Rank adaptive atomic decomposition for low-rank matrix completion and its application on image recovery

Wang, Hengyou; Zhao, Ruizhen; Cen, Yigang

doi:10.1016/j.neucom.2014.05.021

Cited by 20 publications

(9 citation statements)

References 15 publications

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“…-Kodak PhotoCD Dataset (Kodak): 3 The whole dataset consists of 24 clean color images of size 512 × 768 × 3.…”

Section: Ssim = (2µmentioning

confidence: 99%

“…In the past few decades, low-rank matrix completion problem has been widely studied and proven very useful in the application of image recovery [1][2][3][4][5]. Commonly, the method is to stack all the image pixels as column vectors of a matrix, and recovery theory and algorithm are adopted to the resulting matrix which is low-rank or approximately low-rank.…”

Section: Introductionmentioning

confidence: 99%

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Color image recovery using low-rank quaternion matrix completion algorithm

Miao¹,

Kou²

2019

Preprint

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As a new color image representation tool, quaternion has achieved excellent results in color image processing problems. In this paper, we propose a novel low-rank quaternion matrix completion algorithm to recover missing data of color image. Motivated by two kinds of low-rank approximation approaches (low-rank decomposition and nuclear norm minimization) in traditional matrix-based methods, we combine the two approaches in our quaternion matrix-based model. Furthermore, the nuclear norm of the quaternion matrix is replaced by the sum of Frobenius norm of its two low-rank factor quaternion matrices. Based on the relationship between quaternion matrix and its equivalent complex matrix, the problem eventually is converted from quaternion number field to complex number field. An alternating minimization method is applied to solve the model. Simulation results on real world color image recovery show the superior performance and efficiency of the proposed algorithm over some state-of-the-art tensor-based ones.

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“…-Kodak PhotoCD Dataset (Kodak): 3 The whole dataset consists of 24 clean color images of size 512 × 768 × 3.…”

Section: Ssim = (2µmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Color image recovery using low-rank quaternion matrix completion algorithm

Miao¹,

Kou²

2019

Preprint

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“…Recently, iterative thresholding (IT) algorithm showed its efficiency for l 1 -norm minimization problem in compressed sensing [14,15] and the nuclear norm minimization in matrix completion (MC) problem [16]. Also, in [17], we proposed a rank adaptive atomic decomposition algorithm for the low-rank matrix completion problem. From (2) we can see that matrix recovery (RPCA) problem involves minimizing a combination of both the l 1 -norm and the nuclear norm.…”

Section: Solution Overview and Algorithm For Matrix Reconstructionmentioning

confidence: 99%

Defect inspection for TFT-LCD images based on the low-rank matrix reconstruction

et al. 2015

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“…Since the missing values in the dataset make data processing and analysis more difficult, matrix completion becomes an important preprocessing step. Inference methods based on machine learning techniques have shown significant promise for the matrix completion task, which include wide-ranging applications from recommender systems [1] to operations research [2], from image processing [3] to product development [4] and high failure rate experiments [5].…”

Section: Introductionmentioning

confidence: 99%

Self-Supervised Feature Specific Neural Matrix Completion

2020

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Unsupervised matrix completion algorithms mostly model the data generation process by using linear latent variable models. Recently proposed algorithms introduce non-linearity via multi-layer perceptrons (MLP), and self-supervision by setting separate linear regression frameworks for each feature to estimate the missing values. In this paper, we introduce an MLP based algorithm called feature-specific neural matrix completion (FSNMC), which combines self-supervised and non-linear methods. The model parameters are estimated by a rotational scheme which separates the parameter and missing value updates sequentially with additional heuristic steps to prevent over-fitting and speed up convergence. The proposed algorithm specifically targets small to medium sized datasets. Experimental results on real-world and synthetic datasets varying in size with a range of missing value percentages demonstrate the superior accuracy for FSNMC, especially at low sparsities when compared to popular methods in the literature. The proposed method has particular potential in estimating missing data collected via real experimentation in fundamental life sciences.

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Rank adaptive atomic decomposition for low-rank matrix completion and its application on image recovery

Cited by 20 publications

References 15 publications

Color image recovery using low-rank quaternion matrix completion algorithm

Color image recovery using low-rank quaternion matrix completion algorithm

Defect inspection for TFT-LCD images based on the low-rank matrix reconstruction

Self-Supervised Feature Specific Neural Matrix Completion

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