Robust image compressive sensing based on m-estimator and 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.

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.

Speckle noise removal via nonlocal low-rank regularization

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.

In most practical imaging applications, the images with high resolution is desired, but most of imaging images are generally low resolution in practice, which brings many problems. In this paper, we propose an effective image super-resolution reconstruction model using nonlocal low-rank prior. Firstly, this model uses the single image as data input, and the self-similarity inside the single image is used as prior knowledges to improve the matching degree of similar image patches. Then, the reconstruction progress is modeled with maximum a posterior probability framework. Finally, a nonlocal low-rank regularization is adopted to regularize the reconstruction process, which exploits the local and global information of image to improve the reconstruction effect. Experimental results show that the proposed method has achieved better results than the existing methods.KeywordsImage super-resolution reconstructionMaximum a posterior probabilityNonlocal low-rank regularizationAlternative minimization

Hyperspectral image (HSI) acquisitions are degraded by various noises, among which additive Gaussian noise may be the worst-case, as suggested by information theory. In this paper, we present a novel tensor-based HSI denoising approach by fully identifying the intrinsic structures of the clean HSI and the noise. Specifically, the HSI is first divided into local overlapping full-band patches (FBPs), then the nonlocal similar patches in each group are unfolded and stacked into a new third order tensor. As this tensor shows a stronger low-rank property than the original degraded HSI, the tensor weighted nuclear norm minimization (TWNNM) on the constructed tensor can effectively separate the low-rank clean HSI patches. In addition, a regularization strategy with spatial–spectral total variation (SSTV) is utilized to ensure the global spatial–spectral smoothness in both spatial and spectral domains. Our method is designed to model the spatial–spectral non-local self-similarity and global spatial–spectral smoothness simultaneously. Experiments conducted on simulated and real datasets show the superiority of the proposed method.

Channel estimation in Underwater Acoustic Communication (UAC) faces significant challenges due to the non-Gaussian, impulsive noise in ocean environments and the inherent high dimensionality of the estimation task. This paper introduces a robust channel estimation algorithm by solving an l1−l1 optimization problem via the Alternating Direction Method of Multipliers (ADMM), effectively exploiting channel sparsity and addressing impulsive noise outliers. A non-monotone backtracking line search strategy is also developed to improve the convergence behavior. The proposed algorithm is low in complexity and has robust performance. Simulation results show that it exhibits a small performance deterioration of less than 1 dB for Channel Impulse Response (CIR) estimation in impulsive noise environments, nearly matching its performance under Additive White Gaussian Noise (AWGN) conditions. For Delay-Doppler (DD) doubly spread channel estimation, it maintains Bit Error Rate (BER) performance comparable to using ground truth channel information in both AWGN and impulsive noise environments. At-sea experimental validations for channel estimation in Orthogonal Frequency Division Multiplexing (OFDM) systems further underscore the fast convergence speed and high estimation accuracy of the proposed method.

The acquisition and transmission of magnetic resonance images are susceptible to noise, particularly impulse noise. Although the method based on the ℓ0-norm and overlapping group sparse total variation (ℓ0-OGSTV) is effective for impulse noise image restoration, it can only mitigate the staircase artifacts to a certain extent. To boost the impulse noise removal performance of ℓ0-OGSTV, we propose a new restoration model that consists of two terms. Specifically, in the first term, we keep using the ℓ0-norm as the data fidelity term to eliminate impulse noise. In the second term, we first introduce an overlapping group sparsity fractional-order total variation regularizer to eliminate staircase artifacts while preserving structural information. Then, we adopt the minimax-concave penalty to further accurately estimate the image edges. Finally, we employ an alternate direction method of multipliers to solve the proposed optimization model. Clinical experiments demonstrate its effectiveness in denoising medical images.

Contour and texture preservation underwater image restoration via low-rank regularizations

Hyperspectral and multispectral image fusion plays an important role in the fields such as image restoration, space robotics, remote sensing, computer vision, etc. The fused images take advantages of the high spectral resolutions of hyperspectral images and the high spatial resolutions of multispectral images. So there has been a recent outgrowth of interests of research in this field. However, the local structural image regularity and non-local image self-similarity are not yet explored in existing fusion methods. This paper develops a novel method for fusing hyperspectral and multispectral images with non-local structure tensor total variation regularization. Specifically, the weight function to measure self-similarity in non-local domain is introduced on the basis of the definition of structure tensor. Therefore, the proposed method can exploit the regularity and self-similarity of spatial-spectral image’s non-local structures simultaneously. In addition to the general formulation of non-local structure tensor variation, this paper presents the discrete non-local structure tensor variation for hyperspectral and multispectral image fusion whose measurements are discrete. This method can provide an alternative way to measure the image variation of multi-band image. The resulting problem is solved by alternating direction method of multipliers (ADMM), a simple but powerful algorithm for convex optimization problems. The optimization problem is handled by a splitting variables strategy, which is implemented by introducing four auxiliary variables regarding to the required fused image. The iteration related to the proposed non-local structure tensor regularization term is solved by the proximal mapping method. The solutions of other iterations are given through fast Fourier transforms. Extensive computational experiments are performed on various datasets. The results of index evaluation demonstrate the effectiveness of the proposed method. These results also indicate non-local structure tensor total variation regularization has obvious advantages over the state-of-the-art fusion methods.KeywordsImage fusionNon-local tensor regularizationOptimization method

