Rank Regularization Research Articles

Classification of neuronal morphology based on feature reconstruction and self-cure residual networks

Aiming at the problem of high morphological similarity between the different types of neurons and the large intra-class difference, which is easy to lead to low accuracy of neuron classification, a neural morphology classification method based on feature reconstruction and self-cure residual network is proposed. Firstly, to address the problems of edge pixel weakening and feature erosion by padding strategies that tend to occur during the convolution process of conventional convolution, a feature reconstruction module is constructed at the back end of the backbone network to retain important central features and filter damaged edge features. Then, the attention to neuronal morphological features is enhanced by using a self-attentive weight module and a rank regularization loss method, where the self-attention weight module assigns a weight to each sample to capture the sample importance for weighted loss. In addition, the rank regularization module re-ranked these weights in descending order, dividing them into two groups of high and low weights and regularizing the two groups by enforcing margins between the two average weights. The method achieved superior classification results on the NeuroMorpho-rat dataset, with twelve-way classification accuracies of 96.7%, 86.94% and 85.84% on the Img_raw, Img_resample and Img_XYalign datasets, separately. Comparing with the other methods, the present method has a higher classification accuracy of neurons. Comparing with the original ResNet18 network, it can effectively improve the neuron classification accuracy.

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.

Non-local tensor sparse representation and tensor low rank regularization for dynamic MRI reconstruction

Non-local tensor sparse representation and tensor low rank regularization for dynamic MRI reconstruction

Improved Simultaneous Multi-slice imaging with Composition of k-space Interpolations (SMS-COOKIE) for myocardial T1 mapping.

The aim of this study is to develop and evaluate a regularized Simultaneous Multi-Slice (SMS) reconstruction method for improved Cardiac Magnetic Resonance Imaging (CMR). The proposed reconstruction method, SMS with COmpOsition of k-space IntErpolations (SMS-COOKIE) combines the advantages of Iterative Self-consistent Parallel Imaging Reconstruction (SPIRiT) and split slice-Generalized Autocalibrating Partially Parallel Acquisitions (GRAPPA), while allowing regularization for further noise reduction. The proposed SMS-COOKIE was implemented with and without regularization, and validated using a Saturation Pulse-Prepared Heart rate Independent inversion REcovery (SAPPHIRE) myocardial T1 mapping sequence. The performance of the proposed reconstruction method was compared to ReadOut (RO)-SENSE-GRAPPA and split slice-GRAPPA, on both retrospectively and prospectively three-fold SMS-accelerated data with an additional two-fold in-plane acceleration. All SMS reconstruction methods yielded similar T1 values compared to single band imaging. SMS-COOKIE showed lower spatial variability in myocardial T1 with significant improvement over RO-SENSE-GRAPPA and split slice-GRAPPA (P < 10-4). The proposed method with additional locally low rank (LLR) regularization reduced the spatial variability, again with significant improvement over RO-SENSE-GRAPPA and split slice-GRAPPA (P < 10-4). In conclusion, improved reconstruction quality was achieved with the proposed SMS-COOKIE, which also provided lower spatial variability with significant improvement over split slice-GRAPPA.

Smoothing fast proximal gradient algorithm for the relaxation of matrix rank regularization problem

This paper proposes a general inertial smoothing proximal gradient algorithm for solving the Capped-ℓ1 exact continuous relaxation regularization model proposed by Yu and Zhang (2022) [29]. The proposed algorithm incorporates different extrapolations into the gradient and proximal steps. It is proved that, under some general parameter constraints, the singular values of any accumulation point of the sequence generated by the proposed algorithm have the common support set, and the zero singular values can be achieved in a finite number of iterations. Furthermore, any accumulation point is a lifted stationary point of the relaxation model. Numerical experiments illustrate the efficiency of the proposed algorithm on synthetic and real data, respectively.

