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Abstract |
Compressed sensing (CS) is a novel sampling technique which provides a fundamentally new approach to data acquisition. Comparing with the traditional method, compressed sensing asserts that a sparse signal can be reconstructed from very few measurements. Thus, CS has attracted tremendous attention in recent years.
A central problem in compressed sensing is the construction of sensing matrices. While there have been many probabilistic constructions, only a few deterministic ones are known. In this talk, we concern the deterministic construction of sensing matrices in which many powerful mathematical tools are used. On one hand, we construct several families of sensing matrices by using algebraic curves, Steiner systems, di erence sets, and highly nonlinear functions. On the other hand, we build the connection between sensing matrices and many other mathematical objects, such as Maximum Welch-Bound-Equality sequence sets, signal sets, and mutually unbiased bases. In addition, a lot of simulations have been conducted to show that our matrices outperform many other matrices. |