Impulsive noise is always present in real-world image Compressive Sensing (CS) acquisition systems, where existing CS reconstruction performance may seriously deteriorate. In this article, we propose a robust CS formulation for image reconstruction to suppress outliers in the presence of impulsive noise. To address this issue, we consider a novel truncated-Cauchy loss function as the metric of residual error to elevate the reconstruction robustness. Specifically, we design a complementary priors model to incorporate nonconvex nonlocal low-rank prior and deep denoiser prior for high-accuracy image reconstruction. By means of the half-quadratic optimization theory and generalized soft-thresholding technique, we also develop an alternative optimization algorithm for solving the induced nonconvex optimization problem. Numerical simulations demonstrate the robustness and accuracy of the proposed robust CS method compared to some recent CS methods for image reconstruction in impulsive noise.

A novel method is proposed for removing impulse (random-valued and salt-and-pepper) noise from multichannel digital images based on an adapted version of the DEEPLOC algorithm introduced by A. Struyf and P. J. Rousseeuw for calculation of approximate half-space (Tukey's) deepest location (median) in multivariate case. Due to its intrinsic multivariate/multidimensional nature, the proposed method eliminates the noise simultaneously on all channels without their separation, which preserves the spectral correlation between channels in a multichannel image. Denoising results of this new nonlinear spatial domain filter applied to benchmark images outperform currently used state-of-the-art filters for impulse noise removal from multichannel images in terms of both objective effectiveness criteria [peak-signal-to-noise-ratio (PSNR), mean absolute error (MAE), and normalized color distance (NCD)] and visual quality. The proposed filter successfully preserves the edges and fine image details, and is very effective for removal of medium and heavy multichannel impulse noise.

In this paper, we provide a new model for simultaneous denoising and illumination correction. A variational framework based on local maximum likelihood estimation (MLE) and a nonlocal regularization is proposed and studied. The proposed minimization problem can be efficiently solved by the augmented Lagrangian method coupled with a maximum expectation step. Experimental results show that our model can provide more homogeneous denoisng results compared to some earlier variational method. In addition, the new method also produces good results under both Gaussian and non-Gaussian noise such as Gaussian mixture, impulse noise and their mixtures.KeywordsNoisy ImageImpulse NoiseAugmented Lagrangian MethodBias FunctionSplit Bregman MethodThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Remote sensing image reconstruction from undersampled data is very much required by the onboard imaging system to cut down data volume and maintain image quality. Nonlocal low-rank regularization deriving from group sparsity, low rank, singular-value thresholding, and nonconvex surrogate functions have recently emerged for image recovery. To use nonlocal low-rank compressed sensing for remote sensing image reconstruction, spectral and temporal redundancy are considered in this letter by utilizing the similarity of correlated bands or historical records. Prior structural knowledge helps to group nonlocal similar blocks more accurately. Oversmoothness of low-rank regularization is improved by injecting referenced structures selectively. The proposed compressed sensing method is tested on satellite images from MODIS, LandSat-7, LandSat-8, IKONOS, and Google Earth to make clear that it outweighs state-of-the-art methods in maintaining fidelity and high visual details.

Most of the impulse denoisers are either median filter‐based or fuzzy filter‐based, which can only perform well in low noise conditions. This study presents an efficient convolutional neural network (CNN) with particle swarm optimisation (PSO) model for high‐density impulse noise removal. The proposed high‐density impulse noise detection and removal model mainly consists of two parts: the impulse noise removal and impulse noisy pixel detection for restoration. The authors’ model initially leverages the powerful ability of deep CNN architecture to separate noise from the noisy image, then adopts PSO to pinpoint the most optimised threshold values for detecting impulse noisy pixels. An ensemble of these algorithms is an intelligent and adaptive solution, producing a clean output while preserving significant pixel information. Targeting to solve high‐density impulse noise problems, the authors have trained their model with a massive collection of natural images and 14 standard testing images are used for validation purposes. In order to validate the robustness of the proposed method, different levels of high‐density impulse noise are considered. Based on the final denoised images, their model has proven its reliability, in terms of both visual quality and quantitative evaluation, on greyscale and colour images.