Speckle noise removal via nonlocal low-rank regularization

Regularization method is an effective tool for synthetic aperture radar (SAR) image despeckling. Design of the effective regularization terms describing the image priors plays a vital role in this kind of method. In this article, a new combinational regularization model for speckle reduction (CRM-SR) is proposed, in which a regularization term is elaborately designed to contain both a fractional-order total variation (FrTV) regularization and a nonlocal low rank (NLR) regularization. The new regularization model inherits both the advantages of FrTV and NLR and improves the performance of SAR despeckling and, therefore, better preserves the edges and geometrical features of the images during the despeckling process. An efficient algorithm based on alternating direction optimization is derived to solve the proposed combinational regularization model. Experimental results show that the proposed model can effectively remove SAR image speckle and preserve the geometrical features of images according to both subjective visual assessment of image quality and objective evaluation.

Robust image compressive sensing based on m-estimator and nonlocal low-rank regularization

The standard traffic assignment problem (TAP) is often augmented with additional constraints to address non-standard applications. These models are called TAP with side constraints (TAPSC). Despite the rising significance of TAPSC models, the ability to efficiently solve them to satisfactory precision remains limited in real-world applications. The purpose of this paper is to fill this gap by integrating a recently developed high performance TAP solver, known as the path-based Greedy algorithm, with the augmented Lagrangian multiplier (ALM) method. This paper examines how precisely the subproblems in the ALM method should be solved to optimize the overall convergence performance. It is found that insufficiently converged subproblem solutions sometimes lead to catastrophic failures, although pursuing extremely high precision could also be counterproductive. Accordingly, it is proposed to adjust the precision required to solve the subproblems based on an approximate gap measured by the augmented Lagrangian. Results of numerical experiments show that adaptively adjusting the subproblem precision limit produces a 25% speed-up compared with the algorithm with a fixed limit.

The use of non-local self-similarity prior between image blocks can improve image reconstruction performance significantly. We propose a compressive sensing image reconstruction algorithm that combines bilateral total variation and nonlocal low-rank regularization to overcome over-smoothing and degradation of edge information which result from the prior reconstructed image. The proposed algorithm makes use of the preservation of image edge information by bilateral total variation operator to enhance the edge details of the reconstructed image. In addition, we use weighted nuclear norm regularization as a low-rank constraint for similar blocks of the image. To solve this convex optimization problem, the Alternating Direction Method of Multipliers (ADMM) is employed to optimize and iterate the algorithm model effectively. Experimental results show that the proposed algorithm can obtain better image reconstruction quality than conventional algorithms with using total variation regularization or considering the nonlocal structure of the image only. At 10% sampling rate, the peak signal-to-noise ratio gain is up to 2.39 dB in noiseless measurements compared with Nonlocal Low-rank Regularization (NLR-CS). Reconstructed image comparison shows that the proposed algorithm retains more high frequency components. In noisy measurements, the proposed algorithm is robust to noise and the reconstructed image retains more detail information.

In this paper, we propose a time-frequency analysis method to obtain instantaneous frequencies and the corresponding decomposition by solving an optimization problem. In this optimization problem, the basis that is used to decompose the signal is not known a priori. Instead, it is adapted to the signal and is determined as part of the optimization problem. In this sense, this optimization problem can be seen as a dictionary adaptation problem, in which the dictionary is adaptive to one signal rather than a training set in dictionary learning. This dictionary adaptation problem is solved by using the augmented Lagrangian multiplier (ALM) method iteratively. We further accelerate the ALM method in each iteration by using the fast wavelet transform. We apply our method to decompose several signals, including signals with poor scale separation, signals with outliers and polluted by noise and a real signal. The results show that this method can give accurate recovery of both the instantaneous frequencies and the intrinsic mode functions.

Synthetic Aperture Radar (SAR) is a coherent microwave imaging method used for mapping scattering properties of Earth's surface. Speckle is a granular disturbance, modeled as a multiplicative noise, that affects all types of coherent images. Most of the applications demand speckle reduction to be carried out in real-time and require computationally simple and efficient techniques. The paper presents a combination of spatial and frequency domain techniques for removing speckle noise. The algorithm uses a Wiener filter as a preprocessing stage in the spatial domain and adaptive soft thresholding of Wavelet transform coefficients in the frequency domain. Considering multiplicative model for speckle noise, logarithmic transform is applied to Wiener filtered image. Threshold value at each decomposition level and subband is computed from the corresponding standard deviation. Simulation results show that the proposed method is efficient in removing speckle noise compared to an existing algorithm. The results are quantitatively analysed using Peak Signal-to-Noise Ratio (PSNR) and Structural SIMilarity (SSIM) metrics.

This paper studies the problem of the restoration of images corrupted by mixed Gaussian-impulse noise. In recent years, low-rank matrix reconstruction has become a research hotspot in many scientific and engineering domains such as machine learning, image processing, computer vision and bioinformatics, which mainly involves the problem of matrix completion and robust principal component analysis, namely recovering a low-rank matrix from an incomplete but accurate sampling subset of its entries and from an observed data matrix with an unknown fraction of its entries being arbitrarily corrupted, respectively. Inspired by these ideas, we consider the problem of recovering a low-rank matrix from an incomplete sampling subset of its entries with an unknown fraction of the samplings contaminated by arbitrary errors, which is defined as the problem of matrix completion from corrupted samplings and modeled as a convex optimization problem that minimizes a combination of the nuclear norm and the -norm in this paper. Meanwhile, we put forward a novel and effective algorithm called augmented Lagrange multipliers to exactly solve the problem. For mixed Gaussian-impulse noise removal, we regard it as the problem of matrix completion from corrupted samplings, and restore the noisy image following an impulse-detecting procedure. Compared with some existing methods for mixed noise removal, the recovery quality performance of our method is dominant if images possess low-rank features such as geometrically regular textures and similar structured contents; especially when the density of impulse noise is relatively high and the variance of Gaussian noise is small, our method can outperform the traditional methods significantly not only in the simultaneous removal of Gaussian noise and impulse noise, and the restoration ability for a low-rank image matrix, but also in the preservation of textures and details in the image.

