Low-rank Matrix Recovery Algorithm Research Articles

Diagnosis of Intelligent Reflecting Surface in Millimeter-Wave Communication Systems

Intelligent reflecting surface (IRS) is a promising technology for enhancing wireless communication systems. It adaptively configures massive passive reflecting elements to control wireless channel in a desirable way. Due to hardware characteristics and deploying environments, an IRS may be subject to reflecting element blockages and failures, and hence developing diagnostic techniques is of great significance to system monitoring and maintenance. In this paper, we develop diagnostic techniques for IRS systems to locate faulty reflecting elements and retrieve failure parameters. Three cases of channel state information (CSI) availability are considered. In the first case where full CSI is available, a compressed sensing based diagnostic technique is proposed, which significantly reduces the required number of measurements. In the second case where only partial CSI is available, we jointly exploit the sparsity of the millimeter-wave channel and the failure, and adopt compressed sparse and low-rank matrix recovery algorithm to decouple channel and failure. In the third case where no CSI is available, a novel atomic norm is introduced as the sparsity-inducing norm of the cascaded channel, and the diagnosis problem is formulated as a joint sparse recovery problem. Finally, the proposed diagnostic techniques are validated through numerical simulations.

Magnetic Resonance Image under the Low-Rank Matrix Denoising Algorithm in Evaluating the Efficacy of Neoadjuvant Chemo-Radiotherapy for Rectal Cancer

This study was to explore the application value of magnetic resonance imaging (MRI) images obtained by low-rank matrix recovery algorithm (LRMR algorithm) in evaluating the curative effect of rectal cancer patients receiving the neoadjuvant chemo-radiotherapy (nCRT). In this study, an image denoising model was designed based on the LRMR algorithm, the original low-rank data matrix was recovered from the error, and the low-rank matrix was restored by solving the optimal kernel norm, so as to effectively separate the image data information and the interference noise. In addition, the model was applied to 60 patients with rectal cancer who received nCRT to extract the texture parameters and lesion-related data from the MRI images. The results showed that the MRI images optimized by LRMR algorithm were clearer than the original images, contained less excess noise, and had improved imaging accuracy and image quality. The results of typical cases suggested that the front of the rectal wall membrane of a patient in the T-downstage group was not smooth before treatment, the internal angiography was blurred, and the wall membrane was thickened, but the wall membrane became thinner after treatment, the highest position was reduced from 1.46 cm to 0.38 cm, the average value of the apparent diffusion coefficient (ADC) increased from 0.732 × 10−3 mm2/s to 1.196 × 10−3 mm2/s, and the lesion tissue was thicker. It was found that the height, length, and ADC of the lesion after the nCRT showed statistically great difference in contrast to the values before the treatment P < 0.05 . Such results indicated that the nCRT showed obvious effects in the clinical treatment of rectal cancer. In short, the LRMR algorithm could remove the interference noise in the MRI image, and from the information about rectal cancer tumor lesions extracted from that, the height value and length value of tumor lesions in patients given neoadjuvant chemo-radiotherapy were reduced compared with those before treatment, and the apparent diffusion coefficient value was increased, indicating that neoadjuvant chemo-radiotherapy has a significant effect in the clinical treatment of rectal cancer.

Fast Construction of the Radio Map Based on the Improved Low-Rank Matrix Completion and Recovery Method for an Indoor Positioning System

With the development of information technology, indoor positioning technology has been rapidly evolving. Due to the advantages of high positioning accuracy, low cost, and wide coverage simultaneously, received signal strength- (RSS-) based WLAN indoor positioning technology has become one of the mainstream technologies. A radio map is the basis for the realization of the WLAN positioning system. However, by reasons of the huge workload of RSS collection, the instability of wireless signal strength, and the disappearance of signals caused by the occlusion of people and objects, the construction of a radio map is time-consuming and inefficient. In order to rapidly deploy the WLAN indoor positioning system, an improved low-rank matrix completion method is proposed to construct the radio map. Firstly, we evenly arrange a small number of reference points (RP) in the positioning area and collect RSS data on the RP to construct the radio map. Then, the low-rank matrix completion method is used to fill a small amount of data in the radio map into a complete database. The Frobenius parameter (F-parameter) is introduced into the traditional low-rank matrix completion model to control the instability of the model solution when filling the data. To solve the noise problem caused by environment and equipment, a low-rank matrix recovery algorithm is used to eliminate noise. The experimental results show that the improved algorithm achieves the expected goal.

