Sparse Adaptive Iteratively-Weighted Thresholding Algorithm (SAITA) for L p -Regularization Using the Multiple Sub-Dictionary Representation
Both L 1 / 2 and...
| Main Authors: | , , , , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2017-12-01
|
| Series: | Sensors |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1424-8220/17/12/2920 |
| _version_ | 1811185842805276672 |
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| author | Yunyi Li Jie Zhang Shangang Fan Jie Yang Jian Xiong Xiefeng Cheng Hikmet Sari Fumiyuki Adachi Guan Gui |
| author_facet | Yunyi Li Jie Zhang Shangang Fan Jie Yang Jian Xiong Xiefeng Cheng Hikmet Sari Fumiyuki Adachi Guan Gui |
| author_sort | Yunyi Li |
| collection | DOAJ |
| description | Both
L
1
/
2
and
L
2
/
3
are two typical non-convex regularizations of
L
p
(
0
<
p
<
1
), which can be employed to obtain a sparser solution than the
L
1
regularization. Recently, the multiple-state sparse transformation strategy has been developed to exploit the sparsity in
L
1
regularization for sparse signal recovery, which combines the iterative reweighted algorithms. To further exploit the sparse structure of signal and image, this paper adopts multiple dictionary sparse transform strategies for the two typical cases
p
∈
{
1
/
2
,
2
/
3
}
based on an iterative
L
p
thresholding algorithm and then proposes a sparse adaptive iterative-weighted
L
p
thresholding algorithm (SAITA). Moreover, a simple yet effective regularization parameter is proposed to weight each sub-dictionary-based
L
p
regularizer. Simulation results have shown that the proposed SAITA not only performs better than the corresponding
L
1
algorithms but can also obtain a better recovery performance and achieve faster convergence than the conventional single-dictionary sparse transform-based
L
p
case. Moreover, we conduct some applications about sparse image recovery and obtain good results by comparison with relative work. |
| first_indexed | 2024-04-11T13:37:13Z |
| format | Article |
| id | doaj.art-0dbb15d80dcf4dccaafbd2180d582f65 |
| institution | Directory Open Access Journal |
| issn | 1424-8220 |
| language | English |
| last_indexed | 2024-04-11T13:37:13Z |
| publishDate | 2017-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Sensors |
| spelling | doaj.art-0dbb15d80dcf4dccaafbd2180d582f652022-12-22T04:21:26ZengMDPI AGSensors1424-82202017-12-011712292010.3390/s17122920s17122920Sparse Adaptive Iteratively-Weighted Thresholding Algorithm (SAITA) for L p -Regularization Using the Multiple Sub-Dictionary RepresentationYunyi Li0Jie Zhang1Shangang Fan2Jie Yang3Jian Xiong4Xiefeng Cheng5Hikmet Sari6Fumiyuki Adachi7Guan Gui8College of Electronic and Optical Engineering & College of Microelectronics, Nanjing University of Posts and Telecommunications, Nanjing 210023, ChinaCollege of Telecommunication and Information Engineering, Nanjing University of Posts and Telecommunications, Nanjing 210023, ChinaCollege of Telecommunication and Information Engineering, Nanjing University of Posts and Telecommunications, Nanjing 210023, ChinaCollege of Telecommunication and Information Engineering, Nanjing University of Posts and Telecommunications, Nanjing 210023, ChinaCollege of Telecommunication and Information Engineering, Nanjing University of Posts and Telecommunications, Nanjing 210023, ChinaCollege of Electronic and Optical Engineering & College of Microelectronics, Nanjing University of Posts and Telecommunications, Nanjing 210023, ChinaCollege of Telecommunication and Information Engineering, Nanjing University of Posts and Telecommunications, Nanjing 210023, ChinaResearch Organization of Electrical Communication, Tohoku University, Sendai 980-8577, JapanCollege of Telecommunication and Information Engineering, Nanjing University of Posts and Telecommunications, Nanjing 210023, ChinaBoth L 1 / 2 and L 2 / 3 are two typical non-convex regularizations of L p ( 0 < p < 1 ), which can be employed to obtain a sparser solution than the L 1 regularization. Recently, the multiple-state sparse transformation strategy has been developed to exploit the sparsity in L 1 regularization for sparse signal recovery, which combines the iterative reweighted algorithms. To further exploit the sparse structure of signal and image, this paper adopts multiple dictionary sparse transform strategies for the two typical cases p ∈ { 1 / 2 , 2 / 3 } based on an iterative L p thresholding algorithm and then proposes a sparse adaptive iterative-weighted L p thresholding algorithm (SAITA). Moreover, a simple yet effective regularization parameter is proposed to weight each sub-dictionary-based L p regularizer. Simulation results have shown that the proposed SAITA not only performs better than the corresponding L 1 algorithms but can also obtain a better recovery performance and achieve faster convergence than the conventional single-dictionary sparse transform-based L p case. Moreover, we conduct some applications about sparse image recovery and obtain good results by comparison with relative work.https://www.mdpi.com/1424-8220/17/12/2920Lp-norm regularizationadaptive weightediterative thresholdingmultiple dictionariessingle–dictionaryimage restoration |
| spellingShingle | Yunyi Li Jie Zhang Shangang Fan Jie Yang Jian Xiong Xiefeng Cheng Hikmet Sari Fumiyuki Adachi Guan Gui Sparse Adaptive Iteratively-Weighted Thresholding Algorithm (SAITA) for L p -Regularization Using the Multiple Sub-Dictionary Representation Sensors Lp-norm regularization adaptive weighted iterative thresholding multiple dictionaries single–dictionary image restoration |
| title | Sparse Adaptive Iteratively-Weighted Thresholding Algorithm (SAITA) for
L
p
-Regularization Using the Multiple Sub-Dictionary Representation |
| title_full | Sparse Adaptive Iteratively-Weighted Thresholding Algorithm (SAITA) for
L
p
-Regularization Using the Multiple Sub-Dictionary Representation |
| title_fullStr | Sparse Adaptive Iteratively-Weighted Thresholding Algorithm (SAITA) for
L
p
-Regularization Using the Multiple Sub-Dictionary Representation |
| title_full_unstemmed | Sparse Adaptive Iteratively-Weighted Thresholding Algorithm (SAITA) for
L
p
-Regularization Using the Multiple Sub-Dictionary Representation |
| title_short | Sparse Adaptive Iteratively-Weighted Thresholding Algorithm (SAITA) for
L
p
-Regularization Using the Multiple Sub-Dictionary Representation |
| title_sort | sparse adaptive iteratively weighted thresholding algorithm saita for l p regularization using the multiple sub dictionary representation |
| topic | Lp-norm regularization adaptive weighted iterative thresholding multiple dictionaries single–dictionary image restoration |
| url | https://www.mdpi.com/1424-8220/17/12/2920 |
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