NL3DLogTNN: An Effective Hyperspectral Image Denoising Method Combined Non-Local Self-Similarity and Low-Fibered- Rank Regularization

NL3DLogTNN: An Effective Hyperspectral Image Denoising Method Combined Non-Local Self-Similarity and Low-Fibered- Rank Regularization

Simultaneous non-convex low rank regularization for fast magnetic resonance spectroscopy reconstruction

2D magnetic resonance spectroscopy (MRS) is extensively used to analyze the components, structures, and interactions of substances in chemistry and bioengineering. To reduce data acquisition time, the spatiotemporally encoded ultrafast (STEU) MRS employs a fast means to acquire data in the hybrid time and frequency (HTF) plane, but relies on non-uniform sampling (NUS) technique. After that, a proper reconstruction method is essential to recover a high quality 2D MRS from undersampled HTF data. In this work, each column and row of 2D MRS are converted into Hankel matrices, by which a simultaneous low rank regularization model is proposed to exploit the bivariate exponential structure of 2D MRS signal. Additionally, a non-convex surrogate function for rank is integrated in the proposed model to more precisely enforce the low rank property of Hankel matrices. To ensure computational accuracy and convergence, an efficient numerical algorithm is further deduced based on alternating direction method of multipliers (ADMM) iteration. The experimental results have shown that the proposed method significantly outperforms existing 2D MRS reconstruction methods, and presents a strong robustness to low sampling rates, various sampling patterns, and measurement noise with a favorable complexity.

Motion-corrected 4D-Flow MRI for neurovascular applications

Neurovascular 4D-Flow MRI has emerged as a powerful tool for comprehensive cerebrovascular hemodynamic characterization. Clinical studies in at risk populations such as aging adults indicate hemodynamic markers can be confounded by motion-induced bias. This study develops and characterizes a high fidelity 3D self-navigation approach for retrospective rigid motion correction of neurovascular 4D-Flow data. A 3D radial trajectory with pseudorandom ordering was combined with a multi-resolution low rank regularization approach to enable high spatiotemporal resolution self-navigators from extremely undersampled data. Phantom and volunteer experiments were performed at 3.0T to evaluate the ability to correct for different amounts of induced motions. In addition, the approach was applied to clinical-research exams from ongoing aging studies to characterize performance in the clinical setting. Simulations, phantom and volunteer experiments with motion correction produced images with increased vessel conspicuity, reduced image blurring, and decreased variability in quantitative measures. Clinical exams revealed significant changes in hemodynamic parameters including blood flow rates, flow pulsatility index, and lumen areas after motion correction in probed cerebral arteries (Flow: P<0.001 Lt ICA, P=0.002 Rt ICA, P=0.004 Lt MCA, P=0.004 Rt MCA; Area: P<0.001 Lt ICA, P<0.001 Rt ICA, P=0.004 Lt MCA, P=0.004 Rt MCA; flow pulsatility index: P=0.042 Rt ICA, P=0.002 Lt MCA). Motion induced bias can lead to significant overestimation of hemodynamic markers in cerebral arteries. The proposed method reduces measurement bias from rigid motion in neurovascular 4D-Flow MRI in challenging populations such as aging adults.

Tensor Rank Regularization with Bias Compensation for Millimeter Wave Channel Estimation

This paper presents a novel method of tensor rank regularization with bias compensation for channel estimation in a hybrid millimeter wave MIMO-OFDM system. Channel estimation is challenging due to the unknown number of multipath components that determines the channel rank. In general, finding the intrinsic rank of a tensor is a non-deterministic polynomial-time (NP) hard problem. However, by leveraging the sparse characteristics of millimeter wave channels, we propose a modified CANDECOMP/PARAFAC (CP) decomposition-based method that jointly estimates the tensor rank and channel component matrices. Our approach differs from most existing works that assume the number of channel paths is known and the proposed method is able to estimate channel parameters accurately without the prior knowledge of number of multipaths. The objective of this work is to estimate the tensor rank by a novel sparsity-promoting prior that is incorporated into a standard alternating least squares (ALS) function. We introduce a weighting parameter to control the impact of the previous estimate and the tensor rank estimation bias compensation in the regularized ALS. The channel information is then extracted from the estimated component matrices. Simulation results show that the proposed scheme outperforms the baseline l1 strategy in terms of accuracy and robustness. It also shows that this method significantly improves rank estimation success at the expense of slightly more iterations.

