Low-rank Image Research Articles

A non-convex low-rank image decomposition model via unsupervised network

Image decomposition is the separation of a given image into two parts with different features, i.e., structure and texture. In order to extract the image information comprehensively, a non-convex unsupervised image decomposition model is proposed in this paper. Firstly, we propose a new non-convex low-rank regular term to describe the low-rank nature of images, which focuses on optimizing the sum of partial singular values of image matrices using a non-convex truncated nuclear norm. Secondly, unsupervised network is used to capture image information by learning the deep semantic information of the image and then extracting the image structure. Finally, the alternative direction method of multipliers is used to divide the model into three sub-problems and optimize them separately. For the non-convex sub-problem, a two-stage solution scheme is given by employing the singular value decomposition technique, and experimental analysis is carried out on both real and synthetic images. The experimental results show that the proposed non-convex image decomposition method outperforms other state-of-the-art methods in terms of subjective visual effects. Meanwhile, in the quantitative evaluation, the proposed method shows a large improvement compared with other methods, with a maximum improvement of 15 % in the structural similarity index measure (SSIM) index.

Free-breathing, fat-corrected T1 mapping of the liver with stack-of-stars MRI, and joint estimation of T1, PDFF, , and .

Quantitative T1 mapping has the potential to replace biopsy for noninvasive diagnosis and quantitative staging of chronic liver disease. Conventional T1 mapping methods are confounded by fat and inhomogeneities, resulting in unreliable T1 estimations. Furthermore, these methods trade off spatial resolution and volumetric coverage for shorter acquisitions with only a few images obtained within a breath-hold. This work proposes a novel, volumetric (3D), free-breathing T1 mapping method to account for multiple confounding factors in a single acquisition. Free-breathing, confounder-corrected T1 mapping was achieved through the combination of non-Cartesian imaging, magnetization preparation, chemical shift encoding, and a variable flip angle acquisition. A subspace-constrained, locally low-rank image reconstruction algorithm was employed for image reconstruction. The accuracy of the proposed method was evaluated through numerical simulations and phantom experiments with a T1/proton density fat fraction phantom at 3.0 T. Further, the feasibility of the proposed method was investigated through contrast-enhanced imaging in healthy volunteers, also at 3.0 T. The method showed excellent agreement with reference measurements in phantoms across a wide range of T1 values (200 to 1000 ms, slope = 0.998 (95% confidence interval (CI) [0.963 to 1.035]), intercept = 27.1 ms (95% CI [0.4 54.6]), r2 = 0.996), and a high level of repeatability. In vivo imaging studies demonstrated moderate agreement (slope = 1.099 (95% CI [1.067 to 1.132]), intercept = -96.3 ms (95% CI [-82.1 to -110.5]), r2 = 0.981) compared to saturation recovery-based T1 maps. The proposed method produces whole-liver, confounder-corrected T1 maps through simultaneous estimation of T1, proton density fat fraction, and in a single, free-breathing acquisition and has excellent agreement with reference measurements in phantoms.

Multiple Complementary Priors for Multispectral Image Compressive Sensing Reconstruction.

Compressive sensing (CS) techniques using a few compressed measurements have drawn considerable interest in reconstructing multispectral imagery (MSI). Nonlocal-based tensor methods have been widely used for MSI-CS reconstruction, which employ the nonlocal self-similarity (NSS) property of MSI to obtain satisfactory results. However, such methods only consider the internal priors of MSI while ignoring important external image information, for example deep-driven priors learned from a corpus of natural image datasets. Meanwhile, they usually suffer from annoying ringing artifacts due to the aggregation of overlapping patches. In this article, we propose a novel approach for highly effective MSI-CS reconstruction using multiple complementary priors (MCPs). The proposed MCP jointly exploits nonlocal low-rank and deep image priors under a hybrid plug-and-play framework, which contains multiple pairs of complementary priors, namely, internal and external, shallow and deep, and NSS and local spatial priors. To make the optimization tractable, a well-known alternating direction method of multiplier (ADMM) algorithm based on the alternating minimization framework is developed to solve the proposed MCP-based MSI-CS reconstruction problem. Extensive experimental results demonstrate that the proposed MCP algorithm outperforms many state-of-the-art CS techniques in MSI reconstruction. The source code of the proposed MCP-based MSI-CS reconstruction algorithm is available at: https://github.com/zhazhiyuan/MCP_MSI_CS_Demo.git.

