Super-resolution from short-time Fourier transform measurements

Authors

Céline Aubel, David Stotz, and Helmut Bölcskei

Reference

Proc. of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Florence, Italy, pp. 36-40, May 2014

DOI: 10.1109/ICASSP.2014.6853553

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Abstract

While spike trains are obviously not band-limited, the theory of super-resolution tells us that perfect recovery of unknown spike locations and weights from low-pass Fourier transform measurements is possible provided that the minimum spacing, D, between spikes is not too small. Specifically, for a cutoff frequency of f_c, Donoho [2] shows that exact recovery is possible if D  > 1/f_c, but does not specify a corresponding recovery method. On the other hand, Candès and Fernandez-Granda [3] provide a recovery method based on convex optimization, which provably succeeds as long as D > 2/f_c. In practical applications one often has access to windowed Fourier transform measurements, i.e., short-time Fourier transform (STFT) measurements, only. In this paper, we develop a theory of super-resolution from STFT measurements, and we propose a method that provably succeeds in recovering spike trains from STFT measurements provided that D > 1/f_c.

Keywords

Super-resolution, inverse problems in measure spaces, short-time Fourier transform


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