Efficient enhancement of low-rank tensor completion via thin QR decomposition.

Low-rank tensor completion (LRTC), which aims to complete missing entries from tensors with partially observed terms by utilizing the low-rank structure of tensors, has been widely used in various real-world issues. The core tensor nuclear norm minimization (CTNM) method based on Tucker decomposition is one of common LRTC methods. However, the CTNM methods based on Tucker decomposition often have a large computing cost due to the fact that the general factor matrix solving technique involves multiple singular value decompositions (SVDs) in each loop. To address this problem, this article enhances the method and proposes an effective CTNM method based on thin QR decomposition (CTNM-QR) with lower computing complexity. The proposed method extends the CTNM by introducing tensor versions of the auxiliary variables instead of matrices, while using the thin QR decomposition to solve the factor matrix rather than the SVD, which can save the computational complexity and improve the tensor completion accuracy. In addition, the CTNM-QR method's convergence and complexity are analyzed further. Numerous experiments in synthetic data, real color images, and brain MRI data at different missing rates demonstrate that the proposed method not only outperforms in terms of completion accuracy and visualization, but also conducts more efficiently than most state-of-the-art LRTC methods.

Fast DOA Estimation Algorithms via Positive Incremental Modified Cholesky Decomposition for Augmented Coprime Array Sensors.

This paper proposes a fast direction of arrival (DOA) estimation method based on positive incremental modified Cholesky decomposition atomic norm minimization (PI-CANM) for augmented coprime array sensors. The approach incorporates coprime sampling on the augmented array to generate a non-uniform, discontinuous virtual array. It then utilizes interpolation to convert this into a uniform, continuous virtual array. Based on this, the problem of DOA estimation is equivalently formulated as a gridless optimization problem, which is solved via atomic norm minimization to reconstruct a Hermitian Toeplitz covariance matrix. Furthermore, by positive incremental modified Cholesky decomposition, the covariance matrix is transformed from positive semi-definite to positive definite, which simplifies the constraint of optimization problem and reduces the complexity of the solution. Finally, the Multiple Signal Classification method is utilized to carry out statistical signal processing on the reconstructed covariance matrix, yielding initial DOA angle estimates. Experimental outcomes highlight that the PI-CANM algorithm surpasses other algorithms in estimation accuracy, demonstrating stability in difficult circumstances such as low signal-to-noise ratios and limited snapshots. Additionally, it boasts an impressive computational speed. This method enhances both the accuracy and computational efficiency of DOA estimation, showing potential for broad applicability.

GPR Clutter Removal Based on Weighted Nuclear Norm Minimization for Nonparallel Cases.

Ground-penetrating radar (GPR) is an effective geophysical electromagnetic method for underground target detection. However, the target response is usually overwhelmed by strong clutter, thus damaging the detection performance. To account for the nonparallel case of the antennas and the ground surface, a novel GPR clutter-removal method based on weighted nuclear norm minimization (WNNM) is proposed, which decomposes the B-scan image into a low-rank clutter matrix and a sparse target matrix by using a non-convex weighted nuclear norm and assigning different weights to different singular values. The WNNM method's performance is evaluated using both numerical simulations and experiments with real GPR systems. Comparative analysis with the commonly used state-of-the-art clutter removal methods is also conducted in terms of the peak signal-to-noise ratio (PSNR) and the improvement factor (IF). The visualization and quantitative results demonstrate that the proposed method outperforms the others in the nonparallel case. Moreover, it is about five times faster than the RPCA, which is beneficial for practical applications.

Framework for Segmented threshold ℓ0 gradient approximation based network for sparse signal recovery.

Signal reconstruction from compressed sensed data need iterative methods since the sparse measurement matrix is analytically non invertible. The iterative thresholding and ℓ0 function minimization are of special interest as these two operations provide sparse solution. However these methods need an inverse operation corresponding to the measurement matrix for estimating the reconstruction error. The pseudo-inverse of the measurement matrix is used in general for this purpose. Here a sparse signal recovery framework using an approximate inverse matrix Q and iterative segment thresholding of ℓ0 and ℓ1 norm with residue addition is presented. Two recovery algorithms are developed using this framework. The ℓ0 based method is later developed to a basis function dictionary based network for sparse signal recovery. The proposed framework enables the users experiment with different inverse matrix to achieve better efficiency in sparse signal recovery and implement the algorithm in computationally efficient way.

