SAR image regularization with fast approximate discrete minimization

A New Non-Linear Hyperbolic-Parabolic Coupled PDE Model for Image Despeckling

In this work, we propose a non-linear hyperbolic-parabolic coupled Partial Differential Equation (PDE) based model for image despeckling. Here, a separate equation is used to calculate the edge variable, which improves the quality of edge information in the despeckled images. The existence of the weak solution of the present system is achieved via Schauder fixed point theorem. We used a generalized weighted average finite-difference scheme and the Gauss-Seidel iterative technique to solve the coupled system. Numerical studies are reported to show the effectiveness of the proposed approach with respect to standard PDE-based and nonlocal methods available in the literature. Numerical experiments are performed over gray-level images degraded by artificial speckle noise. Additionally, we investigate the noise removal efficiency of the proposed algorithm when applied to real synthetic aperture radar (SAR) and Ultrasound images. Overall, our study confirms that in most cases, the present model performs better than the other PDE-based models and shows competitive performance with the nonlocal technique. To the best of our knowledge, the proposed despeckling approach is the first work that utilizes the advantage of the non-linear coupled hyperbolic-parabolic PDEs for image despeckling.

A No-Reference Edge-Preservation Assessment Index for SAR Image Filters under a Bayesian Framework Based on the Ratio Gradient

Denoising is an essential preprocessing step for most applications using synthetic aperture radar (SAR) images at different processing levels. Besides suppressing the noise, a good filter should also effectively preserve the image edge information. To quantitatively assess the edge-preservation performance of SAR filters, a number of indices have been investigated in the literature; however, most of them do not fully employ the statistical traits of the SAR image. In this paper, we review some of the typical edge-preservation assessment indices. A new referenceless index is then proposed. The ratio gradient is utilized to characterize the difference between two non-overlapping neighborhoods on opposite sides of each pixel in both the speckled and despeckled images. Based on these gradients and the statistical traits of the speckle, the proposed indicator is derived under a Bayesian framework. A series of experiments conducted with both simulated and real SAR datasets reveal that the proposed index shows good performances, in both robustness and consistency. For reproducibility, the source codes of the index and the testing datasets are provided.

Speckle-Free SAR Image Ship Detection

Ship detection is one of important applications for synthetic aperture radar (SAR). Speckle effects usually make SAR image understanding difficult and speckle reduction becomes a necessary pre-processing step for majority SAR applications. This work examines different speckle reduction methods on SAR ship detection performances. It is found out that the influences of different speckle filters are significant which can be positive or negative. However, how to select a suitable combination of speckle filters and ship detectors is lack of theoretical basis and is also data-orientated. To overcome this limitation, a speckle-free SAR ship detection approach is proposed. A similar pixel number (SPN) indicator which can effectively identify salient target is derived, during the similar pixel selection procedure with the context covariance matrix (CCM) similarity test. The underlying principle lies in that ship and sea clutter candidates show different properties of homogeneity within a moving window and the SPN indicator can clearly reflect their differences. The sensitivity and efficiency of the SPN indicator is examined and demonstrated. Then, a speckle-free SAR ship detection approach is established based on the SPN indicator. The detection flowchart is also given. Experimental and comparison studies are carried out with three kinds of spaceborne SAR datasets in terms of different polarizations. The proposed method achieves the best SAR ship detection performances with the highest figures of merits (FoM) of 97.14%, 90.32% and 93.75% for the used Radarsat-2, GaoFen-3 and Sentinel-1 datasets, accordingly.

SAR Image Despeckling by Deep Neural Networks: from a Pre-Trained Model to an End-to-End Training Strategy

Speckle reduction is a longstanding topic in synthetic aperture radar (SAR) images. Many different schemes have been proposed for the restoration of intensity SAR images. Among the different possible approaches, methods based on convolutional neural networks (CNNs) have recently shown to reach state-of-the-art performance for SAR image restoration. CNN training requires good training data: many pairs of speckle-free/speckle-corrupted images. This is an issue in SAR applications, given the inherent scarcity of speckle-free images. To handle this problem, this paper analyzes different strategies one can adopt, depending on the speckle removal task one wishes to perform and the availability of multitemporal stacks of SAR data. The first strategy applies a CNN model, trained to remove additive white Gaussian noise from natural images, to a recently proposed SAR speckle removal framework: MuLoG (MUlti-channel LOgarithm with Gaussian denoising). No training on SAR images is performed, the network is readily applied to speckle reduction tasks. The second strategy considers a novel approach to construct a reliable dataset of speckle-free SAR images necessary to train a CNN model. Finally, a hybrid approach is also analyzed: the CNN used to remove additive white Gaussian noise is trained on speckle-free SAR images. The proposed methods are compared to other state-of-the-art speckle removal filters, to evaluate the quality of denoising and to discuss the pros and cons of the different strategies. Along with the paper, we make available the weights of the trained network to allow its usage by other researchers.

