Subsampled Blind Deconvolution via Nuclear Norm Minimization

Many phenomena can be modeled as systems that preform convolution, including negative effects on data like translation/motion blurs. Blind Deconvolution (BD) is a process used to reverse the negative effects of a system by effectively undoing the convolution. Not only can the signal be recovered, but the impulse response can as well. "Blind" signifies that there is incomplete knowledge of the impulse responses of an LTI system. Solutions exist for preforming BD but they assume data is fully sampled. In this project we start from an existing method [1] for BD then extend to the subsampled case. We show that this new formulation works under similar assumptions. Current results are empirical, but current and future work focuses providing theoretical guarantees for this algorithm.No embargoAcademic Major: Electrical and Computer Engineerin

Sparse recovery on Euclidean Jordan algebras

This paper is concerned with the problem of sparse recovery on Euclidean Jordan algebra (SREJA), which includes the sparse signal recovery problem and the low-rank symmetric matrix recovery problem as special cases. We introduce the notions of restricted isometry property (RIP), null space property (NSP), and s-goodness for linear transformations in s-SREJA, all of which provide sufficient conditions for s-sparse recovery via the nuclear norm minimization on Euclidean Jordan algebra. Moreover, we show that both the s-goodness and the NSP are necessary and sufficient conditions for exact s-sparse recovery via the nuclear norm minimization on Euclidean Jordan algebra. Applying these characteristic properties, we establish the exact and stable recovery results for solving SREJA problems via nuclear norm minimization