Dual-polarimetric Sentinel-1 SAR time series data despeckling using RABASAR with low-rank image

Dual-polarimetric Sentinel-1 SAR time series data despeckling using RABASAR with low-rank image

A continuous-time neurodynamic approach in matrix form for rank minimization

This article proposes a continuous-time neurodynamic approach for solving the rank minimization under affine constraints. As opposed to the traditional neurodynamic approach, the proposed neurodynamic approach extends the form of the variables from the vector form to the matrix form. First, a continuous-time neurodynamic approach with variables in matrix form is developed by combining the optimal rank r projection and the gradient. Then, the optimality of the proposed neurodynamic approach is rigorously analyzed by demonstrating that the objective function satisfies the functional property which is called as (2r,4r)-restricted strong convexity and smoothness ((2r,4r)-RSCS). Furthermore, the convergence and stability analysis of the proposed neurodynamic approach is rigorously conducted by establishing appropriate Lyapunov functions and considering the relevant restricted isometry property (RIP) condition associated with the affine transformation. Finally, through experiments involving low-rank matrix recovery under affine transformations and the completion of low-rank real image, the effectiveness of this approach has been demonstrated, along with its superiority compared to the vector-based approach.

Mixture-Net: Low-rank deep image prior inspired by mixture models for spectral image recovery

This paper proposes a non-data-driven deep neural network for spectral image recovery problems such as denoising, single hyperspectral image super-resolution, and compressive spectral imaging reconstruction. Unlike previous methods, the proposed approach, dubbed Mixture-Net, implicitly learns the prior information through the network. Mixture-Net consists of a deep generative model whose layers are inspired by the linear and non-linear low-rank mixture models, where the recovered image is composed of a weighted sum between the linear and non-linear decomposition. Mixture-Net also provides a low-rank decomposition interpreted as the spectral image abundances and endmembers, helpful in achieving remote sensing tasks without running additional routines. The experiments show the Mixture-Net effectiveness outperforming state-of-the-art methods in recovery quality with the advantage of architecture interpretability.

An Innovative Approach for Removing Stripe Noise in Infrared Images.

The non-uniformity of infrared detectors' readout circuits can lead to stripe noise in infrared images, which affects their effective information and poses challenges for subsequent applications. Traditional denoising algorithms have limited effectiveness in maintaining effective information. This paper proposes a multi-level image decomposition method based on an improved LatLRR (MIDILatLRR). By utilizing the global low-rank structural characteristics of stripe noise, the noise and smooth information are decomposed into low-rank part images, and texture information is adaptively decomposed into several salient part images, thereby better preserving texture edge information in the image. Sparse terms are constructed according to the smoothness of the effective information in the final low-rank part of the image and the sparsity of the stripe noise direction. The modeling of stripe noise is achieved using multi-sparse constraint representation (MSCR), and the Alternating Direction Method of Multipliers (ADMM) is used for calculation. Extensive experiments demonstrated the proposed algorithm's effectiveness and compared it with state-of-the-art algorithms in subjective judgments and objective indicators. The experimental results fully demonstrate the proposed algorithm's superiority and efficacy.

