Low-Rank Matrix Recovery from Noise via an MDL Framework-Based Atomic Norm

Abstract

The recovery of the underlying low-rank structure of clean data corrupted with sparse noise/outliers is attracting increasing interest. However, in many low-level vision problems, the exact target rank of the underlying structure and the particular locations and values of the sparse outliers are not known. Thus, the conventional methods cannot separate the low-rank and sparse components completely, especially in the case of gross outliers or deficient observations. Therefore, in this study, we employ the minimum description length (MDL) principle and atomic norm for low-rank matrix recovery to overcome these limitations. First, we employ the atomic norm to find all the candidate atoms of low-rank and sparse terms, and then we minimize the description length of the model in order to select the appropriate atoms of low-rank and the sparse matrices, respectively. Our experimental analyses show that the proposed approach can obtain a higher success rate than the state-of-the-art methods, even when the number of observations is limited or the corruption ratio is high. Experimental results utilizing synthetic data and real sensing applications (high dynamic range imaging, background modeling, removing noise and shadows) demonstrate the effectiveness, robustness and efficiency of the proposed method.

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

“…e axial ADC showed that the average ADC was 1.278 × 10 −3 mm 2 /s. definite curative effect in the clinical treatment of rectal cancer [16]. e experimental results were in line with expectations because a number of previous studies showed that the denoising model constructed by low-rank matrix algorithm has a positive role in noisy MRI images and can decompose and extract noise so as to achieve the purpose of optimizing images.…”

Artificial Intelligence Algorithm-Based MRI for Differentiation Diagnosis of Prostate Cancer

“…The scanning range was the whole prostate and seminal vesicle. Before scanning, 0.2 mmol/kg gadolinium meglumine and 20 mL normal saline were injected for delayed enhanced scanning [ 20 ]…”

“…Parameters of plain scan sequence: T1WI sequence, axial position, and time of repetition ðtrÞ = 500 ms, time of echo ðteÞ = 8 ms, T2WI sequence, axial position, and TR = 3330 ms, TE = 80 ms, slice thickness = 5 mm, visual field = 21 cm × 21 cm, and matrix = 520 × 520, with scanning range from iliac artery bifurcation level to pelvic floor (2) DWI sequence, axial position, and TR = 2500 ms, TE = 60 ms, layer thickness = 2:5 mm, field of vision = 21 cm × 21 cm, matrix = 130 × 130, and B value was set as 0/800 s/mm 2 , with the scanning range of the whole prostate and seminal vesicle (3) DCE sequence, axial position, and TR = 9:8 ms, TE = 5:2 ms, layer thickness = 4:5 mm, field of vision = 21 cm × 21 cm, and matrix = 252 × 252. The scanning range was the whole prostate and seminal vesicle.Before scanning, 0.2 mmol/kg gadolinium meglumine and 20 mL normal saline were injected for delayed enhanced scanning[20] …”

Signal Processing and Machine Learning for Smart Sensing Applications

“…Qin et al [ 2 ] introduced the minimum description length (MDL) principle and atomic norm into the field of low-rank matrix recovery and proposed a novel non-parametric low-rank matrix approximation method called MDLAN. The existing algorithms had difficulty tackling the proposed optimization problem; thus, the authors considered an approximation of the original problem.…”