Variational Textured Dirichlet Process Mixture Model with Pairwise Constraint for Unsupervised Classification of Polarimetric SAR Images

This paper proposes an unsupervised classification method for multilook polarimetric synthetic aperture radar (Pol-SAR) data. The proposed method simultaneously deals with the heterogeneity and incorporates the local correlation in PolSAR images. Specifically, within the probabilistic framework of the Dirichlet process mixture model (DPMM), an observed PolSAR data point is described by the multiplication of a Wishartdistributed component and a class-dependent random variable (i.e., the textual variable). This modeling scheme leads to the proposed textured DPMM (tDPMM), which possesses more flexibility in characterizing PolSAR data in heterogeneous areas and from high-resolution images due to the introduction of the classdependent texture variable. The proposed tDPMM is learned by solving an optimization problem to achieve its Bayesian inference. With the knowledge of this optimization-based learning, the local correlation is incorporated through the pairwise constraint, which integrates an appropriate penalty term into the objective function so as to encourage the neighboring pixels to fall into the same category and to alleviate the "salt-and-pepper" classification appearance.We develop the learning algorithm with all the closed-form updates. The performance of the proposed method is evaluated with both low-resolution and high-resolution PolSAR images, which involve homogeneous, heterogeneous, and extremely heterogeneous areas. The experimental results reveal that the class-dependent texture variable is beneficial to PolSAR image classification and the pairwise constraint can effectively incorporate the local correlation in PolSAR images.

A Boosting SAR Image Despeckling Method Based on Non-Local Weighted Group Low-Rank Representation

In this paper, we propose a boosting synthetic aperture radar (SAR) image despeckling method based on non-local weighted group low-rank representation (WGLRR). The spatial structure information of SAR images leads to the similarity of the patches. Furthermore, the data matrix grouped by the similar patches within the noise-free SAR image is often low-rank. Based on this, we use low-rank representation (LRR) to recover the noise-free group data matrix. To maintain the fidelity of the recovered image, we integrate the corrupted probability of each pixel into the group LRR model as a weight to constrain the fidelity of recovered noise-free patches. Each single patch might belong to several groups, so different estimations of each patch are aggregated with a weighted averaging procedure. The residual image contains signal leftovers due to the imperfect denoising, so we strengthen the signal by leveraging on the availability of the denoised image to suppress noise further. Experimental results on simulated and actual SAR images show the superior performance of the proposed method in terms of objective indicators and of perceived image quality.

MuLoG, or How to Apply Gaussian Denoisers to Multi-Channel SAR Speckle Reduction?

Speckle reduction is a longstanding topic in synthetic aperture radar (SAR) imaging. Since most current and planned SAR imaging satellites operate in polarimetric, interferometric, or tomographic modes, SAR images are multi-channel and speckle reduction techniques must jointly process all channels to recover polarimetric and interferometric information. The distinctive nature of SAR signal (complex-valued, corrupted by multiplicative fluctuations) calls for the development of specialized methods for speckle reduction. Image denoising is a very active topic in image processing with a wide variety of approaches and many denoising algorithms available, almost always designed for additive Gaussian noise suppression. This paper proposes a general scheme, called MuLoG (MUlti-channel LOgarithm with Gaussian denoising), to include such Gaussian denoisers within a multi-channel SAR speckle reduction technique. A new family of speckle reduction algorithms can thus be obtained, benefiting from the ongoing progress in Gaussian denoising, and offering several speckle reduction results often displaying method-specific artifacts that can be dismissed by comparison between results.

Speckle reduction via higher order total variation approach

Multiplicative noise (also known as speckle) reduction is a prerequisite for many image-processing tasks in coherent imaging systems, such as the synthetic aperture radar. One approach extensively used in this area is based on total variation (TV) regularization, which can recover significantly sharp edges of an image, but suffers from the staircase-like artifacts. In order to overcome the undesirable deficiency, we propose two novel models for removing multiplicative noise based on total generalized variation (TGV) penalty. The TGV regularization has been mathematically proven to be able to eliminate the staircasing artifacts by being aware of higher order smoothness. Furthermore, an efficient algorithm is developed for solving the TGV-based optimization problems. Numerical experiments demonstrate that our proposed methods achieve state-of-the-art results, both visually and quantitatively. In particular, when the image has some higher order smoothness, our methods outperform the TV-based algorithms.