Joint denoising of diffusion-weighted images via structured low-rank patch matrix approximation.

PURPOSE: To develop a joint denoising method that effectively exploits natural information redundancy in MR DWIs via low-rank patch matrix approximation. METHODS: A denoising method is introduced to jointly reduce noise in DWI dataset by exploiting nonlocal self-similarity as well as local anatomical/structural similarity within multiple 2D DWIs acquired with the same anatomical geometry but different diffusion directions. Specifically, for each small 3D reference patch sliding within 2D DWI, nonlocal but similar patches are searched by matching image contents within entire DWI dataset and then structured into a patch matrix. The resulting patch matrices are denoised by enforcing low-rankness via weighted nuclear norm minimization and finally are back-distributed to DWI space. The proposed procedure was evaluated with simulated and in vivo brain diffusion tensor imaging (DTI) datasets and then compared to existing Marchenko-Pastur principal component analysis denoising method. RESULTS: The proposed method achieved significant noise reduction while preserving structural details in all DWIs for both simulated and in vivo datasets. Quantitative evaluation of error maps demonstrated it consistently outperformed Marchenko-Pastur principal component analysis method. Further, the denoised DWIs led to substantially improved DTI parametric maps, exhibiting significantly less noise and revealing more microstructural details. CONCLUSION: The proposed method denoises DWI dataset by utilizing both nonlocal self-similarity and local structural similarity within DWI dataset. This weighted nuclear norm minimization-based low-rank patch matrix denoising approach is effective and highly applicable to various diffusion MRI applications, including DTI as a postprocessing procedure.

Extrapolating missing antibody-virus measurements across serological studies.

The development of new vaccines, as well as our understanding of key processes that shape viral evolution and host antibody repertoires, relies on measuring multiple antibody responses against large panels of viruses. Given the enormous diversity of circulating virus strains and antibody responses, comprehensively testing all antibody-virus interactions is infeasible. Even within individual studies with limited panels, exhaustive testing is not always performed, and there is no common framework for combining information across studies with partially overlapping panels, especially when the assay type or host species differ. Prior studies have demonstrated that antibody-virus interactions can be characterized in a vastly simpler and lower dimensional space, suggesting that relatively few measurements could predict unmeasured antibody-virus interactions. Here, we apply matrix completion to several large-scale influenza and HIV-1 studies. We explore how prediction accuracy evolves as the number of measurements changes and approximates the number of additional measurements necessary in several highly incomplete datasets (suggesting ∼250,000 measurements could be saved). In addition, we show how the method can combine disparate datasets, even when the number of available measurements is below the theoretical limit that guarantees successful prediction. This approach can be readily generalized to other viruses or more broadly to other low-dimensional biological datasets.

Multiple access interference suppression for CDMA systems via ℓ ∞ -minimization.

A key problem in code-division multiple access (CDMA) system is to mitigate the multiple access interference (MAI) from other users while detecting the desired user. The performance of the conventional minimum output energy (MOE) multiuser detector for CDMA system significantly degrades in the presence of signature waveform distortions induced by multipath propagation or timing asynchronism. In this paper, a robust linear programming (ROLP) algorithm for blind multiuser detection is proposed. Different from the existing MOE-based multiuser detection techniques, the proposed ROLP minimizes the ℓ ∞ -norm of the output to exploit the non-Gaussianity of the communication signals. To achieve robustness against signature waveform mismatch, the proposed method constrains the magnitude response of any signature vector within a specified uncertainty set to exceed unity. The uncertainty set is modeled as a rhombus, which differs from the spherical uncertainty region widely taken in the existing robust multiuser detectors. The resulting optimization problem is reformulated into a linear programming program and hence can be solved efficiently. The proposed ROLP is computationally simpler than its robust counterparts that requires solving a second-order cone programming. Simulation results demonstrate the superiority of the ROLP over several robust detectors, which indicate that its performance approaches the optimal performance bound.

