Compressive total variation for image reconstruction and restoration

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

2 Scopus Citations
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Author(s)

  • Peng Li
  • Wengu Chen
  • Michael K. Ng

Related Research Unit(s)

Detail(s)

Original languageEnglish
Pages (from-to)874-893
Journal / PublicationComputers & Mathematics with Applications
Volume80
Issue number5
Online published28 May 2020
Publication statusPublished - 1 Sep 2020

Abstract

In this paper, we make use of the fact that the matrix u is (approximately) low-rank in image inpainting, and the corresponding gradient transform matrices Dxu,Dyu are sparse in image reconstruction and restoration. Therefore we consider that these gradient matrices Dxu,Dyu also are (approximately) low-rank, and also verify it by numerical test and theoretical analysis. We propose a model called compressive total variation (CTV) to characterize the sparsity and low-rank prior knowledge of an image. In order to solve the proposed model, we design a concrete algorithm with provably convergence, which is based on inertial proximal ADMM. The performance of the proposed model is tested for magnetic resonance imaging (MRI) reconstruction, image denoising and image deblurring. The proposed method not only recovers edges of the image but also preserves fine details of the image. And our model is much better than the existing regularization models based on the TGV, Shearlet-TGV, − αℓ2TV and BM3D in test for images with piecewise constant regions. And it visibly improves the performances of TV, − αℓ2TV and TGV, and is comparable to Shearlet-TGV in test for natural images.

Research Area(s)

  • Compressive total variation, Image deblurring, Image denoising, Low-rank, MRI reconstruction, Nuclear norm total (generalized) variation

Citation Format(s)

Compressive total variation for image reconstruction and restoration. / Li, Peng; Chen, Wengu; Ng, Michael K.

In: Computers & Mathematics with Applications, Vol. 80, No. 5, 01.09.2020, p. 874-893.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review