Nonlocal Low Rank Research Articles

A Multidimensional Tensor Low Rank Method for Magnetic Resonance Image Denoising.

In this paper, we present the Magnetic Resonance Image (MRI) denoising method via nonlocal multidimensional low rank tensor transformation constraint (NLRT). We first design a nonlocal MRI denoising method by non-local low rank tensor recovery framework. Furthermore, a multidimensional low rank tensor constraint is used to obtain low-rank prior information combined with 3-dimensional structure feature of MRI image cubes. Our NLRT can achieve denoising by retaining more image detail information. The optimization and updating process of the model is solved via the alternating direction method of multipliers (ADMM) algorithm. Several state-of-the-art denoising methods are selected for comparative experiments. In order to reflect the performance of the denoising method, Rician noise with different levels is added to the experiment to analyze the results. The experimental results prove that our NLTR has more outstanding denoising ability and can obtain better MRI images.

Deep nonlocal low-rank regularization for complex-domain pixel super-resolution.

Pixel super-resolution (PSR) has emerged as a promising technique to break the sampling limit for phase imaging systems. However, due to the inherent nonconvexity of phase retrieval problem and super-resolution process, PSR algorithms are sensitive to noise, leading to reconstruction quality inevitably deteriorating. Following the plug-and-play framework, we introduce the nonlocal low-rank (NLR) regularization for accurate and robust PSR, achieving a state-of-the-art performance. Inspired by the NLR prior, we further develop the complex-domain nonlocal low-rank network (CNLNet) regularization to perform nonlocal similarity matching and low-rank approximation in the deep feature domain rather than the spatial domain of conventional NLR. Through visual and quantitative comparisons, CNLNet-based reconstruction shows an average 1.4 dB PSNR improvement over conventional NLR, outperforming existing algorithms under various scenarios.

Multiplicative noise removal using complementary total generalized variation and nonlocal low rank regularization

The problem of multiplicative image denoising is a typical ill-posed inverse problem which has been extensively studied in the past few decades and is still an open problem. Exploiting appropriate image priors is critical to solve ill-posed inverse image restoration problem. The existing total generalized variation (TGV) based approaches have achieved significant performance in removing the multiplicative noise. However, these TGV regularized approaches only consider the local smoothness prior of the potential clean image, which limits their ability for image restoration. Other than the local smoothness property, the nonlocal self-similarity prior of images can also be exploited to offer helpful remedy for better image reconstruction. In this paper, to simultaneously make use of both the local smoothness prior and nonlocal self-similarity prior, we integrate the TGV regularizer with the nonlocal low rank regularizer to propose a novel variational model for multiplicative image denoising. Specifically, in the objective function, the nonlocal low rank regularization is expressed by the celebrated weighted nuclear norm minimization (WNNM) which has recently been applied to image denoising and presents state-of-art result. Then, we apply the split Bregman algorithm to efficiently solve the resulting model. Numerical experiments demonstrate that the proposed method achieve superior performance over the competing methods, including the state-of-the-art SAR-BM3D method.

Advanced framework for enhancing ultrasound images through an optimized hybrid search algorithm and a novel motion compounding processing chain

Ultrasound imaging is a fast, widespread, and essential diagnostic technique for examining the body’s internal anatomy to find abnormal tissues or diseases. However, speckle noise in ultrasound imaging corrupts fine details and edges and degrades the image’s resolution and contrast, making diagnosing more difficult. In this work, a speckle reduction method using motion compounding is proposed. The objective of this work is ultrasound image enhancement keeping all the diagnostics details and edges. The proposed method uses the pre-locations frames that the sonographer generates before locating the required diagnostic frame. These frames are applied to the proposed optimized Modified Three-Step Search (O-MTSS) algorithm to enhance the final processed frame. The O-MTSS algorithm is a hybrid between the Three Step Search algorithm (TSS) and the New Diamond Search Algorithm (NDS). The method requires a scoring layer for storing additional frames to select optimal frames that will be used for enhancement. The proposed methodology is tested on synthetic and real ultrasound images. The outcomes produce considerable speckle reduction while maintaining the image edges with good computational time for real-time scanning. The result is evaluated by subjective physicians, radiologists, and image evaluation metrics. According to the percentages of the subjective analysis, there is a remarkable improvement in the processed image. The proposed algorithm result is compared with existing algorithms; It is observed that the improvement in terms of signal to noise ratio, peak signal to noise ratio, mean square error, root mean square error and structural similarity index values of the proposed method are 4.6%, 3.32%, 12.02%, 6.2% and 1.57% respectively over Non-Local Low-Rank (NLLR) method. According to qualitative and quantitative analysis, the suggested method outperforms existing speckle reduction techniques regarding edge and fine detail preservation.