Image decomposition combining low-rank and deep image prior

Image decomposition combining low-rank and deep image prior

Low-Rank and Total Variation Regularization with ℓ0 Data Fidelity Constraint for Image Deblurring under Impulse Noise

Impulse noise removal is an important problem in the field of image processing. Although many methods exist to remove impulse noise, there is still room for improvement. This paper proposes a new method for removing impulse noise that combines the nuclear norm and the detection ℓ0TV model while considering the low-rank structure commonly found in visual images. The nuclear norm maintains this structure, while the detection ℓ0TV criterion promotes sparsity in the gradient domain, effectively removing impulse noise while preserving edges and other vital features. To solve the non-convex and non-smooth optimization problem, we use a mathematical process with equilibrium constraints (MPEC) to transform it. Subsequently, the proximal alternating direction multiplication algorithm is used to solve the transformed problem. The convergence of the algorithm is proven under mild conditions. Numerical experiments in denoising and deblurring show that for low-rank images, the proposed method outperforms ℓ1TV with detection, ℓ0TV and ℓ0OGSTV.

A low-rank deep image prior reconstruction for free-breathing ungated spiral functional CMR at 0.55T and 1.5T.

This study combines a deep image prior with low-rank subspace modeling to enable real-time (free-breathing and ungated) functional cardiac imaging on a commercial 0.55T scanner. The proposed low-rank deep image prior (LR-DIP) uses two u-nets to generate spatial and temporal basis functions that are combined to yield dynamic images, with no need for additional training data. Simulations and scans in 13 healthy subjects were performed at 0.55T and 1.5T using a golden angle spiral bSSFP sequence with images reconstructed using [Formula: see text]-ESPIRiT, low-rank plus sparse (L + S) matrix completion, and LR-DIP. Cartesian breath-held ECG-gated cine images were acquired for reference at 1.5T. Two cardiothoracic radiologists rated images on a 1-5 scale for various categories, and LV function measurements were compared. LR-DIP yielded the lowest errors in simulations, especially at high acceleration factors (R [Formula: see text] 8). LR-DIP ejection fraction measurements agreed with 1.5T reference values (mean bias -0.3% at 0.55T and -0.2% at 1.5T). Compared to reference images, LR-DIP images received similar ratings at 1.5T (all categories above 3.9) and slightly lower at 0.55T (above 3.4). Feasibility of real-time functional cardiac imaging using a low-rank deep image prior reconstruction was demonstrated in healthy subjects on a commercial 0.55T scanner.

High-efficiency 3D black-blood thoracic aorta imaging with patch-based low-rank tensor reconstruction.

Three-dimensional (3D) black-blood (BB) vessel wall imaging is a promising noninvasive imaging technique for assessing thoracic aortic diseases. We aimed to develop and evaluate a fast thoracic aorta vessel wall imaging method with patch-based low-rank tensor (Pt-LRT) reconstruction using the 3D-modulated variable flip angle fast-spin echo (vFA-FSE) sequence. The Pt-LRT technique adopts a low-rank tensor image model with regularization to explore the local low-rankness and nonlocal redundancies of the images to assess the thoracic aorta vessel wall. It uses high-order tensors to capture correlations between data in multiple dimensions and reconstructs images from highly undersampled data. For this study, 12 healthy participants and 2 patients with thoracic aortic diseases were evaluated at 3T magnetic resonance (MR). The reconstruction results were compared to the traditional generalized autocalibrating partially parallel acquisitions (GRAPPA) and ℓ1-SPIRiT reconstruction to assess the feasibility of the proposed framework. Quantitative analyses of the vessel wall thickness (VWT), internal diameter (ID), lumen area (LA), and contrast-to-noise ratio (CNR) between the lumen and vessel wall were performed on all healthy participants. Results demonstrated no significant differences between the GRAPPA and the proposed Pt-LRT in VWT, ID, or LA of the aorta (P<0.05). A higher mean CNR was attained with 3D patch-based low-rank tensor reconstruction than with ℓ1-SPIRiT reconstruction (49.4±10.8 vs. 38.9±8.2). The proposed 3D BB thoracic aorta vessel wall imaging method can reduce the scan time and produce an image quality that is in good agreement with the conventional GRAPPA acquisition, which takes approximately more than 8 min. This study also shows that the proposed Pt-LRT method substantially improves the visualization and sharpness of the vessel wall and the definition of the tissue boundary compared to the imaging obtained with ℓ1-SPIRiT.

