Digital Gabor filters are indispensable tools of local time-frequency analysis in signal processing. With strong orientation selectivity, discrete (tight) Gabor frames generated by 2D Gabor filters also see their wide applications in image processing and volume data processing. However, owing to the lack of multi-scale structures, discrete Gabor frames are less effective than multiresolution an...

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 ...

complex exponentials. Bastiaans [2] dubbed this family of functions the Gabor elementary functions (GEF). He also Computation of the finite discrete Gabor transform can be accomplished in a variety of ways. Three representative methgeneralized the notion of Gabor’s expansion to include ods (matrix inversion, Zak transform, and relaxation network) non-Gaussian windows. were evaluated in terms of...

A Gabor system generated by a window function φ and a rectangular lattice aZ× Z/b is given by G(φ, aZ× Z/b) := {e−2πint/bφ(t−ma) : (m,n) ∈ Z× Z}. One of fundamental problems in Gabor analysis is to identify window functions φ and time-frequency shift lattices aZ × Z/b such that the corresponding Gabor system G(φ, aZ × Z/b) is a Gabor frame for L(R), the space of all square-integrable functions ...

Automated inspection of apple quality involves computer recognition of good apples and blemished apples based on geometric or statistical features derived from apple images. This paper introduces a Gabor feature-based kernel principal component analysis (PCA) method by combining Gabor wavelet representation of apple images and the kernel PCA method for apple quality inspection using near-infrar...

A Gabor or Weyl-Heisenberg frame for L2(Rd) is generated by time-frequency shifts of a square-integrable function, the Gabor atom, along a time-frequency lattice. The dual frame is again a Gabor frame, generated by the dual atom. In general, Gabor frames are not stable under a perturbation of the lattice constants; that is, even for arbitrarily small changes of the parameters the frame property...