Field of experts regularized nonlocal low rank matrix approximation for image denoising

The restoration of image degraded by noise is an essential preprocessing step for various imaging technologies. Nonlocal low rank matrix approximation has been successfully applied to image denoising due to the capability of recovering the underlying low rank structures. Unfortunately, existing rank minimization models ignore the correlation among image patches and their performance is degraded when encountering the heavy noise. To address this, we propose a field of experts regularized nonlocal low rank matrix approximation (RFoE) denoising model, which integrates a global field of experts (FoE) regularization, a fidelity term, and a nonlocal low rank constraint into a unified framework. The weighted nuclear norm is adopted as the low rank constraint while the FoE prior is utilized to capture the global structure information. An alternating direction minimization algorithm based on half quadratic splitting can effectively solve this model. Extensive experimental results demonstrate that the proposed RFoE model has a superior performance.

Iterative self-consistent parallel magnetic resonance imaging reconstruction based on nonlocal low-rank regularization

Iterative self-consistent parallel imaging reconstruction (SPIRiT) is an effective self-calibrated reconstruction model for parallel magnetic resonance imaging (PMRI). The joint L1 norm of wavelet or tight frame coefficients and joint total variation (TV) regularization terms are incorporated into the SPIRiT model to improve the reconstruction performance. The simultaneous two-directional low-rankness (STDLR) in k-space data is incorporated into SPIRiT to realize improved reconstruction. Recent methods have exploited the nonlocal self-similarity (NSS) of images by imposing nonlocal low-rankness of similar patches to achieve a superior performance. To fully utilize both the NSS in Magnetic resonance (MR) images and calibration consistency in the k-space domain, we propose a nonlocal low-rank (NLR)-SPIRiT model by incorporating NLR regularization into the SPIRiT model. We apply the weighted nuclear norm (WNN) as a surrogate of the rank and employ the Nash equilibrium (NE) formulation and alternating direction method of multipliers (ADMM) to efficiently solve the NLR-SPIRiT model. The experimental results demonstrate the superior performance of NLR-SPIRiT over the state-of-the-art methods via three objective metrics and visual comparison.

Hybrid Deep Learning Framework for Reduction of Mixed Noise via Low Rank Noise Estimation

In this paper, an innovative hybridized deep learning framework (EN-CNN) is presented for image noise reduction where the noise originates from heterogeneous sources. More specifically, EN-CNN is applied to the benchmark natural images affected by a mixture of additive white gaussian noise (AWGN) and impulsive noise (IN). Reduction of mixed noise (AWGN and IN) is relatively more involved as compared to removing simply one type of noise. In fact, mitigating the impact of a mixture of multiple noise types becomes exceedingly challenging due to simultaneous presence of different noise statistics. Although, various effective deep learning approaches such as [1] and the classical state-of-the-art approaches like WNNM [2] have been used to suppress AWGN noise only, the same techniques are not suitable in case of mixed noise. In this context, EN-CNN can not only infer changed noise statistics but can also effectively eliminate residual noise. Firstly, EN-CNN employs the classical method of neighborhood filtering followed by non-local low rank estimation to respectively reduce IN noise and estimate the residual noise characteristics after reducing IN noise. As a result of this step, we obtain a pre-processed image with residual noise statistics. Secondly, convolutional neural network (CNN) is applied to the pre-processed image based on the noise statistics inferred in the first step. This two pronged strategy, in conjunction with the deep learning mechanism, effectively handles the mixed noise suppression. As a result, the suggested framework yields promising results as compared to various state-of-the-art approaches.

Hyperspectral Image Denoising With Weighted Nonlocal Low-Rank Model and Adaptive Total Variation Regularization

Hyperspectral image (HSI) is always corrupted by various types of noise during image capturing, such as Gaussian noise, stripe noise, deadline noise, impulse noise, and more. Such complicated noise significantly degrades imaging quality and thus limits the performance of downstream vision tasks. Current HSI denoising methods tackle this problem by modeling either the spectral-spatial prior of HSI or the noise characteristic of HSI, and few work consider the two aspects simultaneously. In this paper, we propose a new HSI denoising method by simultaneously modeling the HSI prior and the HSI noise characteristic. Specifically, we firstly utilize the non independent and identically distributed (non i.i.d.) mixture of Gaussian (MoG) assumption to characterize the complex noise, which corresponds to optimize a weighted fidelity function. Secondly, we exploit HSI’s non-local similarity and spatial-spectral correlation priors by applying non-local low rank model. Thirdly, we design an adaptive edge preserving total variation regularization term to characterize the non-local smooth property of HSI. Finally, we propose a new denoising model and develop effective ADMM algorithm to solve it. Extensive experiments on simulated data and real data substantiate the superiority of the proposed method beyond state-of-the-arts.

