Composition of Binary Compressed Sensing Matrices

In the recent past, various methods have been proposed to construct deterministic compressed sensing (CS) matrices. Of interest has been the construction of binary sensing matrices as they are useful for multiplierless and faster dimensionality reduction. In most of these binary constructions, the matrix size depends on primes or their powers. In this study, we propose a composition rule which exploits sparsity and block structure of existing binary CS matrices to construct matrices of general size. We also show that these matrices satisfy optimal theoretical guarantees and have similar density compared to matrices obtained using Kronecker product. Simulation work shows that the synthesized matrices provide comparable results against Gaussian random matrices

Deterministic Constructions of Binary Measurement Matrices from Finite Geometry

Deterministic constructions of measurement matrices in compressed sensing (CS) are considered in this paper. The constructions are inspired by the recent discovery of Dimakis, Smarandache and Vontobel which says that parity-check matrices of good low-density parity-check (LDPC) codes can be used as {provably} good measurement matrices for compressed sensing under $\ell_1$-minimization. The performance of the proposed binary measurement matrices is mainly theoretically analyzed with the help of the analyzing methods and results from (finite geometry) LDPC codes. Particularly, several lower bounds of the spark (i.e., the smallest number of columns that are linearly dependent, which totally characterizes the recovery performance of $\ell_0$-minimization) of general binary matrices and finite geometry matrices are obtained and they improve the previously known results in most cases. Simulation results show that the proposed matrices perform comparably to, sometimes even better than, the corresponding Gaussian random matrices. Moreover, the proposed matrices are sparse, binary, and most of them have cyclic or quasi-cyclic structure, which will make the hardware realization convenient and easy.Comment: 12 pages, 11 figure

A new fingerprint design using optical orthogonal codes

Digital fingerprinting has been proposed to restrict illegal distribution of digital media, where every piece of media has a unique fingerprint as an identifying feature that can be traceable. However, fingerprint systems are vulnerable when multiple users form collusion by combining their copies to create a forged copy. The collusion is modeled as an average linear attack, where multiple weighted copies are averaged and the Gaussian noise is then added to the averaged copy. In this thesis, a new fingerprint design with robustness to collusion is proposed, which is to accommodate more users and parameters than other existing fingerprint designs. A base matrix is constructed by cyclic shifts of binary sequences in an optical orthogonal code and then extended by a Hadamard matrix. Finally, each column of the resulting matrix is used as a fingerprint. The focused detection is used to determine whether a user is innocent or guilty in average linear attacks. Simulation results show that the performance of our new fingerprint design is comparable to that of orthogonal and simplex fingerprints