scholarly journals Stable Sparse Model with Non-Tight Frame

2020 ◽  
Vol 10 (5) ◽  
pp. 1771 ◽  
Author(s):  
Min Zhang ◽  
Yunhui Shi ◽  
Na Qi ◽  
Baocai Yin
Keyword(s):  
Image Restoration ◽  
Sparse Representation ◽  
Tight Frame ◽  
Closed Form Expression ◽  
Dual Frame ◽  
Two Phase ◽  
Sparse Models ◽  
Frame Operator ◽  
Sparse Model ◽  
Sparse System

Overcomplete representation is attracting interest in image restoration due to its potential to generate sparse representations of signals. However, the problem of seeking sparse representation must be unstable in the presence of noise. Restricted Isometry Property (RIP), playing a crucial role in providing stable sparse representation, has been ignored in the existing sparse models as it is hard to integrate into the conventional sparse models as a regularizer. In this paper, we propose a stable sparse model with non-tight frame (SSM-NTF) via applying the corresponding frame condition to approximate RIP. Our SSM-NTF model takes into account the advantage of the traditional sparse model, and meanwhile contains RIP and closed-form expression of sparse coefficients which ensure stable recovery. Moreover, benefitting from the pair-wise of the non-tight frame (the original frame and its dual frame), our SSM-NTF model combines a synthesis sparse system and an analysis sparse system. By enforcing the frame bounds and applying a second-order truncated series to approximate the inverse frame operator, we formulate a dictionary pair (frame pair) learning model along with a two-phase iterative algorithm. Extensive experimental results on image restoration tasks such as denoising, super resolution and inpainting show that our proposed SSM-NTF achieves superior recovery performance in terms of both subjective and objective quality.

scholarly journals Data-Driven Redundant Transform Based on Parseval Frames

2020 ◽  
Vol 10 (8) ◽  
pp. 2891 ◽  
Author(s):  
Min Zhang ◽  
Yunhui Shi ◽  
Na Qi ◽  
Baocai Yin
Keyword(s):  
Singular Values ◽  
Data Driven ◽  
Dual Frame ◽  
Two Phase ◽  
Sparse Models ◽  
Sparse System ◽  
Parseval Frames ◽  
Proposed Model ◽  
Objective Quality

The sparsity of images in a certain transform domain or dictionary has been exploited in many image processing applications. Both classic transforms and sparsifying transforms reconstruct images by a linear combination of a small basis of the transform. Both kinds of transform are non-redundant. However, natural images admit complicated textures and structures, which can hardly be sparsely represented by square transforms. To solve this issue, we propose a data-driven redundant transform based on Parseval frames (DRTPF) by applying the frame and its dual frame as the backward and forward transform operators, respectively. Benefitting from this pairwise use of frames, the proposed model combines a synthesis sparse system and an analysis sparse system. By enforcing the frame pair to be Parseval frames, the singular values and condition number of the learnt redundant frames, which are efficient values for measuring the quality of the learnt sparsifying transforms, are forced to achieve an optimal state. We formulate a transform pair (i.e., frame pair) learning model and a two-phase iterative algorithm, analyze the robustness of the proposed DRTPF and the convergence of the corresponding algorithm, and demonstrate the effectiveness of our proposed DRTPF by analyzing its robustness against noise and sparsification errors. Extensive experimental results on image denoising show that our proposed model achieves superior denoising performance, in terms of subjective and objective quality, compared to traditional sparse models.

Non-local sparse models for image restoration

2009 ◽  
Author(s):  
Julien Mairal ◽  
Francis Bach ◽  
Jean Ponce ◽  
Guillermo Sapiro ◽  
Andrew Zisserman
Keyword(s):  
Image Restoration ◽  
Sparse Models ◽  
Non Local

Simultaneous Shape and Permittivity Reconstruction in ECT With Sparse Representation: Two-Phase Distribution Imaging

2021 ◽  
Vol 70 ◽  
pp. 1-14
Author(s):  
Wenbin Tian ◽  
Peng Suo ◽  
Dong Liu ◽  
Shijie Sun ◽  
Jiangtao Sun ◽  
...  
Keyword(s):  
Sparse Representation ◽  
Phase Distribution ◽  
Two Phase

scholarly journals A Novel Blind Restoration and Reconstruction Approach for CT Images Based on Sparse Representation and Hierarchical Bayesian-MAP

Algorithms ◽  
2019 ◽  
Vol 12 (8) ◽  
pp. 174
Author(s):  
Sun ◽  
Zhang ◽  
Li ◽  
Meng
Keyword(s):  
Image Reconstruction ◽  
Radiation Dose ◽  
Image Restoration ◽  
Sparse Representation ◽  
Iterative Reconstruction ◽  
Model Parameters ◽  
Projection Data ◽  
Ct Image ◽  
High Quality ◽  
Ct Image Reconstruction

Computed tomography (CT) image reconstruction and restoration are very important in medical image processing, and are associated together to be an inverse problem. Image iterative reconstruction is a key tool to increase the applicability of CT imaging and reduce radiation dose. Nevertheless, traditional image iterative reconstruction methods are limited by the sampling theorem and also the blurring of projection data will propagate unhampered artifact in the reconstructed image. To overcome these problems, image restoration techniques should be developed to accurately correct a wide variety of image degrading effects in order to effectively improve image reconstruction. In this paper, a blind image restoration technique is embedded in the compressive sensing CT image reconstruction, which can result in a high-quality reconstruction image using fewer projection data. Because a small amount of data can be obtained by radiation in a shorter time, high-quality image reconstruction with less data is equivalent to reducing radiation dose. Technically, both the blurring process and the sparse representation of the sharp CT image are first modeled as a serial of parameters. The sharp CT image will be obtained from the estimated sparse representation. Then, the model parameters are estimated by a hierarchical Bayesian maximum posteriori formulation. Finally, the estimated model parameters are optimized to obtain the final image reconstruction. We demonstrate the effectiveness of the proposed method with the simulation experiments in terms of the peak signal to noise ratio (PSNR), and structural similarity index (SSIM).

Sparse representation-based image restoration via nonlocal supervised coding

2016 ◽  
Vol 23 (5) ◽  
pp. 776-783 ◽  
Author(s):  
Ao Li ◽  
Deyun Chen ◽  
Guanglu Sun ◽  
Kezheng Lin
Keyword(s):  
Image Restoration ◽  
Sparse Representation

Image Classification Base on Sparse Representation with Basis Design

2013 ◽  
Vol 709 ◽  
pp. 515-518
Author(s):  
Hao Feng Huang ◽  
Shao Ying Chen
Keyword(s):  
Representation Theory ◽  
Sparse Representation ◽  
Image Classification ◽  
Design Method ◽  
Classification Model ◽  
Classification Method ◽  
Sparse Model

An image classification method based on sparse representation with basis design is proposed. We construct a classification model under the sparse representation theory. The sparse model can lead to be better performance under a suitable dictionary, so the basis design method can follow the same process as discussed in[6].The experiments show that the proposed method improves the result.

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