Starting from a general operator representation in the time-frequency domain, this paper addresses the problem of approximating linear operators by operators that are diagonal or band-diagonal with respect to Gabor frames. A characterization of operators that can be realized as Gabor multipliers is given and necessary conditions for the existence of (Hilbert-Schmidt) optimal Gabor multiplier ap...

An elementary function that is now commonly referred to Gabor function, Gabor filter and Gabor wavelet was derived from uncertainty relation for information by Gabor to overcome the representation limit of Fourier analysis. Analyzing a signal by a Gabor filter in terms of convolution or spatial filtering, two pieces of information—phase and magnitude—can be obtained. In the paper, Gabor filter ...

This article presents a scheme for image decomposition and perfect reconstruction based on Gabor wavelets. Gabor functions have been used extensively in areas related to the human visual system due to their localization in space and bandlimited properties. However, since the standard two-sided Gabor functions are not orthogonal and lead to nearly singular Gabor matrices, they have been used in ...

Using a variant of the Sobolev Embedding Theorem, we prove an uncertainty principle related to Gabor systems that generalizes the Balian-Low Theorem. Namely, if f ∈ H(R) and f̂ ∈ H /2(R) with 1 < p < ∞, 1 p + 1 p′ = 1, then the Gabor system G(f, 1, 1) is not a frame for L(R). In the p = 1 case, we obtain a generalization of the result in [BCPS].

We introduce an object recognition system in which objects are represented as a sparse and spatially organized set of local (bent) line segments. The line segments correspond to binarized Gabor wavelets or banana wavelets, which are bent and stretched Gabor wavelets. These features can be metrically organized, the metric enables an efficient learning of object representations. Learning can be p...