main alternative methods

A Tutorial on Speckle Reduction in Synthetic Aperture Radar Images

Speckle is a granular disturbance, usually modeled as a multiplicative noise, that affects synthetic aperture radar (SAR) images, as well as all coherent images. Over the last three decades, several methods have been proposed for the reduction of speckle, or despeckling, in SAR images. Goal of this paper is making a comprehensive review of despeckling methods since their birth, over thirty years ago, highlighting trends and changing approaches over years. The concept of fully developed speckle is explained. Drawbacks of homomorphic filtering are pointed out. Assets of multiresolution despeckling, as opposite to spatial-domain despeckling, are highlighted. Also advantages of undecimated, or stationary, wavelet transforms over decimated ones are discussed. Bayesian estimators and probability density function (pdf) models in both spatial and multiresolution domains are reviewed. Scale-space varying pdf models, as opposite to scale varying models, are promoted. Promising methods following non-Bayesian approaches, like nonlocal (NL) filtering and total variation (TV) regularization, are reviewed and compared to spatial- and wavelet-domain Bayesian filters. Both established and new trends for assessment of despeckling are presented. A few experiments on simulated data and real COSMO-SkyMed SAR images highlight, on one side the costperformance tradeoff of the different methods, on the other side the effectiveness of solutions purposely designed for SAR heterogeneity and not fully developed speckle. Eventually, upcoming methods based on new concepts of signal processing, like compressive sensing, are foreseen as a new generation of despeckling, after spatial-domain and multiresolution-domain method

Optical Coherence Tomography Noise Reduction Using Anisotropic Local Bivariate Gaussian Mixture Prior in 3D Complex Wavelet Domain

In this paper, MMSE estimator is employed for noise-free 3D OCT data recovery in 3D complex wavelet domain. Since the proposed distribution for noise-free data plays a key role in the performance of MMSE estimator, a priori distribution for the pdf of noise-free 3D complex wavelet coefficients is proposed which is able to model the main statistical properties of wavelets. We model the coefficients with a mixture of two bivariate Gaussian pdfs with local parameters which are able to capture the heavy-tailed property and inter- and intrascale dependencies of coefficients. In addition, based on the special structure of OCT images, we use an anisotropic windowing procedure for local parameters estimation that results in visual quality improvement. On this base, several OCT despeckling algorithms are obtained based on using Gaussian/two-sided Rayleigh noise distribution and homomorphic/nonhomomorphic model. In order to evaluate the performance of the proposed algorithm, we use 156 selected ROIs from 650 × 512 × 128 OCT dataset in the presence of wet AMD pathology. Our simulations show that the best MMSE estimator using local bivariate mixture prior is for the nonhomomorphic model in the presence of Gaussian noise which results in an improvement of 7.8 ± 1.7 in CNR

Sparseland model for speckle suppression of B-mode ultrasound images

Speckle is a multiplicative noise which is inherent in medical ultrasound images. Speckles contributes high variance between neighboring pixels reducing the visual quality of an image. Suppression of speckle noise significantly improves the diagnostic content present in the image. In this paper, we propose how sparseland model can be used for speckle suppression. The performance of the model is evaluated based on variance to mean ratio of a patch in the filtered image. The algorithm is tested on both software generated images and real time ultrasound images. The proposed algorithm has performed similar to past adaptive speckle suppression filters and seems promising in improving diagnostic content

Computer-Assisted Algorithms for Ultrasound Imaging Systems

Ultrasound imaging works on the principle of transmitting ultrasound waves into the body and reconstructs the images of internal organs based on the strength of the echoes. Ultrasound imaging is considered to be safer, economical and can image the organs in real-time, which makes it widely used diagnostic imaging modality in health-care. Ultrasound imaging covers the broad spectrum of medical diagnostics; these include diagnosis of kidney, liver, pancreas, fetal monitoring, etc. Currently, the diagnosis through ultrasound scanning is clinic-centered, and the patients who are in need of ultrasound scanning has to visit the hospitals for getting the diagnosis. The services of an ultrasound system are constrained to hospitals and did not translate to its potential in remote health-care and point-of-care diagnostics due to its high form factor, shortage of sonographers, low signal to noise ratio, high diagnostic subjectivity, etc. In this thesis, we address these issues with an objective of making ultrasound imaging more reliable to use in point-of-care and remote health-care applications. To achieve the goal, we propose (i) computer-assisted algorithms to improve diagnostic accuracy and assist semi-skilled persons in scanning, (ii) speckle suppression algorithms to improve the diagnostic quality of ultrasound image, (iii) a reliable telesonography framework to address the shortage of sonographers, and (iv) a programmable portable ultrasound scanner to operate in point-of-care and remote health-care applications

Speckle Noise Reduction in Medical Ultrasound Images Using Modelling of Shearlet Coefficients as a Nakagami Prior

