How to construct log-Gabor Filters?

Orthogonal and biorthogonal wavelets became very popular image processing tools but exhibit major drawbacks, namely a poor resolution in orientation and the lack of translation invariance due to aliasing between subbands. We propose here the construction of log-Gabor wavelet transforms which allow exact reconstruction and strengthen the excellent mathematical properties of the Gabor filters. Two major improvements on the previous Gabor wavelet schemes are proposed: first the highest frequency bands are covered by narrowly localized oriented filters. Secondly, the set of filters cover uniformly the Fourier domain including the highest and lowest frequencies and thus exact reconstruction is achieved using the same filters in both the direct and the inverse transforms (which means that the transform is selfinvertible). In this paper the procedure for constructing log-Gabor filters is described and a Matlab toolbox that implements such multiresolution scheme is available from the authors.