Regional Self-Attention Convolutional Neural Network for Facial Expression Recognition

Facial expression recognition (FER) has been a challenging task in the field of artificial intelligence. In this paper, we propose a novel model, named regional self-attention convolutional neural network (RSACNN), for FER. Different from the previous methods, RSACNN makes full use of the facial texture of expression salient region, so yields a robust feature representation for FER. The proposed model contains two novel parts: regional local multiple pattern (RLMP) based on the improved K-means algorithm and the regional self-attention module (RSAM). First, RLMP uses the improved K-means algorithm to dynamically cluster the pixels to ensure the robustness of texture features with expression salient variation. Besides, the texture description is enhanced by extending the binary pattern to the multiple patterns and integrating the information of gray difference between pixels in the region. Next, RSAM can adaptively form weights for each region through the self-attention mechanism, and use rank regularization loss (RRLoss) to constrain the weights of different regions. By jointly combining RLMP and RSAM, RSACNN can effectively enhance the feature representation of expression salient regions, so that the performance of expression recognition can be improved. Extensive experiments on public datasets, i.e. CK[Formula: see text], Oulu-CASIA, Fer2013 and SFEW, prove the superiority of our method over state-of-the-art approaches.

Simultaneous Non-Convex Low Rank Regularization for Fast Magnetic Resonance Spectroscopy Reconstruction

Simultaneous Non-Convex Low Rank Regularization for Fast Magnetic Resonance Spectroscopy Reconstruction

Motion compensation combining with local low rank regularization for low dose dynamic CT myocardial perfusion reconstruction

Dynamic CT myocardial perfusion imaging (DCT-MPI) is a reliable examination tool for the assessment of myocardium and vascular, while its special scan protocol may result in excessive radiation exposure to patients and inevitable inter-frame motion. Lowering the tube current is a simple way to reduce radiation exposure. However, low mAs will certainly cause severe image noise, thus may further impact the accuracy of functional hemodynamic parameters, which are used for the assessment of blood supply. In this work, we present a novel scheme applying motion compensation and local low rank regularization (MC-LLR) for obtaining high quality motion compensated DCT-MPI images. Specifically, motion compensation by using robust data decomposition registration (RDDR) was introduced. Robust principal component analysis coupled with optical flow-based registration algorithm were used in RDDR. Then, the local low rank constraint on the motion compensated time series images was applied for the DCT-MPI reconstruction. One healthy mini pig and two patient datasets were used to evaluate the proposed MC-LLR algorithm. Results show that the present method achieved satisfactory image quality with higher CNRs, smaller rRMSEs, and more accurate hemodynamic parameter maps.

Tensor Q-rank: new data dependent definition of tensor rank

Recently, the \({ Tensor}~{ Nuclear}~{ Norm}~{ (TNN)}\) regularization based on t-SVD has been widely used in various low tubal-rank tensor recovery tasks. However, these models usually require smooth change of data along the third dimension to ensure their low rank structures. In this paper, we propose a new definition of data dependent tensor rank named tensor Q-rank by a learnable orthogonal matrix \(\mathbf {Q}\), and further introduce a unified data dependent low rank tensor recovery model. According to the low rank hypothesis, we introduce two explainable selection methods of \(\mathbf {Q}\), under which the data tensor may have a more significant low tensor Q-rank structure than that of low tubal-rank structure. Specifically, maximizing the variance of singular value distribution leads to Variance Maximization Tensor Q-Nuclear norm (VMTQN), while minimizing the value of nuclear norm through manifold optimization leads to Manifold Optimization Tensor Q-Nuclear norm (MOTQN). Moreover, we apply these two models to the low rank tensor completion problem, and then give an effective algorithm and briefly analyze why our method works better than TNN based methods in the case of complex data with low sampling rate. Finally, experimental results on real-world datasets demonstrate the superiority of our proposed models in the tensor completion problem with respect to other tensor rank regularization models.