Nested multi-scale transform fusion model: The response evaluation of chemoradiotherapy for patients with lung tumors

Background and Objective: The response evaluation of chemoradiotherapy is an important method of precision treatment for patients with malignant lung tumors. In view of the existing evaluation criteria for chemoradiotherapy, it is difficult to synthesize the geometric and shape characteristics of lung tumors. In the present, the response evaluation of chemoradiotherapy is limited. Therefore, this paper constructs a response evaluation system of chemoradiotherapy based on PET/CT images. Methods: There are two parts in the system: a nested multi-scale fusion model and an attribute sets for the Response evaluation of chemoradiotherapy (AS-REC). In the first part, a new nested multi-scale transform method, i.e., latent low-rank representation (LATLRR) and non-subsampled contourlet transform (NSCT), is proposed. Then, the average gradient self-adaptive weighting is used for the low-frequency fusion rule, and the regional energy fusion rule is used for the high-frequency fusion rule. Further, the low-rank part fusion image is obtained by the inverse NSCT, and the fusion image is generated by adding the low-rank part fusion image and the significant part fusion image. In the second part, AS-REC is constructed to evaluate the growth direction of the tumor, the degree of tumor metabolic activity, and the tumor growth state. Results: the numerical results clearly show that the performance of our proposed method outperforms in comparison with several existing methods, among them, the value of Qabf increased by up to 69%. Conclusions: Through the experiment of three reexamination patients, the effectiveness of the evaluation system of radiotherapy and chemotherapy are proved.

Accurate Multiobjective Low-Rank and Sparse Model for Hyperspectral Image Denoising Method

Due to the unavoidable influence of sparse and Gaussian noise during the process of data acquisition, the quality of hyperspectral images (HSIs) is degraded and their applications are greatly limited. It is therefore necessary to restore clean HSIs. In the traditional methods, low-rank and sparse matrix decomposition methods are usually applied to restore the pure data matrix from the observed data matrix. However, due to the fact that the optimization of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${l}_{0}$ </tex-math></inline-formula> -norm for the sparse modeling is a nonconvex and NP-hard problem, convex relaxation and regularization parameters are usually introduced. However, convex relaxation often leads to inaccurate sparse modeling results, and the sensitive regularization parameters can lead to unstable results. Thus, in this article, to address these issues, an accurate multiobjective low-rank and sparse denoising framework is proposed for HSIs to achieve accurate modeling. The <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${l}_{0}$ </tex-math></inline-formula> -norm is directly modeled as the sparse noise and is optimized by an evolutionary algorithm, and the denoising problem is converted into a multiobjective optimization problem through simultaneously optimizing the low-rank term, the sparse term, and the data fidelity term, without sensitive regularization parameters. However, since the low-rank clean image and sparse noise of the HSI are encoded into a solution, the length of the solution is too long to be optimized. In this article, a subfitness strategy is constructed to achieve effective optimization by comparing the objective function values corresponding to each band for each solution. The experiments undertaken with simulated images in 11 noise cases and four real noisy images confirm the effectiveness of the proposed method.

Enhancing Underwater Imagery via Latent Low-Rank Decomposition and Image Fusion

The quality of underwater images is usually degraded due to the absorption and scattering effect of seawater, which leads to image distortion and reduces the accuracy and efficiency of subsequent vision tasks. To solve the above problems, an enhancement method for underwater images based on latent low-rank decomposition and image fusion is proposed in this article. First, a color correction method based on adaptive channel compensation is implemented to remove color distortion. Second, an improved Laplace sharpening method and gamma correction technology are applied to effectively improve the sharpness and contrast of the underwater image. Finally, a dual-image weighted image fusion based on latent low-rank representation is proposed to integrate the enhanced image. The experimental results show that this method can obtain better results than other traditional methods on both color reproduction and detail preservation. Furthermore, a set of application tests is executed to further demonstrate the effectiveness of the proposed method.