Smoothing inertial neurodynamic approach for sparse signal reconstruction via Lp-norm minimization.

In this paper, we propose a smoothing inertial neurodynamic approach (SINA) which is used to deal with Lp-norm minimization problem to reconstruct sparse signals. Note that the considered optimization problem is nonsmooth, nonconvex and non-Lipschitz. First, the problem is transformed into a smooth optimization problem based on smoothing approximation method, and the Lipschitz property of gradient of the smooth objective function is discussed. Then, SINA based on Karush-Kuhn-Tucker (KKT) condition, smoothing approximation and inertial dynamical approach, is designed to handle smooth optimization problem. The existence, uniqueness, global convergence and optimality of the solution of the SINA are discussed by the Cauchy-Lipschitz-Picard theorem, energy function and KKT condition. In addition, for p=1, the SINA has a mean sublinear convergence rate O1∕t under some mild conditions. Finally, some numerical examples on sparse signal reconstruction and image restoration are given to illustrate the theoretical results and the efficiency of SINA.

Constrained L1-Norm Minimization Method for Range-Based Source Localization under Mixed Sparse LOS/NLOS Environments.

Under mixed sparse line-of-sight/non-line-of-sight (LOS/NLOS) conditions, how to quickly achieve high positioning accuracy is still a challenging task and a critical problem in the last dozen years. To settle this problem, we propose a constrained L1 norm minimization method which can reduce the effects of NLOS bias for improve positioning accuracy and speed up calculation via an iterative method. We can transform the TOA-based positioning problem into a sparse optimization one under mixed sparse LOS/NLOS conditions if we consider NLOS bias as outliers. Thus, a relatively good method to deal with sparse localization problem is L1 norm. Compared with some existing methods, the proposed method not only has the advantages of simple and intuitive principle, but also can neglect NLOS status and corresponding NLOS errors. Experimental results show that our algorithm performs well in terms of computational time and positioning accuracy.

De Novo Prediction of Drug-Target Interactions Using Laplacian Regularized Schatten p-Norm Minimization.

In pharmaceutical sciences, a crucial step of the drug discovery is the identification of drug-target interactions (DTIs). However, only a small portion of the DTIs have been experimentally validated. Moreover, it is an extremely laborious, expensive, and time-consuming procedure to capture new interactions between drugs and targets through traditional biochemical experiments. Therefore, designing computational methods for predicting potential interactions to guide the experimental verification is of practical significance, especially for de novo situation. In this article, we propose a new algorithm, namely Laplacian regularized Schatten p-norm minimization (LRSpNM), to predict potential target proteins for novel drugs and potential drugs for new targets where there are no known interactions. Specifically, we first take advantage of the drug and target similarity information to dynamically prefill the partial unknown interactions. Then based on the assumption that the interaction matrix is low-rank, we use Schatten p-norm minimization model combined with Laplacian regularization terms to improve prediction performance in the new drug/target cases. Finally, we numerically solve the LRSpNM model by an efficient alternating direction method of multipliers algorithm. We evaluate LRSpNM on five data sets and an extensive set of numerical experiments show that LRSpNM achieves better and more robust performance than five state-of-the-art DTIs prediction algorithms. In addition, we conduct two case studies for new drug and new target prediction, which illustrates that LRSpNM can successfully predict most of the experimental validated DTIs.

Underdetermined DOA Estimation for Wideband Signals via Focused Atomic Norm Minimization.

In underwater acoustic signal processing, direction of arrival (DOA) estimation can provide important information for target tracking and localization. To address underdetermined wideband signal processing in underwater passive detection system, this paper proposes a novel underdetermined wideband DOA estimation method equipped with the nested array (NA) using focused atomic norm minimization (ANM), where the signal source number detection is accomplished by information theory criteria. In the proposed DOA estimation method, especially, after vectoring the covariance matrix of each frequency bin, each corresponding obtained vector is focused into the predefined frequency bin by focused matrix. Then, the collected averaged vector is considered as virtual array model, whose steering vector exhibits the Vandermonde structure in terms of the obtained virtual array geometries. Further, the new covariance matrix is recovered based on ANM by semi-definite programming (SDP), which utilizes the information of the Toeplitz structure. Finally, the Root-MUSIC algorithm is applied to estimate the DOAs. Simulation results show that the proposed method outperforms other underdetermined DOA estimation methods based on information theory in term of higher estimation accuracy.