Active Contour Model for Ultrasound Images with Rayleigh Distribution

Ultrasound images are often corrupted by multiplicative noises with Rayleigh distribution. The noises are strong and often called speckle noise, so segmentation is a hard work with this kind of noises. In this paper, we incorporate multiplicative noise removing model into active contour model for ultrasound images segmentation. To model gray level behavior of ultrasound images, the classic Rayleigh probability distribution is considered. Our model can segment the noisy ultrasound images very well. Finally, a fast method called Split‐Bregman method is used for the easy implementation of segmentation. Experiments on a variety of synthetic and real ultrasound images validate the performance of our method.

Speckle-constrained variational methods for image restoration in optical coherence tomography

A number of despeckling methods for optical coherence tomography (OCT) have been proposed. In these digital filtering techniques, speckle noise is often simplified as additive white Gaussian noise due to the logarithmic compression for the signal. The approximation is not completely consistent with the characteristic of OCT speckle noise, and cannot be reasonably extended to deconvolution algorithms. This paper presents a deconvolution model that combines the variational regularization term with the statistical characteristic constraints of data corrupted by OCT speckle noise. In the data fidelity term, speckle noise is modeled as signal dependent, and the point spread function of OCT systems is included. The regularization functional introduces a priori information on the original images, and a regularization term based on block matching 3D modeling is used to construct the variational model in the paper. Finally, the method is applied to the restoration of actual OCT raw data of human skin. The numerical results demonstrate that the proposed deconvolution algorithm can simultaneously enhance regions of images containing detail and remove OCT speckle noise.

Multiplicative noise removal via a learned dictionary

Multiplicative noise removal is a challenging image processing problem, and most existing methods are based on the maximum a posteriori formulation and the logarithmic transformation of multiplicative denoising problems into additive denoising problems. Sparse representations of images have shown to be efficient approaches for image recovery. Following this idea, in this paper, we propose to learn a dictionary from the logarithmic transformed image, and then to use it in a variational model built for noise removal. Extensive experimental results suggest that in terms of visual quality, peak signal-to-noise ratio, and mean absolute deviation error, the proposed algorithm outperforms state-of-the-art methods.

SAR image segmentation based on level set approach and G⁰A model

This paper proposes an image segmentation method for synthetic aperture radar (SAR), exploring statistical properties of SAR data to characterize image regions. We consider G⁰A distribution parameters for SAR image segmentation, combined to the level set framework. The G⁰A distribution belongs to a class of G distributions that have been successfully used to model different regions in amplitude SAR images for data modeling purpose. Such statistical data model is fundamental to deriving the energy functional to perform region mapping, which is input into our level set propagation numerical scheme that splits SAR images into homogeneous, heterogeneous, and extremely heterogeneous regions. Moreover, we introduce an assessment procedure based on stochastic distance and the G⁰A model to quantify the robustness and accuracy of our approach. Our results demonstrate the accuracy of the algorithms regarding experiments on synthetic and real SAR data.

A new multiplicative denoising variational model based on mth root transformation

In coherent imaging systems, such as the synthetic aperture radar (SAR), the observed images are contaminated by multiplicative noise. Due to the edge-preserving feature of the total variation (TV), variational models with TV regularization have attracted much interest in removing multiplicative noise. However, the fidelity term of the variational model, based on maximum a posteriori estimation, is not convex, and so, it is usually difficult to find a global solution. Hence, the logarithmic function is used to transform the nonconvex variational model to the convex one. In this paper, instead of using the log, we exploit the m th root function to relax the nonconvexity of the variational model. An algorithm based on the augmented Lagrangian function, which has been applied to solve the log transformed convex variational model, can be applied to solve our proposed model. However, this algorithm requires solving a subproblem, which does not have a closed-form solution, at each iteration. Hence, we propose to adapt the linearized proximal alternating minimization algorithm, which does not require inner iterations for solving the subproblems. In addition, the proposed method is very simple and highly parallelizable; thus, it is efficient to remove multiplicative noise in huge SAR images. The proposed model for multiplicative noise removal shows overall better performance than the convex model based on the log transformation.

