Showing papers by "Ozgur Yilmaz published in 2014"

Sigma–Delta quantization of sub-Gaussian frame expansions and its application to compressed sensing

Abstract: Suppose that the collection {ei} m=1 forms a frame for R k , where each entry of the vector ei is a sub-Gaussian random variable. We consider expansions in such a frame, which are then quantized using a Sigma-Delta scheme. We show that an arbitrary signal in R k can be re- covered from its quantized frame coefficients up to an error which decays root-exponentially in the oversampling rate m/k. Here the quantization scheme is assumed to be chosen appropriately depending on the over- sampling rate and the quantization alphabet can be coarse. The result holds with high probability on the draw of the frame uniformly for all signals. The crux of the argument is a bound on the extreme singular val- ues of the product of a deterministic matrix and a sub-Gaussian frame. For fine quantization alphabets, we leverage this bound to show poly- nomial error decay in the context of compressed sensing. Our results extend previous results for structured deterministic frame expansions and Gaussian compressed sensing measurements. compressed sensing, quantization, random frames, root-exponential accuracy, Sigma-Delta, sub-Gaussian matrices 2010 Math Subject Classification: 94A12, 94A20, 41A25, 15B52

Non-Convex Compressed Sensing Using Partial Support Information

Abstract: In this paper we address the recovery conditions of weighted lp minimization for signal reconstruction from compressed sensing measurements when partial support information is available. We show that weighted lp minimization with 0 < p < 1 is stable and robust under weaker suficient conditions compared to weighted lp minimization. Moreover, the suficient recovery conditions of weighted lp are weaker than those of regular lp minimization if at least 50% of the support estimate is accurate. We also review some algorithms which exist to solve the non-convex lp problem and illustrate our results with numerical experiments.

Seismic trace interpolation with approximate message passing

Abstract: Approximate message passing (AMP) is a computationally effective algorithm for recovering high dimensional signals from a few compressed measurements. In this paper we use AMP to solve the seismic trace interpolation problem. We also show that we can exploit the fast AMP algorithm to improve the recovery results of seismic trace interpolation in curvelet domain, both in terms of convergence speed and recovery performance by using AMP in Fourier domain as a preprocessor for the `1 recovery in Curvelet domain.