Multimodal Medical Image Fusion using Rolling Guidance Filter with CNN and Nuclear Norm Minimization.

BACKGROUND: Medical image fusion is very important for the diagnosis and treatment of diseases. In recent years, there have been a number of different multi-modal medical image fusion algorithms that can provide delicate contexts for disease diagnosis more clearly and more conveniently. Recently, nuclear norm minimization and deep learning have been used effectively in image processing. METHODS: A multi-modality medical image fusion method using a rolling guidance filter (RGF) with a convolutional neural network (CNN) based feature mapping and nuclear norm minimization (NNM) is proposed. At first, we decompose medical images to base layer components and detail layer components by using RGF. In the next step, we get the basic fused image through the pretrained CNN model. The CNN model with pre-training is used to obtain the significant characteristics of the base layer components. And we can compute the activity level measurement from the regional energy of CNN-based fusion maps. Then, a detail fused image is gained by NNM. That is, we use NNM to fuse the detail layer components. At last, the basic and detail fused images are integrated into the fused result. RESULTS: From the comparison with the most advanced fusion algorithms, the results of experiments indicate that this fusion algorithm has the best effect in visual evaluation and objective standard. CONCLUSION: The fusion algorithm using RGF and CNN-based feature mapping, combined with NNM, can improve fusion effects and suppress artifacts and blocking effects in the fused results.

Locally linear transform based three-dimensional gradient L 0 -norm minimization for spectral CT reconstruction.

PURPOSE: Spectral computed tomography (CT) is proposed by extending the conventional CT along the energy dimension. One newly implementation is to employ an energy-discriminating photon counting detector (PCD), which can distinguish photon energy and divide a whole x-ray spectrum into several energy bins with appropriate post-processing steps. The state-of-the-art PCD-based spectral CT has superior energy resolution and material distinguishability, and it further has a great potential in both medical and industrial applications. To improve the reconstruction quality and decomposition accuracy, in this work, we propose an optimization-based spectral CT reconstruction method with an innovational sparsity constraint. METHODS: We first employ a locally linear transform to the reconstructed channel images, and the structural similarity along the spectral dimension is effectively converted to a one-dimensional (1D) gradient sparsity. Then, combining the prior knowledge of piecewise constant in the spatial domain (e.g., a two-dimensional (2D) gradient sparsity feature), we unify both spectral and spatial dimensions and establish a joint three-dimensional (3D) gradient sparsity. In addition, we use the L 0 -norm to measure the proposed sparsity and incorporate it as a smoothness constraint to concretize a general optimization framework. Furthermore, we develop the corresponding iterative algorithm to solve the optimization problem. RESULTS: Both visual results and quantitative indexes of numerical simulations and phantom experiments demonstrate the proposed method outperform the conventional filtered backprojection (FBP), total variation (TV), 2D L0 -norm (L0 ), and TV with low rank (TVLR)-based methods. From the image and ROI comparisons, we find the proposed method performs well in noise suppression, detail maintenance, and decomposition accuracy. However, the FBP suffers severe noise, the TV and L0 are difficult to work consistently among different energy bins, and the TVLR fails to avoid gray value shift. The image quality assessments, such as peak signal-to-noise ratio (PSNR), normal mean absolute deviation (NMAD). and structural similarity (SSIM), also consistently indicate the proposed method can effectively removing noise and keeping fine structures in both channel-wise reconstructions and material decompositions. CONCLUSIONS: By employing a locally linear transform, the structural similarity among spectral channel images is converted to a 1D gradient sparsity and the gray value shift is effectively avoided when the difference measurement is minimized. The 3D L0 -norm jointly and uniformly measures the gradient sparsity in both spectral and spatial dimensions. The cooperation of locally linear transform and 3D L0 -norm well reinforces the global sparse features and keeps the correlation along spectral dimension without bringing gray-value distortions. The corresponding constraint optimization model is fast and stably solved by using an alternative direction technique. Both numerical simulations and phantom experiments confirm the superior performance of the proposed method in noise suppression, structure maintenance, and accurate decomposition.