Edge Preserved Low-Rank SAR Image Despeckling via Hierarchical Prior Knowledge Regulation

Synthetic aperture radar (SAR) image despeckling is a challenging task as speckle noise is spatially correlated and signal-dependent, and appears as a grainy texture superimposed on images. Although traditional low-rank SAR image despeckling methods have shown promising performance, they have the problem of producing over-smoothed images with blurred edges due to their low-rank characteristics. In this paper, we propose a novel edge preserved SAR despeckling method named EP-LRSID, which can keep rich edge details while reducing speckle noise. Specifically, EP-LRSID takes a fresh look at the low-rank model, i.e., we can obtain structural edge information from residuals which is viewed as noise and simply disregarded by the traditional low-rank methods. To obtain discriminative edge information from residuals, the edge subspace is obtained in a manifold framework by using a dynamic affinity graph regularization. Moreover, a new hierarchical prior knowledge regulation is designed to make different kinds of pixels processed hierarchically, especially the strong scattering points in SAR images. By introducing this prior knowledge, our low-rank model can obtain more confidential low-rank parts and edge parts, thus structural information including edges can be better preserved in this way. Extensive experiments on several real and synthetic datasets demonstrate that EP-LRSID can achieve the highest despeckling performance with edge preservation than other state-of-the-art despeckling algorithms.

Randomized Tensor Robust PCA for Noisy Hyperspectral Image Classification

Removing noise from hyperspectral images can be very beneficial for improving classification accuracy. Recently, tensor robust principal component analysis (TRPCA) has been successfully employed to reduce noise in hyperspectral images. In TRPCA, a minimization involving a tensor nuclear norm and a ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -norm is employed to separate the low-rank hyperspectral image from the sparse noise. Tensor nuclear norm minimization is solved by iteratively performing tensor singular value thresholding (T-SVT). However, TRPCA possesses high computational complexity primarily due to the implementation of the T-SVT operator. The conventional approach for T-SVT is first to perform full tensor singular value decomposition (T-SVD), and then to shrink the singular values of the frontal slices in the frequency domain. However, when the solution of tensor nuclear norm minimization is a low-rank tensor, a good strategy is to incrementally find the singular values until they fall below the threshold. In this letter, we propose a randomized blocked algorithm for computing tensor singular value thresholding, and we leverage the compression attained by the fast Fourier transform (FFT) to accelerate TRPCA. Numerical experiments indicate that our method is significantly faster than performing TRPCA via the full T-SVD while maintaining classification accuracy.

An Edge Computing Algorithm Based on Multi-Level Star Sensor Cloud

Star sensors are an important means of autonomous navigation and access to space information for satellites. They have been widely deployed in the aerospace field. To satisfy the requirements for high resolution, timeliness, and confidentiality of star images, we propose an edge computing algorithm based on the star sensor cloud. Multiple sensors cooperate with each other to form a sensor cloud, which in turn extends the performance of a single sensor. The research on the data obtained by the star sensor has very important research and application values. First, a star point extraction model is proposed based on the fuzzy set model by analyzing the star image composition, which can reduce the amount of data computation. Then, a mapping model between content and space is constructed to achieve low-rank image representation and efficient computation. Finally, the data collected by the wireless sensor is delivered to the edge server, and a different method is used to achieve privacy protection. Only a small amount of core data is stored in edge servers and local servers, and other data is transmitted to the cloud. Experiments show that the proposed algorithm can effectively reduce the cost of communication and storage, and has strong privacy.