Method of Multispectral Image Denoising Based on Whole and Sub-Sparsity

Multi-Spectral Image(MSI) denoising is an important preprocessing procedure to improve the performance of high-level processing. Tensor-based approach is one of the most popular methods for MSI denoising, since MSIs can be seen as multi-dimension arrays containing both spatial and spectral information. There are two main information in MSI, Global Correlation along Spectrum(GCS) and Nonlocal Self Similarity across space(NSS). Most tensor based approaches exploited these two characteristics by low-rank regularizations, mainly based on CANDERCOMP/PARAFAC(CP) decomposition and Tucker decomposition. However, they did not show a clear physical meaning. In this paper, we exploit the fact that pixels in MSI often cover several different materials and so that tensor data is mixed. Based on this, we divide tensor into several sub-tensors and propose a novel low rank regularization called Whole and Sub-Sparsity(WSS): GCS is modeled in the sub-tensors and NSS is modeled in the original tensor, which shows a clear physical meaning. Besides, to solve our model, we develop the corresponding algorithm by employing alternating direction method of multipliers(ADMM) framework. Experiment results show that our method is competitive compared to all state of the art MSI denoising methods.

TV2++: a novel spatial-temporal total variation for super resolution with exponential-type norm

Recently, many super-resolution algorithms have been proposed to recover high-resolution images to improve visualization and help better analyze images. Among them, total variation regularization (TV) methods have been proven to have a good effect in retaining image edge information. However, these TV methods do not consider the temporal correlation between images. Our algorithm designs a new TV regularization (TV2++) to take advantage of the time dimension information of the images, further improving the utilization of useful information in the images. In addition, the union of global low rank regularization and TV regularization further enhances the image super-resolution recovery. And we extend the exponential-type penalty (ETP) function on singular values of a matrix to enhance low-rank matrix recovery. A novel image super-resolution algorithm based on the ETP norm and TV2++ regularization is proposed. And the alternating direction method of multipliers (ADMM) is applied to solve the optimization problems effectively. Numerous experimental results prove that the proposed algorithm is superior to other algorithms.

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.

A Low Rank Dynamic Mode Decomposition Model for Short-Term Traffic Flow Prediction

Traffic flow data has three main characteristics: large amount of noise and incompleteness, temporal and spatial correlation, and dynamic sequential property. Problems of noise, loss and incompleteness could decrease the prediction performance and make it difficult for transportation system management. Inspired by recent work on low rank representation (LRR) and dynamic mode decomposition (DMD), we propose a Low Rank Dynamic Mode Decomposition (LRDMD) model which solves the aforementioned problems simultaneously. LRDMD predicts traffic flow by using a state transition matrix which characterizes the relationship between temporally neighboring fragments of traffic flow with low rank regularization. We conduct experiments of traffic flow prediction of different time intervals using loop coil detector data of Qingdao, and the results show that LRDMD outperforms state-of-the-art methods.

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.

PTL-LTM model for complex action recognition using local-weighted NMF and deep dual-manifold regularized NMF with sparsity constraint

Complex action recognition possesses significant academic research value, potential commercial value and broad market application prospect. For improving its performance, a local-weighted nonnegative matrix factorization with rank regularization constraint (LWNMF_RC) is firstly presented, which removes complex background and then obtains motion salient regions. Secondly, a dual-manifold regularized nonnegative matrix factorization with sparsity constraint (DMNMF_SC) is proposed, which not only considers the short-term and middle-term temporal dependencies implied in data manifold, but also mines the geometric structure hidden in feature manifold. In addition, the introduction of sparsity constraint makes features possess better discriminativeness. Thirdly, a deep DMNMF_SC method is constructed, which acquires more hierarchical and discriminative features. Finally, a long-term temporal memory model with probability transfer learning (PTL-LTM) is proposed, which accurately memorizes the long-term temporal dependency among multiple simple action segments and, meanwhile, makes full use of the probability features of rich labeled simple actions and then applies the knowledge learned from simple actions for complex action recognition. Consequently, the performance is effectively improved.

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.