The diagnosis of UltraSound (US) medical images is affected due to the presence of speckle noise. This noise degrades the diagnostic quality of US images by reducing small details and edges present in the image. This paper presents a novel method based on shearlet coefficients modeling of log-transformed US images. Noise-free log-transformed coefficients are modeled as Nakagami distribution and speckle noise coefficients are modeled as Gaussian distribution. Method of Log Cumulants (MoLC) and Method of Moments (MoM) are used for parameter estimation of Nakagami distribution and noise free shearlet coefficients respectively. Then noise free shearlet coefficients are obtained using Maximum a Posteriori (MaP) estimation of noisy coefficients. The experimental results were presented by performing various experiments on synthetic and real US images. Subjective and objective quality assessment of the proposed method is presented and is compared with six other existing methods. The effectiveness of the proposed method over other methods can be seen from the obtained results

Effective SAR image despeckling based on bandlet and SRAD

Despeckling of a SAR image without losing features of the image is a daring task as it is intrinsically affected by multiplicative noise called speckle. This thesis proposes a novel technique to efficiently despeckle SAR images. Using an SRAD filter, a Bandlet transform based filter and a Guided filter, the speckle noise in SAR images is removed without losing the features in it. Here a SAR image input is given parallel to both SRAD and Bandlet transform based filters. The SRAD filter despeckles the SAR image and the despeckled output image is used as a reference image for the guided filter. In the Bandlet transform based despeckling scheme, the input SAR image is first decomposed using the bandlet transform. Then the coefficients obtained are thresholded using a soft thresholding rule. All coefficients other than the low-frequency ones are so adjusted. The generalized cross-validation (GCV) technique is employed here to find the most favorable threshold for each subband. The bandlet transform is able to extract edges and fine features in the image because it finds the direction where the function gives maximum value and in the same direction it builds extended orthogonal vectors. Simple soft thresholding using an optimum threshold despeckles the input SAR image. The guided filter with the help of a reference image removes the remaining speckle from the bandlet transform output. In terms of numerical and visual quality, the proposed filtering scheme surpasses the available despeckling schemes

Machine Learning And Image Processing For Noise Removal And Robust Edge Detection In The Presence Of Mixed Noise

The central goal of this dissertation is to design and model a smoothing filter based on the random single and mixed noise distribution that would attenuate the effect of noise while preserving edge details. Only then could robust, integrated and resilient edge detection methods be deployed to overcome the ubiquitous presence of random noise in images. Random noise effects are modeled as those that could emanate from impulse noise, Gaussian noise and speckle noise. In the first step, evaluation of methods is performed based on an exhaustive review on the different types of denoising methods which focus on impulse noise, Gaussian noise and their related denoising filters. These include spatial filters (linear, non-linear and a combination of them), transform domain filters, neural network-based filters, numerical-based filters, fuzzy based filters, morphological filters, statistical filters, and supervised learning-based filters. In the second step, switching adaptive median and fixed weighted mean filter (SAMFWMF) which is a combination of linear and non-linear filters, is introduced in order to detect and remove impulse noise. Then, a robust edge detection method is applied which relies on an integrated process including non-maximum suppression, maximum sequence, thresholding and morphological operations. The results are obtained on MRI and natural images. In the third step, a combination of transform domain-based filter which is a combination of dual tree – complex wavelet transform (DT-CWT) and total variation, is introduced in order to detect and remove Gaussian noise as well as mixed Gaussian and Speckle noise. Then, a robust edge detection is applied in order to track the true edges. The results are obtained on medical ultrasound and natural images. In the fourth step, a smoothing filter, which is a feed-forward convolutional network (CNN) is introduced to assume a deep architecture, and supported through a specific learning algorithm, l2 loss function minimization, a regularization method, and batch normalization all integrated in order to detect and remove impulse noise as well as mixed impulse and Gaussian noise. Then, a robust edge detection is applied in order to track the true edges. The results are obtained on natural images for both specific and non-specific noise-level

Image Restoration for Remote Sensing: Overview and Toolbox

Remote sensing provides valuable information about objects or areas from a distance in either active (e.g., RADAR and LiDAR) or passive (e.g., multispectral and hyperspectral) modes. The quality of data acquired by remotely sensed imaging sensors (both active and passive) is often degraded by a variety of noise types and artifacts. Image restoration, which is a vibrant field of research in the remote sensing community, is the task of recovering the true unknown image from the degraded observed image. Each imaging sensor induces unique noise types and artifacts into the observed image. This fact has led to the expansion of restoration techniques in different paths according to each sensor type. This review paper brings together the advances of image restoration techniques with particular focuses on synthetic aperture radar and hyperspectral images as the most active sub-fields of image restoration in the remote sensing community. We, therefore, provide a comprehensive, discipline-specific starting point for researchers at different levels (i.e., students, researchers, and senior researchers) willing to investigate the vibrant topic of data restoration by supplying sufficient detail and references. Additionally, this review paper accompanies a toolbox to provide a platform to encourage interested students and researchers in the field to further explore the restoration techniques and fast-forward the community. The toolboxes are provided in https://github.com/ImageRestorationToolbox.Comment: This paper is under review in GRS