Hybrid Multimodal Medical Image Fusion Method Based on LatLRR and ED-D2GAN

In order to better preserve the anatomical structure information of Computed Tomography (CT) source images and highlight the metabolic information of lesion regions in Positron Emission Tomography (PET) source images, a hybrid multimodal medical image fusion method (LatLRR-GAN) based on Latent low-rank representation (LatLRR) and the dual discriminators Generative Adversarial Network (ED-D2GAN) is proposed. Firstly, considering the denoising capability of LatLRR, source images were decomposed by LatLRR. Secondly, the ED-D2GAN model was put forward as the low-rank region fusion method, which can fully extract the information contained by the low-rank region images. Among them, encoder and decoder networks were used in the generator; convolutional neural networks were also used in dual discriminators. Thirdly, a threshold adaptive weighting algorithm based on the region energy ratio is proposed as the salient region fusion rule, which can improve the overall sharpness of the fused image. The experimental results show that compared with the best methods of the other six methods, this paper is effective in multiple objective evaluation metrics, including the average gradient, edge intensity, information entropy, spatial frequency and standard deviation. The results of the two experiments are improved by 35.03%, 42.42%, 4.66%, 8.59% and 11.49% on average.

A Patch-Based Composite Denoising Algorithm for Wireless Transmission

Many image denoising approaches in recent years are based on patch processing. Particularly, patch-based denoising algorithms under the low-rank (LR) model show outstanding performance in wireless transmission. However, constructing proper dictionaries is a key issue that affects the denoising results. On the basis of this idea, we propose a patch-based composite method for image denoising named similar patch LR (SPLR), which introduces a nonlocal model and structure similarity index measure (SSIM) to evaluate patches similarity. This evaluation method can explore the similarity of image patches to the full extent and construct a similar patches dictionary with an LR property. In addition, to improve the robustness of denoising, we divide the noise part into two parts, and use <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L_{0}$</tex-math></inline-formula> <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$-$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L_{2,0}$</tex-math></inline-formula> <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$-$</tex-math></inline-formula> norm, two different norm constraints to manage different types of noise. Extensive experiments show that the denoising performance and the robustness to noise of SPLR is better than that of the widely used and state-of-the-art, LR image denoising algorithms.

MR Multitasking-based multi-dimensional assessment of cardiovascular system (MT-MACS) with extended spatial coverage and water-fat separation.

To extend the MR MultiTasking-based Multidimensional Assessment of Cardiovascular System (MT-MACS) technique with larger spatial coverage and water-fat separation for comprehensive aortocardiac assessment. MT-MACS adopts a low-rank tensor image model for 7D imaging, with three spatial dimensions for volumetric imaging, one cardiac motion dimension for cine imaging, one respiratory motion dimension for free-breathing imaging, one T2-prepared inversion recovery time dimension for multi-contrast assessment, and one T2*-decay time dimension for water-fat separation. Nine healthy subjects were recruited for the 3T study. Overall image quality was scored on bright-blood (BB), dark-blood (DB), and gray-blood (GB) contrasts using a 4-point scale (0-poor to 3-excellent) by two independent readers, and their interreader agreement was evaluated. Myocardial wall thickness and left ventricular ejection fraction (LVEF) were quantified on DB and BB contrasts, respectively. The agreement in these metrics between MT-MACS and conventional breath-held, electrocardiography-triggered 2D sequences were evaluated. MT-MACS provides both water-only and fat-only images with excellent image quality (average score=3.725/3.780/3.835/3.890 for BB/DB/GB/fat-only images) and moderate to high interreader agreement (weighted Cohen's kappa value=0.727/0.668/1.000/1.000 for BB/DB/GB/fat-only images). There were good to excellent agreements in myocardial wall thickness measurements (intraclass correlation coefficients [ICC]=0.781/0.929/0.680/0.878 for left atria/left ventricle/right atria/right ventricle) and LVEF quantification (ICC=0.716) between MT-MACS and 2D references. All measurements were within the literature range of healthy subjects. The refined MT-MACS technique provides multi-contrast, phase-resolved, and water-fat imaging of the aortocardiac systems and allows evaluation of anatomy and function. Clinical validation is warranted.