CFAR Detection Based on the Nonlocal Low-Rank and Sparsity-Driven Laplacian Regularization for HFSWR

Target detection in high-frequency surface-wave radar (HFSWR) systems is a challenging task due to various sources of interference. In this article, we propose a robust constant false alarm rate (CFAR) detector to solve the problem of target detection for the HFSWR by exploiting the prior information on the detection environment. Clutter amplitudes in the HFSWR are commonly assumed to follow the Weibull distribution. Additionally, distribution parameters of the clutter have nonlocal self-similarity, and targets have sparsity as well as a certain geometric structure. We design an objective function based on the Bayesian framework, which consists of a data fidelity term and some regularization terms. Specifically, we use the nonlocal low-rank (NLR) regularization to represent the prior information regarding distribution parameters of clutter, and we adopt the combination of the sparsity and Laplacian regularization to represent the prior information regarding targets. The proposed objective function inherits advantages of the NLR, sparsity, and Laplacian regularization, thereby improving the performance of the proposed detector in the nonhomogeneous clutter. By optimizing the proposed objective function, we obtain estimates of clutter statistics for every cell under test and perform the CFAR detection. Experiments on both simulated data and experimental HFSWR data demonstrate that the proposed detector has a good false alarm regulation property and detection performance in the nonhomogeneous clutter.

Medical Image Denoising Algorithm Based on Sparse Nonlocal Regularized Weighted Coding and Low Rank Constraint

Medical image information may be polluted by noise in the process of generation and transmission, which will seriously hinder the follow-up image processing and medical diagnosis. In medical images, there is a typical mixed noise composed of additive white Gaussian noise (AWGN) and impulse noise. In the conventional denoising methods, impulse noise is first removed, followed by the elimination of white Gaussian noise (WGN). However, it is difficult to separate the two kinds of noises completely in practical application. The existing denoising algorithm of weight coding based on sparse nonlocal regularization, which can simultaneously remove AWGN and impulse noise, is plagued by the problems of incomplete noise removal and serious loss of details. The denoising algorithm based on sparse representation and low rank constraint can preserve image details better. Thus, a medical image denoising algorithm based on sparse nonlocal regularization weighted coding and low rank constraint is proposed. The denoising effect of the proposed method and the original algorithm on computed tomography (CT) image and magnetic resonance (MR) image are compared. It is revealed that, under different σ and ρ values, the PSNR and FSIM values of CT and MRI images are evidently superior to those of traditional algorithms, suggesting that the algorithm proposed in this work has better denoising effects on medical images than traditional denoising algorithms.

Mixed Noise Removal Using Adaptive Median Based Non-Local Rank Minimization

In this paper, we present an innovative mechanism for image restoration problems in which the image is corrupted by a mixture of additive white Gaussian noise (AWGN) and impulse noise (IN). Mixed noise removal is much more challenging problem in contrast to the problems where either only one type of noise model (either Gaussian or impulse) is involved. Several well-known and efficient algorithms exist to effectively remove either Gaussian noise or Impulse noise, independently. However, in practice, noise may occur as a mixture of such noise models. Thus, the existing techniques devised to handle individual types of noise may not perform well. Moreover, the complexity of the problem hinges on the fact that the removal of either type of noise from the given image affects the noise statistics in the residual image. Therefore, a rigorous mechanism is required which not only infers altered noise statistics but also removes the residual noise in an effective manner. In this regard, an innovative approach is introduced to restore the underlying image in three key steps. Firstly, the intensity values, affected by impulsive noise, are identified by analyzing noise statistics with the help of adaptive median filtering. The identified intensity values are then aggregated by exploiting nonlocal data redundancy prior. Thus the first step enables the remaining noise to follow the zero mean Gaussian distribution in the median filtered image. Secondly, we estimate Gaussian noise in the resulting image, which acts as a key parameter in the subsequent singular value thresholding process for rank minimization. Finally, a reduced rank optimization applied to the pre-processed image obtained in the first step. The experimental results indicate that the proposed AMNLRA (Adaptive Median based Non-local Low Rank Approximation) approach can effectively tackle mixed noise complexity as compared to numerous state of the art algorithms.