Spectral-spatial classification of hyperspectral data based on a stochastic minimum spanning forest approach

In this paper, a new method for supervised hyperspectral data classification is proposed. In particular, the notion of stochastic minimum spanning forest (MSF) is introduced. For a given hyperspectral image, a pixelwise classification is first performed. From this classification map, M marker maps are generated by randomly selecting pixels and labeling them as markers for the construction of MSFs. The next step consists in building an MSF from each of the M marker maps. Finally, all the M realizations are aggregated with a maximum vote decision rule in order to build the final classification map. The proposed method is tested on three different data sets of hyperspectral airborne images with different resolutions and contexts. The influences of the number of markers and of the number of realizations M on the results are investigated in experiments. The performance of the proposed method is compared to several classification techniques (both pixelwise and spectral-spatial) using standard quantitative criteria and visual qualitative evaluation.

Alternating minimization algorithm for speckle reduction with a shifting technique

Speckles (multiplicative noise) in synthetic aperture radar (SAR) make it difficult to interpret the observed image. Due to the edge-preserving feature of total variation (TV), variational models with TV regularization have attracted much interest in reducing speckles. Algorithms based on the augmented Lagrangian function have been proposed to efficiently solve speckle-reduction variational models with TV regularization. However, these algorithms require inner iterations or inverses involving the Laplacian operator at each iteration. In this paper, we adapt Tseng's alternating minimization algorithm with a shifting technique to efficiently remove the speckle without any inner iterations or inverses involving the Laplacian operator. The proposed method is very simple and highly parallelizable; therefore, it is very efficient to despeckle huge-size SAR images. Numerical results show that our proposed method outperforms the state-of-the-art algorithms for speckle-reduction variational models with a TV regularizer in terms of central-processing-unit time.

A novel power spectrum calculation method using phase-compensation and weighted averaging for the estimation of ultrasound attenuation

An estimation of ultrasound attenuation in soft tissues is critical in the quantitative ultrasound analysis since it is not only related to the estimations of other ultrasound parameters, such as speed of sound, integrated scatterers, or scatterer size, but also provides pathological information of the scanned tissue. However, estimation performances of ultrasound attenuation are intimately tied to the accurate extraction of spectral information from the backscattered radiofrequency (RF) signals. In this paper, we propose two novel techniques for calculating a block power spectrum from the backscattered ultrasound signals. These are based on the phase-compensation of each RF segment using the normalized cross-correlation to minimize estimation errors due to phase variations, and the weighted averaging technique to maximize the signal-to-noise ratio (SNR). The simulation results with uniform numerical phantoms demonstrate that the proposed method estimates local attenuation coefficients within 1.57% of the actual values while the conventional methods estimate those within 2.96%. The proposed method is especially effective when we deal with the signal reflected from the deeper depth where the SNR level is lower or when the gated window contains a small number of signal samples. Experimental results, performed at 5MHz, were obtained with a one-dimensional 128 elements array, using the tissue-mimicking phantoms also show that the proposed method provides better estimation results (within 3.04% of the actual value) with smaller estimation variances compared to the conventional methods (within 5.93%) for all cases considered.

Field map reconstruction in magnetic resonance imaging using Bayesian estimation

Field inhomogeneities in Magnetic Resonance Imaging (MRI) can cause blur or image distortion as they produce off-resonance frequency at each voxel. These effects can be corrected if an accurate field map is available. Field maps can be estimated starting from the phase of multiple complex MRI data sets. In this paper we present a technique based on statistical estimation in order to reconstruct a field map exploiting two or more scans. The proposed approach implements a Bayesian estimator in conjunction with the Graph Cuts optimization method. The effectiveness of the method has been proven on simulated and real data.

Iterative weighted maximum likelihood denoising with probabilistic patch-based weights

Image denoising is an important problem in image processing since noise may interfere with visual or automatic interpretation. This paper presents a new approach for image denoising in the case of a known uncorrelated noise model. The proposed filter is an extension of the nonlocal means (NL means) algorithm introduced by Buades , which performs a weighted average of the values of similar pixels. Pixel similarity is defined in NL means as the Euclidean distance between patches (rectangular windows centered on each two pixels). In this paper, a more general and statistically grounded similarity criterion is proposed which depends on the noise distribution model. The denoising process is expressed as a weighted maximum likelihood estimation problem where the weights are derived in a data-driven way. These weights can be iteratively refined based on both the similarity between noisy patches and the similarity of patches extracted from the previous estimate. We show that this iterative process noticeably improves the denoising performance, especially in the case of low signal-to-noise ratio images such as synthetic aperture radar (SAR) images. Numerical experiments illustrate that the technique can be successfully applied to the classical case of additive Gaussian noise but also to cases such as multiplicative speckle noise. The proposed denoising technique seems to improve on the state of the art performance in that latter case.