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The problem of sparse phase retrieval is considered where the measurement vectors are deterministic and Fourier-like. Under some mild assumptions, O(slog N) measurements are proved to be sufficient to recover an s-sparse complex vector of dimension N from its phaseless measurement via convex programming. The key contribution is to show that unlike existing work in sparse phase retrieval, the so-called...
This paper considers the problem of estimating the symmetric and Toeplitz covariance matrix of compressive samples of wide sense stationary random vectors. A new structured deterministic sampling method known as the "Generalized Nested Sampling" is introduced which enables compressive quadratic sampling of symmetric Toeplitz matrices., by fully exploiting the inherent redundancy in the Toeplitz...
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