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Unimodular waveforms x are constructed on the integers with the property that the autocorrelation of x is one at the origin and zero elsewhere. There are three different constructions: exponentials of the form e 2πin α θ , sequences taken from roots of unity, and sequences constructed from the elements of real Hadamard matrices. The first is expected and(More)
We explore the stability of image reconstruction algorithms under deterministic compressed sensing. Recently, we have proposed [1-3] deterministic compressed sensing algorithms for 2D images. These algorithms are suitable when Daube-chies wavelets are used as the sparsifying basis. In the initial work, we have shown that the algorithms perform well for(More)
A recently proposed approach for compressed sensing, or compressive sampling, with deterministic measurement matrices made of chirps is applied to images that possess varying degrees of sparsity in their wavelet representations. The " fast reconstruction " algorithm enabled by this deterministic sampling scheme as developed by Applebaum et al. [1] produces(More)
An image reconstruction algorithm using compressed sensing (CS) with deterministic matrices of second-order Reed-Muller (RM) sequences is introduced. The 1D algorithm of Howard et al. using CS with RM sequences suffers significant loss in speed and accuracy when the degree of sparsity is not high, making it inviable for 2D signals. This paper describes an(More)
Given K > 0 and a positive integer M, the function △ K,M (t) = K max(1− |t| M , 0) represents an isosceles triangle on the real line R having height K and base 2M. For a given K and M, a constant amplitude sequence is constructed on the integers Z having autocorrelation △ K,M restricted to Z. With this setup, a large class of bounded sequences z is shown to(More)