Brushlets: A Tool for Directional Image Analysis and Image Compression

Abstract

We construct a new adaptive basis of functions which is reasonably well localized with only one peak in frequency. We develop a compression algorithm that exploits this basis to obtain the most economical representation of the image in terms of textured patterns with different orientations, frequencies, sizes, and positions. The technique directly works in the Fourier domain and has potential applications for compression of highly textured images, texture analysis, etc. ᭧ 1997 Academic Press

LV volume quantification via spatiotemporal analysis of real-time 3-D echocardiography

“…By measuring a predefined cost function, such as entropy, the algorithm selects an optimal tiling of the Fourier domain where the energy of the signal is "best" decomposed. Meyer and Coifman [33] applied this algorithm on brushlet functions for compression of highly textured images. In the current application, optimal speckle noise removal is desired and a cost function adapted to denoising performance should be designed to carry out an optimal-basis search.…”

“…Brushlet functions are a new family of steerable wavelet packets based on the expansion of the Fourier transform (FT) of a signal onto windowed complex exponential functions. These functions, first introduced by Coifman and Meyer [33] for compression of highly texturized images, are well localized in both time and frequency. However, we point out that the goals of compression are completely opposite to this application.…”

“…This strategy is best suited for denoising and cardiac boundary enhancement as first suggested by Noble et al [32] with directional Gabor filters. In this paper, we use a new set of basis functions called brushlets, introduced by Coifman and Meyer in 1997 [33].…”

A multiresolution framework for local similarity based image denoising

“…Shrinkage methods in the transform domain approximate the image by modeling and efficiently representing important image features such as discontinuities [5], edges [6,7,8], curves [9,10,11], contours [12,13], ridges [14,15], and textured regions [16,17,18,19] present in the image or locally linear planes [20] in video sequences. Generally speaking, shrinkage methods first transform the image into some other domain, highlighting important image features, and thresholding the transform coefficients.…”

Sparse Image Representation by Directionlets

“…Apart from exploiting geometrical coherence, multi-directional (M-DIR) processing has also been applied to image denoising and classification. Examples of such transforms are the steerable pyramids (Simoncelli et al 1992), the cortex transform (Watson, 1987), complex wavelets (Kingsbury, 2001), the directional wavelet analysis (Zuidwijk, 2000), directional filter banks (Bamberger and Smith, 1992, Phoong et al, 1995, Rosiles and Smith, 2003, brushlets (Meyer and Coifman, 1997), and the associative representation of visual information (Granlund and Knutsson, 1990). Some other methods involve directionally adaptive processing in order to preserve edges in images (Muresan and Parks, 2000, Orchard, 2001, Hirakawa andParks, 2005), whereas the method proposed by Cunha et al (2006) imposes DVM in either critically sampled or oversampled filter banks.…”