Finding Subsampling Index Sets for Kronecker Product of Unitary Matrices for Incoherent Tight Frames
Frames are recognized for their importance in many fields of communications, signal processing, quantum physics, and so on. In this paper, we design an incoherent tight frame by selecting some rows of a matrix that is the Kronecker product of Fourier and unitary matrices. The Kronecker-product-based...
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| Format: | Article |
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MDPI AG
2022-10-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/12/21/11055 |
| _version_ | 1797469192994160640 |
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| author | Jooeun Kwon Nam Yul Yu |
| author_facet | Jooeun Kwon Nam Yul Yu |
| author_sort | Jooeun Kwon |
| collection | DOAJ |
| description | Frames are recognized for their importance in many fields of communications, signal processing, quantum physics, and so on. In this paper, we design an incoherent tight frame by selecting some rows of a matrix that is the Kronecker product of Fourier and unitary matrices. The Kronecker-product-based frame allows its elements to have a small number of phases, regardless of the frame length, which is suitable for low-cost implementation. To obtain the Kronecker-product-based frame with low mutual coherence, we first derive an objective function by transforming the Gram matrix expression to compute the coherence. If the Hadamard matrix is employed as a unitary matrix, the objective function can be computed efficiently with low complexity. Then, we find a subsampling index set for the Kronecker-product-based frame by minimizing the objective function. In simulations, we show that the Kronecker-product-based frames can achieve similar mutual coherence to optimized harmonic frames of a large number of phases. We apply the frames to compressed sensing (CS) as the measurement matrices, where the Kronecker-product-based frames demonstrate reliable performance of sparse signal recovery. |
| first_indexed | 2024-03-09T19:17:59Z |
| format | Article |
| id | doaj.art-4a2505753aa64558afbe13edea6e1afa |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-03-09T19:17:59Z |
| publishDate | 2022-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Sciences |
| spelling | doaj.art-4a2505753aa64558afbe13edea6e1afa2023-11-24T03:37:20ZengMDPI AGApplied Sciences2076-34172022-10-0112211105510.3390/app122111055Finding Subsampling Index Sets for Kronecker Product of Unitary Matrices for Incoherent Tight FramesJooeun Kwon0Nam Yul Yu1School of Electrical Engineering and Computer Science, Gwangju Institute of Science and Technology (GIST), Gwangju 61005, KoreaSchool of Electrical Engineering and Computer Science, Gwangju Institute of Science and Technology (GIST), Gwangju 61005, KoreaFrames are recognized for their importance in many fields of communications, signal processing, quantum physics, and so on. In this paper, we design an incoherent tight frame by selecting some rows of a matrix that is the Kronecker product of Fourier and unitary matrices. The Kronecker-product-based frame allows its elements to have a small number of phases, regardless of the frame length, which is suitable for low-cost implementation. To obtain the Kronecker-product-based frame with low mutual coherence, we first derive an objective function by transforming the Gram matrix expression to compute the coherence. If the Hadamard matrix is employed as a unitary matrix, the objective function can be computed efficiently with low complexity. Then, we find a subsampling index set for the Kronecker-product-based frame by minimizing the objective function. In simulations, we show that the Kronecker-product-based frames can achieve similar mutual coherence to optimized harmonic frames of a large number of phases. We apply the frames to compressed sensing (CS) as the measurement matrices, where the Kronecker-product-based frames demonstrate reliable performance of sparse signal recovery.https://www.mdpi.com/2076-3417/12/21/11055compressed sensingincoherent tight framekronecker productmutual coherence |
| spellingShingle | Jooeun Kwon Nam Yul Yu Finding Subsampling Index Sets for Kronecker Product of Unitary Matrices for Incoherent Tight Frames Applied Sciences compressed sensing incoherent tight frame kronecker product mutual coherence |
| title | Finding Subsampling Index Sets for Kronecker Product of Unitary Matrices for Incoherent Tight Frames |
| title_full | Finding Subsampling Index Sets for Kronecker Product of Unitary Matrices for Incoherent Tight Frames |
| title_fullStr | Finding Subsampling Index Sets for Kronecker Product of Unitary Matrices for Incoherent Tight Frames |
| title_full_unstemmed | Finding Subsampling Index Sets for Kronecker Product of Unitary Matrices for Incoherent Tight Frames |
| title_short | Finding Subsampling Index Sets for Kronecker Product of Unitary Matrices for Incoherent Tight Frames |
| title_sort | finding subsampling index sets for kronecker product of unitary matrices for incoherent tight frames |
| topic | compressed sensing incoherent tight frame kronecker product mutual coherence |
| url | https://www.mdpi.com/2076-3417/12/21/11055 |
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