High-rate interpolation of random signals from nonideal samples
IEEE Transactions on Signal Processing
Nonideal sampling and interpolation from noisy observations in shift-invariant spaces
IEEE Transactions on Signal Processing
Cardinal exponential splines: part I - theory and filtering algorithms
IEEE Transactions on Signal Processing
Nonideal Sampling and Regularization Theory
IEEE Transactions on Signal Processing
A Unified Approach to Dual Gabor Windows
IEEE Transactions on Signal Processing
A competitive minimax approach to robust estimation of random parameters
IEEE Transactions on Signal Processing
Linear minimax regret estimation of deterministic parameters with bounded data uncertainties
IEEE Transactions on Signal Processing
Dual Gabor frames: theory and computational aspects
IEEE Transactions on Signal Processing
Generalized smoothing splines and the optimal discretization of the Wiener filter
IEEE Transactions on Signal Processing
A minimum squared-error framework for generalized sampling
IEEE Transactions on Signal Processing - Part I
Signal enhancement using beamforming and nonstationarity withapplications to speech
IEEE Transactions on Signal Processing
Blind source separation based on time-frequency signalrepresentations
IEEE Transactions on Signal Processing
System Identification in the Short-Time Fourier Transform Domain With Crossband Filtering
IEEE Transactions on Audio, Speech, and Language Processing
| Hi-index | 35.68 |
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.