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Noninvertible Gabor Transforms

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3 Author(s)
Matusiak, Ewa ; Dept. of Electr. Eng., Technion - Israel Inst. of Technol., Haifa, Israel ; Michaeli, T. ; Eldar, Y.C.

Time-frequency analysis, such as the Gabor transform, plays an important role in many signal processing applications. The redundancy of such representations is often directly related to the computational load of any algorithm operating in the transform domain. To reduce complexity, it may be desirable to increase the time and frequency sampling intervals beyond the point where the transform is invertible, at the cost of an inevitable recovery error. In this paper we initiate the study of recovery procedures for noninvertible Gabor representations. We propose using fixed analysis and synthesis windows, chosen e.g., according to implementation constraints, and to process the Gabor coefficients prior to synthesis in order to shape the reconstructed signal. We develop three methods for signal recovery. The first follows from the consistency requirement, namely that the recovered signal has the same Gabor representation as the input signal. The second, is based on minimization of a worst-case error. Last, we develop a recovery technique based on the assumption that the input signal lies in some subspace of L2 . We show that for each of the criteria, the manipulation of the transform coefficients amounts to a 2D twisted convolution, which we show how to perform using a filter-bank. When the undersampling factor is an integer, the processing reduces to standard 2D convolution. We provide simulation results demonstrating the advantages and weaknesses of each of the algorithms.

Published in:

Signal Processing, IEEE Transactions on  (Volume:58 ,  Issue: 5 )

Date of Publication:

May 2010

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