We describe approximate digital implementations of two new mathematical transforms, namely, the ridgelet transform and the curvelet transform. Our implementations offer exact reconstruction, stability against perturbations, ease of implementation, and low computational complexity. A central tool is Fourier-domain computation of an approximate digital Radon transform. We introduce a very simple ...

Directional information is an important and unique feature of multidimensional signals. As a result of a separable extension from one-dimensional (1-D) bases, multidimensional wavelet transforms have very limited directionality. Furthermore, different directions are mixed in certain wavelet subbands. In this paper, we propose a simple directional extension for wavelets (DEW) that fixes this sub...

This article introduces a systematic study for computational aspects of classical wavelet transforms over finite fields using tools from computational harmonic analysis and also theoretical linear algebra. We present a concrete formulation for the Frobenius norm of the classical wavelet transforms over finite fields. It is shown that each vector defined over a finite field can be represented as...

The occurrence of cycle slips is a major limiting factor for achievement of sub-decimeter accuracy in positioning with GPS (Global Positioning System). In the past, several authors introduced a method based on different combinations of GPS data together with Kalman filter to solve the problem of the cycle slips. In this paper the same philosophy is used but with discrete wavelet transforms. For...

In this paper, we study the problem of compressing a signal buried in additive white Gaussian noise. The approach we propose is to design an asymptotically optimal quantizer in the the wavelet domain. The undecimated discrete wavelet transform is shift-invariant and redundant, thus it is robust compared with the decimated and orthogonal discrete wavelet transform (DWT). Compared with the origin...

In this paper we introduced new wavelet based algorithm for speckle reduction of synthetic aperture radar images, which uses combination of undecimated wavelet transformation, wiener filter (which is an adaptive filter) and mean filter. Further more instead of using existing thresholding techniques such as sure shrinkage, Bayesian shrinkage, universal thresholding, normal thresholding, visu thr...

this article introduces a systematic study for computational aspects of classical wavelet transforms over finite fields using tools from computational harmonic analysis and also theoretical linear algebra. we present a concrete formulation for the frobenius norm of the classical wavelet transforms over finite fields. it is shown that each vector defined over a finite field can be represented as...