A nonlocal low rank model for poisson noise removal

<p style='text-indent:20px;'>Patch-based methods, which take the advantage of the redundancy and similarity among image patches, have attracted much attention in recent years. However, these methods are mainly limited to Gaussian noise removal. In this paper, the Poisson noise removal problem is considered. Unlike Gaussian noise which has an identical and independent distribution, Poisson noise is signal dependent, which makes the problem more challenging. By incorporating the prior that a group of similar patches should possess a low-rank structure, and applying the maximum a posterior (MAP) estimation, the Poisson noise removal problem is formulated as an optimization one. Then, an alternating minimization algorithm is developed to find the minimizer of the objective function efficiently. Convergence of the minimizing sequence will be established, and the efficiency and effectiveness of the proposed algorithm will be demonstrated by numerical experiments.

A mixed model with multi-fidelity terms and nonlocal low rank regularization for natural image noise removal

Reconstructing an original image from its corrupted observation is an important and fundamental problem in many image processing applications. Generally, the L1-norm or L2-norm combined with a regularization term (the total variation (TV), total generalized variation (TGV) or nuclear norm) is used to fit the impulse noise and Gaussian noise, respectively. However, these methods can only be used to remove a single type of noise from images, and traditional regularization terms often have difficulties in capturing some important prior knowledge of images, such as nonlocal self-similarity, low rank and sparsity. To overcome the above issues, we propose a mixed noise removal model with L1-L2 fidelity terms and a popular nonlocal low-rank regularization term, which has been shown to have more effective image denoising performance than traditional regularization methods. To solve this model, the split Bregman iteration method (SBIM) is adopted to decompose the difficult minimization optimization problem into four simple subproblems. Extensive experiments on natural images demonstrate that the effectiveness of the proposed method is better than that of other state-of-the-art methods.

Nonlocal Low-Rank Abundance Prior for Compressive Spectral Image Fusion

Compressive spectral imaging (SI) (CSI) acquires few random projections of an SI reducing acquisition, storage, and, in some cases, processing costs. Then, this acquisition framework has been widely used in various tasks, such as target detection, video processing, and fusion. Particularly, compressive spectral image fusion (CSIF) aims at obtaining a high spatial-spectral resolution SI from two sets of compressed measurements: one from a hyperspectral image with a high-spectral low-spatial resolution, and one from a multispectral image with high-spatial low-spectral resolution. Most of the literature approaches include prior information, such as global low rank, smoothness, and sparsity, to solve the resulting ill-posed CSIF inverse problem. More recently, the high self-similarities exhibited by SIs have been successfully used to improve the performance of CSI inverse problems, including a nonlocal low-rank (NLLR) prior. However, to the best of our knowledge, this NLLR prior has not been implemented in the solution of the CSIF inverse problem. Therefore, this article formulates an approach that jointly includes the global low rank, the smoothness, and the NLLR priors to solve the CSIF inverse problem. The global low-rank prior is introduced with the linear mixture model that describes the SI as a linear combination of a set of few end-members to specific abundances. In this article, either the end-members are accurately estimated from the compressed measurements or initialized from a fast reconstruction of the hyperspectral image. Also, it assumes that the abundances preserve the smoothness and NLLR priors of the SI so that the fused image is obtained from the end-members and abundances that result when minimizing a cost function including the sum of two data fidelity terms and two regularizations: the smoothness and the NLLR. Simulations over three data sets show that the proposed approach increases the CSIF performance compared with literature approaches.

SAR Image Despeckling Based on Combination of Fractional-Order Total Variation 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.

Hybrid-Weighted Total Variation and Nonlocal Low-Rank-Based Image Compressed Sensing Reconstruction

To reconstruct natural images from compressed sensing (CS) measurements accurately and effectively, a CS image reconstruction algorithm based on hybrid-weighted total variation (HWTV) and nonlocal low-rank (NLR) is proposed. It considers the local smoothness and nonlocal self-similarity (NSS) in image, improves traditional hybrid total variation (TV) model, and constructs a new edge detection operator with mean curvature to adaptively select the TV. The HWTV combines the advantages of first-order TV and second-order TV to preserve the edges of the image and avoid the staircase effect in the smooth areas. And NLR can effectively reduce the redundant information and retain the structural information of the image. In addition, the proposed algorithm constructs prior regularization terms with improved HWTV model and NLR model, and utilizes soft threshold function and smooth but non-convex function to solve the TV and low-rank optimization problems, respectively. Finally, the alternative direction multiplier method (ADMM) iterative strategy is used to separate the target model into several sub-problems, and the most efficient methods are adopted to solve each sub-problem. Experimental results show that, compared with the state-of-the-art CS reconstruction algorithms, the proposed algorithm can achieve higher reconstruction quality, especially in the case of low sampling rates.

