Electrical and Electronic Engineering, Imperial College London
Doi
Abstract
The problem of estimating sparse signals based on incomplete set of noiseless or
noisy measurements has been investigated for a long time from different perspec-
tives. In this dissertation, after the review of the theory of compressed sensing (CS)
and existing structured sensing matrices, a new class of convolutional sensing matri-
ces based on deterministic sequences are developed in the first part. The proposed
matrices can achieve a near optimal bound with O(K log(N)) measurements for
non-uniform recovery. Not only are they able to approximate compressible signals
in the time domain, but they can also recover sparse signals in the frequency and
discrete cosine transform domain. The candidates of the deterministic sequences
include maximum length sequence (or called m-sequence), Golay's complementary
sequence and Legendre sequence etc., which will be investigated respectively. In
the second part, Golay-paired Hadamard matrices are introduced as structured
sensing matrices, which are constructed from the Hadamard matrix, followed by
diagonal Golay sequences. The properties and performances are analyzed in the
following. Their strong structures ensure special isometry properties, and make
them be easier applicable to hardware potentially. Finally, we exploit novel CS
principles successfully in a few real applications, including radar imaging and dis-
tributed source coding. The performance and the effectiveness of each scenario are verified in both theory and simulations
