Exploiting Prior Knowledge in Compressed Sensing

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Intellectual Merit: The field of compressive sensing (CS) promises to revolutionize digital processing broadly. The key idea is the use of nonadaptive linear projections to acquire an efficient, dimensionally reduced representation of a signal or image directly using just a few measurements. However, there are two limitations in current practical CS algorithms that constrain their application in practical scenarios. First, most of the work in CS deals with deterministic signals and does not assume any prior knowledge about them. In many applications, however, additional a priori information on the underlying signals is available, in addition to their sparsity. The a priori information may come either deterministically or statistically, e.g., through second order statistics. Our preliminary results show that exploiting it leads to a substantial performance improvement. The second constraint in standard CS is the need to perform reconstruction in a basis where the signal of interest admits a sparse representation, which reduces flexibility in practical applications. This research addresses these limitations by exploring how a priori information can be used in the general framework of CS to achieve improved performance, even when reconstruction is performed in a basis where the signal of interest does not admit a sparse representation. Furthermore, as a proof of concept, we will build a hardware demonstration system to show the feasibility of the proposed techniques in practical CS and with real-world signals.Broader Impact: Advances in compressive sensing may have a profound impact broadly, including applications in spectroscopy, imaging, communications, as well as consumer electronics. This project will include an integrated educational program involving two Ph.D. students and three undergraduate students, who will be introduced into this new field.