Robust Image Compressive Sensing Based on Truncated Cauchy Loss and Nonlocal Low-Rank Regularization

This work presents a novel robust image compressive sensing reconstruction approach. In contrast to the existing work, we employ the truncated Cauchy loss function to measure the errors induced during the measurement, showing strong robustness to impulsive noise and outliers. To ensure high quality reconstructed images, we utilize a non-local low rank regularizer - with truncated Schatten-p norm being the surrogate function of rank - to capture the self-similar property inherent in most natural images. Considering the fact that the whole optimization model is neither convex nor smooth, to solve it effectively, we firstly use the half-quadratic strategy to transform the loss function into a quadratic objective by introducing some auxiliary variables, and then iteratively and alternatively optimize different groups of variables. Extensive experimental results demonstrate its effectiveness in terms of both quantitative indexes of Peak Signal-to-Noise Ratio (PSNR) and Structural SIMilarity (SSIM), and visual quality under impulsive noise.

3D Tensor Based Nonlocal Low Rank Approximation in Dynamic PET Reconstruction.

Reconstructing images from multi-view projections is a crucial task both in the computer vision community and in the medical imaging community, and dynamic positron emission tomography (PET) is no exception. Unfortunately, image quality is inevitably degraded by the limitations of photon emissions and the trade-off between temporal and spatial resolution. In this paper, we develop a novel tensor based nonlocal low-rank framework for dynamic PET reconstruction. Spatial structures are effectively enhanced not only by nonlocal and sparse features, but momentarily by tensor-formed low-rank approximations in the temporal realm. Moreover, the total variation is well regularized as a complementation for denoising. These regularizations are efficiently combined into a Poisson PET model and jointly solved by distributed optimization. The experiments demonstrated in this paper validate the excellent performance of the proposed method in dynamic PET.

Single image super-resolution incorporating example-based gradient profile estimation and weighted adaptive p-norm

Single image super-resolution (SR) aims to estimate a high-resolution (HR) image from only one observed low-resolution (LR) image. It is a severely ill-posed problem that needs image priors to ensure a reliable HR estimation. Since different priors usually emphasize different aspects of image characteristics, it’s a big challenge to impose a balanced-and-overall image property constraint on single image SR. In this paper, we cast single image SR into a maximum a posteriori optimization problem and combine two types of complementary priors to answer this challenge. One prior is a novel local gradient field prior derived from example-based gradient field estimation (EGFE) that focuses on recovering the sharpness of gradient profiles. It is good at enhancing the edge sharpness and restoring fine texture details. Whereas the other is a powerful non-local low rank prior implemented in a weighted adaptive p-norm model (WANM). By imposing lp penalties adaptive to regional saliency and weighted constraints, the WANM prior performs well in preserving edge smoothness and suppressing image noise and reconstruction artifacts. An improved Split Bregman Iteration method that adaptively attenuates the regularization strength is further developed to solve the proposed EGFE-WANM SR problem. Comprehensive experiments are conducted and the results show that the proposed EGFE-WANM SR method outperforms many state-of-the-art methods in both objective evaluations and subjective visual comparisons.

Risk for antipsychotic-induced extrapyramidal symptoms: a focus on monoamine receptors on peripheral blood lymphocytes

Single image super-resolution (SR) aims to estimate a high-resolution (HR) image from only one observed low-resolution (LR) image. It is a severely ill-posed problem that needs image priors to ensure a reliable HR estimation. Since different priors usually emphasize different aspects of image characteristics, it’s a big challenge to impose a balanced-and-overall image property constraint on single image SR. In this paper, we cast single image SR into a maximum a posteriori optimization problem and combine two types of complementary priors to answer this challenge. One prior is a novel local gradient field prior derived from example-based gradient field estimation (EGFE) that focuses on recovering the sharpness of gradient profiles. It is good at enhancing the edge sharpness and restoring fine texture details. Whereas the other is a powerful non-local low rank prior implemented in a weighted adaptive p-norm model (WANM). By imposing lp penalties adaptive to regional saliency and weighted constraints, the WANM prior performs well in preserving edge smoothness and suppressing image noise and reconstruction artifacts. An improved Split Bregman Iteration method that adaptively attenuates the regularization strength is further developed to solve the proposed EGFE-WANM SR problem. Comprehensive experiments are conducted and the results show that the proposed EGFE-WANM SR method outperforms many state-of-the-art methods in both objective evaluations and subjective visual comparisons.