Towards design and implementation of efficient compressed sensing techniques

Abstract

The objective of compressed sensing is not only to recover information about signal of limited dimension. newlineThe asymptotic behavior of different well established algorithms has well indicated that the signal newlinedimension plays an important role to define algorithmic behavior, and it can be easily predicted that the newlinelarge dimensional signals are very difficult to be recovered in resource constraint environment. The large newlinedimension signals require sensing matrix of high volume and it requires huge amount of time to recover newlineapproximate signal as it computational time is directly proportional to signal dimension. The majority of algorithm newlineneeds number of measurements m = O(klogn) and computational time O(n3:5) for l1-minimization, newlineO(mkn) for Orthogonal Matching Pursuit etc., where k is the signal sparsity, m is number of measurements, newlinen is signal dimension. The reduction in time complexity can be realized if signals are processed by blocks, newlinewhereas the storage issues is managed through structured or sparse sensing matrix. The block processing of newlinenatural images and structured sensing matrix are center of the discussion in this thesis. newline