Two-Step Proximal Gradient Algorithm for Low-Rank Matrix Completion

Wang, Qiuyu; Cao, Wenjiao; Zhang, Jin

doi:10.19139/soic.v4i2.201

Cited by 2 publications

(1 citation statement)

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“…In [17], authors proposed a two-step proximal gradient algorithm to solve nuclear norm regularized least squares for the purpose of recovering low-rank data matrix from sampling of its entries. Each iteration generated by the proposed algorithm is a combination of the latest three points, namely, the previous point, the current iterate, and its proximal gradient point.…”

Section: Literature Reviewmentioning

confidence: 99%

Collaborating filtering using unsupervised learning for image reconstruction from missing data

Banouar

Mohaoui

Raghay

2018

EURASIP J. Adv. Signal Process.

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In the image acquisition process, important information in an image can be lost due to noise, occlusion, or even faulty image sensors. Therefore, we often have images with missing and/or corrupted pixels. In this work, we address the problem of image completion using a matrix completion approach that minimizes the nuclear norm to recover missing pixels in the image. The image matrix has a low rank. The proposed approach uses the nuclear norm function as a surrogate of the rank function in the aim to resolve the problem of rank minimization that is known as an NP-hard problem. It is an adaptation of the collaborating filtering approach used for users' profile construction. The main advantage of this approach is that it uses a learning process to classify pixels into clusters and exploits them to run a predictive method in the aim to recover the missing or unknown data. For performance evaluation, the proposed approach and the existing matrix completion methods are compared for image reconstruction according to the PSNR measure. These methods are applied on a dataset composed of standard images used for image processing. All the recovered images obtained during experimentation are also dressed to compare them visually. Simulation results verify that the proposed approach achieves better performances than the existing matrix completion methods used for image reconstruction from missing data.

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Section: Literature Reviewmentioning

confidence: 99%