Low Complexity Beamspace Super Resolution for DOA Estimation of Linear Array.

Beamspace processing has become much attractive in recent radar and wireless communication applications, since the advantages of complexity reduction and of performance improvements in array signal processing. In this paper, we concentrate on the beamspace DOA estimation of linear array via atomic norm minimization (ANM). The existed generalized linear spectrum estimation based ANM approaches suffer from the high computational complexity for large scale array, since their complexity depends upon the number of sensors. To deal with this problem, we develop a low dimensional semidefinite programming (SDP) implementation of beamspace atomic norm minimization (BS-ANM) approach for DFT beamspace based on the super resolution theory on the semi-algebraic set. Then, a computational efficient iteration algorithm is proposed based on alternating direction method of multipliers (ADMM) approach. We develop the covariance based DOA estimation methods via BS-ANM and apply the BS-ANM based DOA estimation method to the channel estimation problem for massive MIMO systems. Simulation results demonstrate that the proposed methods exhibit the superior performance compared to the state-of-the-art counterparts.

A smoothing neural network for minimization l1-lp in sparse signal reconstruction with measurement noises.

This paper investigates a smoothing neural network (SNN) to solve a robust sparse signal reconstruction in compressed sensing (CS), where the objective function is nonsmooth l1-norm and the feasible set satisfies an inequality of lp-norm 2≥p≥1 which is used for measuring residual errors. With a smoothing approximate technique, the non-smooth and non-Lipschitz continuous issues of the l1-norm and the gradient of lp-norm can be solved efficiently. We propose a SNN which is modeled by a differential equation and give its circuit implementation. In this case, we prove the proposed SNN converges to the optimal of considered problem. Simulation results are discussed to demonstrate the efficiency of the proposed algorithm.

[Timing calibration comparison research of integrated TOF-PET/MR].

Integrated TOF-PET/MR is a multimodal imaging system which can acquire high-quality magnetic resonance (MR) and positron emission tomography (PET) images at the same time, and it has time of flight (TOF) function. The TOF-PET system usually features better image quality compared to traditional PET because it is capable of localizing the lesion on the line of response where annihilation takes place. TOF technology measures the time difference between the detectors on which the two 180-degrees-seperated photons generated from positron annihilation are received. Since every individual crystal might be prone to its timing bias, timing calibration is needed for a TOF-PET system to work properly. Three approaches of timing calibration are introduced in this article. The first one named as fan-beam method is an iterative method that measures the bias of the Gaussian distribution of timing offset created from a fan-beam area constructed using geometric techniques. The second one is to find solutions of the overdetermination equations set using L1 norm minimization and is called L1-norm method. The last one called L2-norm method is to build histogram of the TOF and find the peak, and uses L2 norm minimization to get the result. This article focuses on the comparison of the amount of the data and the calculation time needed by each of the three methods. To avoid location error of the cylinder radioactive source during data collection, we developed a location calibration algorithm which could calculate accurate position of the source and reduce image artifacts. The experiment results indicate that the three approaches introduced in this article could enhance the qualities of PET images and standardized uptake values of cancer regions, so the timing calibration of integrated TOF-PET/MR system was realized. The fan-beam method has the best image quality, especially in small lesions. In integrated TOF-PET/MR timing calibration, we recommend using fan-beam method.

Practical stabilization of time-delay fractional-order systems by parametric controllers.

This paper stabilization of time-delayed fractional-order systems by unlimited controllers is considered. To achieve the best controller so that the system be stable, the parameters of the feedback matrices are determinate with the minimum norm. Various constraints applied by the designer to obtain the desired performance criteria. We use the partial eigenvalue assignment (PEVA) method to decrease the constraints and ranks of matrices. The presented method is implemented in two numerical examples.

