Degree Name
Master of Science
Graduate Program
Mathematics
Advisor
Pericak-Spector, Kathleen
Abstract
This paper presents and studies analytically a new compressive sensing (CS) approach with the aim of bringing this technique closer to successful commercialization in image sensor circuits. Unlike existing CS techniques that use random measurement matrices (RMM) to encode a signal given in form of a vector of discrete samples, the proposed technique utilizes carefully chosen custom measurement matrices. In CS measurement operation, RMM are often used to achieve small coherence between the measurement matrix and the sparse representation bases. However, when applied in practice, RMM based CS designs typically lead to complicated hardware design and thus have a large circuit overhead to obtain random summations. The proposed custom measurement matrix achieves about the same level of incoherence as the RMMs, but results in a dramatically simplified CS measurement circuit, improving both energy efficiency and circuit scalability, and thus the attractiveness of this technique for industrial commercialization. The proposed method is evaluated analytically in terms of Peak Signal to Noise Ratio (PSNR), a measure for the quality of the reconstructed compared to the original signal. Matlab simulations are also conducted to evaluate the effectiveness of the proposed technique, and to compare simulated and estimated PSNRs. Finally, the proposed technique is extended to two-dimensional projections with the aim of further improving signal quality, in particular with high compression rates. A newly formulated minimization problem is proposed to combine the projections in both dimensions to a single optimization problem.