Principal Component Analysis (PCA) as a tool for dimensionality reduction is widely used in many areas. In the area of bioinformatics, each involved variable corresponds to a specific gene. In order to improve the robustness of PCA-based method, this paper proposes a novel graph-Laplacian PCA algorithm by adopting L1/2 constraint (L1/2 gLPCA) on error function for feature (gene) extraction. The error function based on L1/2-norm helps to reduce the influence of outliers and noise. Augmented Lagrange Multipliers (ALM) method is applied to solve the subproblem. This method gets better results in feature extraction than other state-of-the-art PCA-based methods. Extensive experimental results on simulation data and gene expression data sets demonstrate that our method can get higher identification accuracies than others.

Spatial spectral total variation has been widely used in the hyperspectral image (HSI) denoising algorithms. However, the total variation norm only penalizes the gradient magnitudes of HSIs, which may influence the recovery of denoised image edges. In this paper, we proposed a new l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> gradient regularized low-rank tensor model for removing HSI mixed noises. The low-rank tensor Tucker decomposition is applied for recovering the clean HSI part by using the HSI global correlation. The l0 gradient regularization controls the number of non-zero gradients directly and is designed to explore the spatial-spectral property of hyperspectral images and preserve important image features. The optimization problem is solved by the Augmented Lagrange Multiplier (ALM) method efficiently. The real-world data experiment demonstrates the better performance of our method.

This paper presents an effective design approach for reducing the weight of a flexible rotor in ball bearings with rotational speed and load dependent stiffness characteristics under constraints on the system eigenvalues and bearing fatigue life. Design variables are chosen to be the inner radii of shaft elements, the positions of ball bearings, and the preloads on the bearings. The stiffness characteristics of high speed ball bearings are completely described as functions of applied loads and spin speed, and applied to the dynamic behavior analysis of a rotor-bearing system. A transfer matrix method is used to obtain eigenvalues of the system and an augmented Lagrange multiplier (ALM) method is employed as an optimization technique. A multi-stepped rotor supported by two angular contact ball bearings is analyzed and designed to show the speed and load dependent stiffness effect on the system dynamic behavior and to demonstrate the effectiveness of the proposed optimum design approach. The results show that the effect of the stiffness on the system dynamic behavior is noticeable and that the suggested design approach is effective. [S0739-3717(00)00803-5]

Background Subtraction (BS) is one of the key steps in video analysis. Many background models have been proposed and achieved promising performance on public data sets. However, due to challenges such as illumination change, dynamic background etc. the resulted foreground segmentation often consists of holes as well as background noise. In this regard, we consider generalized fused lasso regularization to quest for intact structured foregrounds. Together with certain assumptions about the background, such as the low-rank assumption or the sparse-composition assumption (depending on whether pure background frames are provided), we formulate BS as a matrix decomposition problem using regularization terms for both the foreground and background matrices. Moreover, under the proposed formulation, the two generally distinctive background assumptions can be solved in a unified manner. The optimization was carried out via applying the augmented Lagrange multiplier (ALM) method in such a way that a fast parametric-flow algorithm is used for updating the foreground matrix. Experimental results on several popular BS data sets demonstrate the advantage of the proposed model compared to state-of-the-arts.

Tensorized multi-dimensional multi-view clustering based on nonnegative matrix factorization.

Quality is a very important parameter for all objects and their functionalities. In image-based object recognition, image quality is a prime criterion. For authentic image quality evaluation, ground truth is required. But in practice, it is very difficult to find the ground truth. Usually, image quality is being assessed by full reference metrics, like MSE (Mean Square Error) and PSNR (Peak Signal to Noise Ratio). In contrast to MSE and PSNR, recently, two more full reference metrics SSIM (Structured Similarity Indexing Method) and FSIM (Feature Similarity Indexing Method) are developed with a view to compare the structural and feature similarity measures between restored and original objects on the basis of perception. This paper is mainly stressed on comparing different image quality metrics to give a comprehensive view. Experimentation with these metrics using benchmark images is performed through denoising for different noise concentrations. All metrics have given consistent results. However, from representation perspective, SSIM and FSIM are normalized, but MSE and PSNR are not; and from semantic perspective, MSE and PSNR are giving only absolute error; on the other hand, SSIM and PSNR are giving perception and saliency-based error. So, SSIM and FSIM can be treated more understandable than the MSE and PSNR.

The low-rank matrix approximation (LRMA) is an efficient image denoising method to reduce additive Gaussian noise. However, the existing low-rank matrix approximation does not perform well in terms of Rician noise removal for magnetic resonance imaging (MRI). To this end, we propose a novel MR image denoising approach based on the extended difference of Gaussian (DoG) filter and nonlocal low-rank regularization. In the proposed method, a novel nonlocal self-similarity evaluation with the tight frame is exploited to improve the patch matching. To remove the Rician noise and preserve the edge details, the extended DoG filter is exploited to the nonlocal low-rank regularization model. The experimental results demonstrate that the proposed method can preserve more edge and fine structures while removing noise in MR image as compared with some of the existing methods.

Speckle noise removal in SAR images using Multi-Objective PSO (MOPSO) algorithm