A unified framework for oscillatory integral transforms: When to use NUFFT or butterfly factorization?

This paper concerns the fast evaluation of the matvec g=Kf for K∈CN×N, which is the discretization of an oscillatory integral transform g(x)=∫K(x,ξ)f(ξ)dξ with a kernel function K(x,ξ)=α(x,ξ)e2πiΦ(x,ξ), where α(x,ξ) is a smooth amplitude function, and Φ(x,ξ) is a piecewise smooth phase function with O(1) discontinuous points in x and ξ. A unified framework is proposed to compute Kf with O(Nlog⁡N) time and memory complexity via the non-uniform fast Fourier transform (NUFFT) or the butterfly factorization (BF), together with an O(N) fast algorithm to determine whether NUFFT or BF is more suitable. This framework works for two cases: 1) explicit formulas for the amplitude and phase functions are known; 2) only indirect access of the amplitude and phase functions are available. Especially in the case of indirect access, our main contributions are: 1) an O(Nlog⁡N) algorithm for recovering the amplitude and phase functions is proposed based on a new low-rank matrix recovery algorithm; 2) a new stable and nearly optimal BF with amplitude and phase functions in a form of a low-rank factorization (IBF-MAT1) is proposed to evaluate the matvec Kf. Numerical results are provided to demonstrate the effectiveness of the proposed framework. 1IBF-MAT means interpolative butterfly factorization based on low-rank matrix information instead of explicit formulas used in the IBF in [22].

Reweighted Low-Rank Matrix Analysis With Structural Smoothness for Image Denoising.

In this paper, we develop a new low-rank matrix recovery algorithm for image denoising. We incorporate the total variation (TV) norm and the pixel range constraint into the existing reweighted low-rank matrix analysis to achieve structural smoothness and to significantly improve quality in the recovered image. Our proposed mathematical formulation of the low-rank matrix recovery problem combines the nuclear norm, TV norm, and norm, thereby allowing us to exploit the low-rank property of natural images, enhance the structural smoothness, and detect and remove large sparse noise. Using the iterative alternating direction and fast gradient projection methods, we develop an algorithm to solve the proposed challenging non-convex optimization problem. We conduct extensive performance evaluations on single-image denoising, hyper-spectral image denoising, and video background modeling from corrupted images. Our experimental results demonstrate that the proposed method outperforms the state-of-the-art low-rank matrix recovery methods, particularly for large random noise. For example, when the density of random sparse noise is 30%, for single-image denoising, our proposed method is able to improve the quality of the restored image by up to 4.21 dB over existing methods.

Learning Low-Rank Representations with Classwise Block-Diagonal Structure for Robust Face Recognition

Face recognition has been widely studied due to its importance in various applications. However, the case that both training images and testing images are corrupted is not well addressed. Motivated by the success of low-rank matrix recovery, we propose a novel semi-supervised low-rank matrix recovery algorithm for robust face recognition. The proposed method can learn robust discriminative representations for both training images and testing images simultaneously by exploiting the classwise block-diagonal structure. Specifically, low-rank matrix approximation can handle the possible contamination of data. Moreover, the classwise block-diagonal structure is exploited to promote discrimination of representations for robust recognition. The above issues are formulated into a unified objective function and we design an efficient optimization procedure based on augmented Lagrange multiplier method to solve it. Extensive experiments on three public databases are performed to validate the effectiveness of our approach. The strong identification capability of representations with block-diagonal structure is verified.

Fisher discrimination based low rank matrix recovery for face recognition

In this paper, we consider the issue of computing low rank (LR) recovery of matrices with sparse errors. Based on the success of low rank matrix recovery in statistical learning, computer vision and signal processing, a novel low rank matrix recovery algorithm with Fisher discrimination regularization (FDLR) is proposed. Standard low rank matrix recovery algorithm decomposes the original matrix into a set of representative basis with a corresponding sparse error for modeling the raw data. Motivated by the Fisher criterion, the proposed FDLR executes low rank matrix recovery in a supervised manner, i.e., taking the with-class scatter and between-class scatter into account when the whole label information are available. The paper shows that the formulated model can be solved by the augmented Lagrange multipliers and provides additional discriminating power over the standard low rank recovery models. The representative bases learned by the proposed method are encouraged to be closer within the same class, and as far as possible between different classes. Meanwhile, the sparse error recovered by FDLR is not discarded as usual, but treated as a feedback in the following classification tasks. Numerical simulations demonstrate that the proposed algorithm achieves the state of the art results.