Stable Sparse Model with Non-Tight Frame
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 p...
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doaj-6469215f8ff847f1b04233bd28ef97932020-11-25T03:01:45ZengMDPI AGApplied Sciences2076-34172020-03-01105177110.3390/app10051771app10051771Stable Sparse Model with Non-Tight FrameMin Zhang0Yunhui Shi1Na Qi2Baocai Yin3Beijing Key Laboratory of Multimedia and Intelligent Software Technology, Faculty of Information Technology, Beijing University of Technology, Beijing 100124, ChinaBeijing Key Laboratory of Multimedia and Intelligent Software Technology, Faculty of Information Technology, Beijing University of Technology, Beijing 100124, ChinaBeijing Key Laboratory of Multimedia and Intelligent Software Technology, Faculty of Information Technology, Beijing University of Technology, Beijing 100124, ChinaBeijing Key Laboratory of Multimedia and Intelligent Software Technology, Faculty of Information Technology, Beijing University of Technology, Beijing 100124, ChinaOvercomplete 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.https://www.mdpi.com/2076-3417/10/5/1771sparse dictionarystable recoveryframerip |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Min Zhang Yunhui Shi Na Qi Baocai Yin |
spellingShingle |
Min Zhang Yunhui Shi Na Qi Baocai Yin Stable Sparse Model with Non-Tight Frame Applied Sciences sparse dictionary stable recovery frame rip |
author_facet |
Min Zhang Yunhui Shi Na Qi Baocai Yin |
author_sort |
Min Zhang |
title |
Stable Sparse Model with Non-Tight Frame |
title_short |
Stable Sparse Model with Non-Tight Frame |
title_full |
Stable Sparse Model with Non-Tight Frame |
title_fullStr |
Stable Sparse Model with Non-Tight Frame |
title_full_unstemmed |
Stable Sparse Model with Non-Tight Frame |
title_sort |
stable sparse model with non-tight frame |
publisher |
MDPI AG |
series |
Applied Sciences |
issn |
2076-3417 |
publishDate |
2020-03-01 |
description |
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. |
topic |
sparse dictionary stable recovery frame rip |
url |
https://www.mdpi.com/2076-3417/10/5/1771 |
work_keys_str_mv |
AT minzhang stablesparsemodelwithnontightframe AT yunhuishi stablesparsemodelwithnontightframe AT naqi stablesparsemodelwithnontightframe AT baocaiyin stablesparsemodelwithnontightframe |
_version_ |
1724692174396719104 |