New flexible deterministic compressive measurement matrix based on finite Galois field
Abstract Nowadays, the deterministic construction of sensing matrices is a hot topic in compressed sensing. The coherence of the measurement matrix is an important research area in the design of deterministic compressed sensing. To solve this problem, this paper proposes a novel sparse deterministic...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2022-01-01
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| Series: | IET Image Processing |
| Subjects: | |
| Online Access: | https://doi.org/10.1049/ipr2.12348 |
| _version_ | 1798035556998840320 |
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| author | Vahdat Kazemi Ali Shahzadi Hossein Khaleghi Bizaki |
| author_facet | Vahdat Kazemi Ali Shahzadi Hossein Khaleghi Bizaki |
| author_sort | Vahdat Kazemi |
| collection | DOAJ |
| description | Abstract Nowadays, the deterministic construction of sensing matrices is a hot topic in compressed sensing. The coherence of the measurement matrix is an important research area in the design of deterministic compressed sensing. To solve this problem, this paper proposes a novel sparse deterministic measurement matrix, which basically accesses the optimal low coherence of the measurement matrix. Firstly, a class of sparse square matrix is constructed based on finite fields' arithmetic. Then, the Hadamard matrix, or (discrete Fourier transform) DFT matrix, is nestled into the square matrix to construct an asymptotically optimal deterministic measurement matrix. That is, the relevant column vectors have orthogonal characteristics. Using this feature, the measurement matrix can be further optimized to reduce its mutual coherence, almost achieving the lower bound of the coherence (Welch bound). The two types of deterministic measurement matrices proposed are sparse with low mutual coherence and flexible measurement sizes. So, the proposed deterministic measurement matrices require less memory and time for the recovery as well as reducing the complexity due to their sparse structure. The simulation results show that compared with the existing (several typical) random matrices, the proposed method can reduce the mutual coherence and computational complexity of the measurement matrix. |
| first_indexed | 2024-04-11T20:59:50Z |
| format | Article |
| id | doaj.art-19762c847ab84c9ca36a036d84c13b50 |
| institution | Directory Open Access Journal |
| issn | 1751-9659 1751-9667 |
| language | English |
| last_indexed | 2024-04-11T20:59:50Z |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | IET Image Processing |
| spelling | doaj.art-19762c847ab84c9ca36a036d84c13b502022-12-22T04:03:32ZengWileyIET Image Processing1751-96591751-96672022-01-0116123925110.1049/ipr2.12348New flexible deterministic compressive measurement matrix based on finite Galois fieldVahdat Kazemi0Ali Shahzadi1Hossein Khaleghi Bizaki2Department of Electrical and Computer Engineering Semnan University Semnan IranDepartment of Electrical and Computer Engineering Semnan University Semnan IranDepartment of Electrical and Computer Engineering Malek Ashtar University of Technology Tehran IranAbstract Nowadays, the deterministic construction of sensing matrices is a hot topic in compressed sensing. The coherence of the measurement matrix is an important research area in the design of deterministic compressed sensing. To solve this problem, this paper proposes a novel sparse deterministic measurement matrix, which basically accesses the optimal low coherence of the measurement matrix. Firstly, a class of sparse square matrix is constructed based on finite fields' arithmetic. Then, the Hadamard matrix, or (discrete Fourier transform) DFT matrix, is nestled into the square matrix to construct an asymptotically optimal deterministic measurement matrix. That is, the relevant column vectors have orthogonal characteristics. Using this feature, the measurement matrix can be further optimized to reduce its mutual coherence, almost achieving the lower bound of the coherence (Welch bound). The two types of deterministic measurement matrices proposed are sparse with low mutual coherence and flexible measurement sizes. So, the proposed deterministic measurement matrices require less memory and time for the recovery as well as reducing the complexity due to their sparse structure. The simulation results show that compared with the existing (several typical) random matrices, the proposed method can reduce the mutual coherence and computational complexity of the measurement matrix.https://doi.org/10.1049/ipr2.12348AlgebraSignal processing and detectionOptimisation techniquesInterpolation and function approximation (numerical analysis)Other topics in statisticsOptimisation techniques |
| spellingShingle | Vahdat Kazemi Ali Shahzadi Hossein Khaleghi Bizaki New flexible deterministic compressive measurement matrix based on finite Galois field IET Image Processing Algebra Signal processing and detection Optimisation techniques Interpolation and function approximation (numerical analysis) Other topics in statistics Optimisation techniques |
| title | New flexible deterministic compressive measurement matrix based on finite Galois field |
| title_full | New flexible deterministic compressive measurement matrix based on finite Galois field |
| title_fullStr | New flexible deterministic compressive measurement matrix based on finite Galois field |
| title_full_unstemmed | New flexible deterministic compressive measurement matrix based on finite Galois field |
| title_short | New flexible deterministic compressive measurement matrix based on finite Galois field |
| title_sort | new flexible deterministic compressive measurement matrix based on finite galois field |
| topic | Algebra Signal processing and detection Optimisation techniques Interpolation and function approximation (numerical analysis) Other topics in statistics Optimisation techniques |
| url | https://doi.org/10.1049/ipr2.12348 |
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