Fast adaptive wavelet packet image compression

Abstract

Wavelets are ill-suited to represent oscillatory patterns: rapid variations of intensity can only be described by the small scale wavelet coefficients, which are often quantized to zero, even at high bit rates. Our goal is to provide a fast numerical implementation of the best wavelet packet algorithm in order to demonstrate that an advantage can be gained by constructing a basis adapted to a target image. Emphasis is placed on developing algorithms that are computationally efficient. We developed a new fast two-dimensional (2-D) convolution decimation algorithm with factorized nonseparable 2-D filters. The algorithm is four times faster than a standard convolution-decimation. An extensive evaluation of the algorithm was performed on a large class of textured images. Because of its ability to reproduce textures so well, the wavelet packet coder significantly out performs one of the best wavelet coder on images such as Barbara and fingerprints, both visually and in term of PSNR.

Low bit-rate efficient compression for seismic data

“…The fast decomposition is described in [16]. 2) Uniform scalar quantization: The quantiztion operates differently in the encoder and the decoder.…”

“…Instead of using adaptive arithmetic coder as in Section II-A, we can use the run-length encoding that is being used in [16]. Then, in each quantization loop we encode by run-length the appropriate bit across the zerotree decomposition.…”

“…To alleviate this problem new compression methods were devised. They are based on wavelet, larger libraries of waveforms, called wavelet packets [9], [10], [16], local cosine transform [8] and its associated multiresolution and best-basis methodology, and hybrid of wavelet with either wavelet packet or local cosine [17]. The previous successful wavelet based compression methods [2], [3], [5], [18], [19] for multimedia applications used quantization techniques that were based on zerotree coding of correlated coefficients among related coefficients in the multiresolution decomposition which exploits the correlation among the wavelet coefficients from the same spatial place at different resolutions.…”

“…They are also applicable to regular still (multimedia) images [16], [17]. Method 7 is also new for the seismic processing.…”

“…All the wavelet decompositions that are used in this paper are fast and they are based on one-dimensional (1-D) and two-dimensional (2-D) filter factorization which is described in detail in [16]. They are faster than the separable regular tensor (side by side) wavelet decomposition by factor of at least 4 [5].…”