Abstract
In the theory of compressed sensing, restricted isometry property (RIP) decides the universality and reconstruction robustness of an observation matrix. At present, an observation matrix based on RD-AIC (RD-AIC-based observation matrix) can compress sparse continuous signals with a simple structure, but RIP analysis of this matrix is lack and challenging to prove. In this paper, this problem is relaxed. Instead, we demonstrate the incoherence analysis process, derive the orthogonality and nonsingularity of the matrix, propose the generalized relevance calculation steps of the matrix, and propose the hardware parameter design principles to improve the incoherence of the matrix. Moreover, compression and reconstruction experiments used in power quality disturbance signals are developed for testing the incoherence. The results show that the RD-AIC-based observation matrix has substantial incoherence under suitable hardware parameters, equivalent to the Gaussian random matrix and the Bernoulli random matrix.
Highlights
Compressed sensing (CS) is an efficient theory for signal compression [1], widely applied in medical imaging, radar imaging, and wireless sensors [2,3,4]. e classical CS theory is distributed CS, 1-bit CS, and blind CS [5,6,7], and the recent CS theory has developed with advanced control theory and deep learning technology
Gaussian random matrix, Bernoulli random matrix, Toeplitz matrix, and Chaotic matrix [12,13,14,15] have been proved, which satisfied restricted isometry property (RIP), and are optimal for sparse recovery, they have limited use in practice because of complicated hardware structure, high complexity of calculation, and extensive expense on storage. erefore, they are still stuck in theory and are only used to compress discrete signals: y(m) Φx(n), (1)
An analog-to-information converter (AIC) is a vital under-sampling technique based on CS theory and samples the analog signals at the sub-Nyquist rate [16]
Summary
Compressed sensing (CS) is an efficient theory for signal compression [1], widely applied in medical imaging, radar imaging, and wireless sensors [2,3,4]. e classical CS theory is distributed CS, 1-bit CS, and blind CS [5,6,7], and the recent CS theory has developed with advanced control theory and deep learning technology. (1) A noncoherent analysis method based on the RDAIC-based observation matrix is demonstrated to avoid an NP-hard problem for RIP proving (2) An orthogonality and nonsingularity of RD-AICbased observation matrix are deduced for the first time, solving the premise of applying discriminant theorems (3) A design rule of hardware parameters is proposed, which can be used to enhance the incoherence of RD-AIC-based observation matrix (4) Compression and reconstruction experiments used in power quality disturbance signals are developed for testing the incoherence is paper is structured into five sections. 0, n ≠ C, where Ψ ∈ RN×N is the transform function matrix that is consisted of the discretized φn(n), P∈∈RN×N is the binary random sequence matrix that is consisted of the discretized pc(n), H ∈ RN×N is the unit impulse response matrix that is consisted of the circular movement of the discretized h(n), and B∈∈RM×N is the uniform sampling matrix consisted of the direct sum of M same κ vectors. Where ΦRD−AIC ∈ RM×N and c (M/N) × 100% is the compression ratio. e smaller the value of c, the less the number of samples
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