Underdetermined DOA Estimation of Wideband LFM Signals Based on Gridless Sparse Reconstruction in the FRF Domain.

An underdetermined direction of arrival (DOA) estimation method of wideband linear frequency modulated (LFM) signals is proposed without grid mismatch. According to the concentration property of LFM signal in the fractional Fourier (FRF) domain, the received sparse model of wideband signals with time-variant steering vector is firstly derived based on a coprime array. Afterwards, by interpolating virtual sensors, a virtual extended uniform linear array (ULA) is constructed with more degrees of freedom, and its covariance matrix in the FRF domain is recovered by employing sparse matrix reconstruction. Meanwhile, in order to avoid the grid mismatch problem, the modified atomic norm minimization is used to retrieve the covariance matrix with the consecutive basis. Different from the existing methods that approximately assume the frequency and the steering vector of the wideband signals are time-invariant in every narrowband frequency bin, the proposed method not only can directly solve more DOAs of LFM signals than the number of physical sensors with time-variant frequency and steering vector, but also obtain higher resolution and more accurate DOA estimation performance by the gridless sparse reconstruction. Simulation results demonstrate the effectiveness of the proposed method.

Retrospective correction of intensity inhomogeneity with sparsity constraints in transform-domain: Application to brain MRI.

An effective retrospective correction method is introduced in this paper for intensity inhomogeneity which is an inherent artifact in MR images. Intensity inhomogeneity problem is formulated as the decomposition of acquired image into true image and bias field which are expected to have sparse approximation in suitable transform domains based on their known properties. Piecewise constant nature of the true image lends itself to have a sparse approximation in framelet domain. While spatially smooth property of the bias field supports a sparse representation in Fourier domain. The algorithm attains optimal results by seeking the sparsest solutions for the unknown variables in the search space through L1 norm minimization. The objective function associated with defined problem is convex and is efficiently solved by the linearized alternating direction method. Thus, the method estimates the optimal true image and bias field simultaneously in an L1 norm minimization framework by promoting sparsity of the solutions in suitable transform domains. Furthermore, the methodology doesn't require any preprocessing, any predefined specifications or parametric models that are critically controlled by user-defined parameters. The qualitative and quantitative validation of the proposed methodology in simulated and real human brain MR images demonstrates the efficacy and superiority in performance compared to some of the distinguished algorithms for intensity inhomogeneity correction.

Timing calibration comparison research of integrated TOF-PET/MR / 生物医学工程学杂志

Integrated TOF-PET/MR is a multimodal imaging system which can acquire high-quality magnetic resonance (MR) and positron emission tomography (PET) images at the same time, and it has time of flight (TOF) function. The TOF-PET system usually features better image quality compared to traditional PET because it is capable of localizing the lesion on the line of response where annihilation takes place. TOF technology measures the time difference between the detectors on which the two 180-degrees-seperated photons generated from positron annihilation are received. Since every individual crystal might be prone to its timing bias, timing calibration is needed for a TOF-PET system to work properly. Three approaches of timing calibration are introduced in this article. The first one named as fan-beam method is an iterative method that measures the bias of the Gaussian distribution of timing offset created from a fan-beam area constructed using geometric techniques. The second one is to find solutions of the overdetermination equations set using L1 norm minimization and is called L1-norm method. The last one called L2-norm method is to build histogram of the TOF and find the peak, and uses L2 norm minimization to get the result. This article focuses on the comparison of the amount of the data and the calculation time needed by each of the three methods. To avoid location error of the cylinder radioactive source during data collection, we developed a location calibration algorithm which could calculate accurate position of the source and reduce image artifacts. The experiment results indicate that the three approaches introduced in this article could enhance the qualities of PET images and standardized uptake values of cancer regions, so the timing calibration of integrated TOF-PET/MR system was realized. The fan-beam method has the best image quality, especially in small lesions. In integrated TOF-PET/MR timing calibration, we recommend using fan-beam method.