Best-basis Selection Research Articles

EGHWT: The Extended Generalized Haar\u2013Walsh Transform

Extending computational harmonic analysis tools from the classical setting of regular lattices to the more general setting of graphs and networks is very important, and much research has been done recently. The generalized Haar–Walsh transform (GHWT) developed by Irion and Saito (2014) is a multiscale transform for signals on graphs, which is a generalization of the classical Haar and Walsh–Hadamard transforms. We propose the extended generalized Haar–Walsh transform (eGHWT), which is a generalization of the adapted time–frequency tilings of Thiele and Villemoes (1996). The eGHWT examines not only the efficiency of graph-domain partitions but also that of “sequency-domain” partitions simultaneously. Consequently, the eGHWT and its associated best-basis selection algorithm for graph signals significantly improve the performance of the previous GHWT with the similar computational cost, O(N log N), where N is the number of nodes of an input graph. While the GHWT best-basis algorithm seeks the most suitable orthonormal basis for a given task among more than (1.5)^N possible orthonormal bases in mathbb {R}^N, the eGHWT best-basis algorithm can find a better one by searching through more than 0.618cdot (1.84)^N possible orthonormal bases in mathbb {R}^N. This article describes the details of the eGHWT best-basis algorithm and demonstrates its superiority using several examples including genuine graph signals as well as conventional digital images viewed as graph signals. Furthermore, we also show how the eGHWT can be extended to 2D signals and matrix-form data by viewing them as a tensor product of graphs generated from their columns and rows and demonstrate its effectiveness on applications such as image approximation.

Automatic best-basis selection for geophysical tomographic inverse problems

Automatic best-basis selection for geophysical tomographic inverse problems

Medical ultrasound image compression using joint optimization of thresholding quantization and best-basis selection of wavelet packets

This paper introduces an efficient image-coding algorithm using wavelet packets. The algorithm combines the top-down search approach with an operational rate-distortion (R-D) cost function to select the best wavelet packet basis at low-computational cost. The proposed method jointly optimizes the best-basis selection, coefficient ''thresholding'' and quantizer selection within the minimum description length (MDL) framework to develop a wavelet packet image coder named as JTQ-WP. We present results to verify the usefulness and versatility of this adaptive image coder both on medical US-images and natural images. The experimental results show that the joint optimization has a dramatic effect on the compression performance of medical ultrasound images. To further demonstrate the potential performance of the proposed method in comparison with the current state-of-the-art image coding algorithms, the results on Barbara image are also presented. The results show a coding gain of 0.91 dB over the benchmark wavelet-coding algorithm, SPIHT, on the Barbara image at a bit-rate of 0.25 bpp.

Wavelets in temporal and spatial processing of biomedical images.

We review some of the most recent advances in the area of wavelet applications in medical imaging. We first review key concepts in the processing of medical images with wavelet transforms and multiscale analysis, including time-frequency tiling, overcomplete representations, higher dimensional bases, symmetry, boundary effects, translational invariance, orientation selectivity, and best-basis selection. We next describe some applications in magnetic resonance imaging, including activation detection and denoising of functional magnetic resonance imaging and encoding schemes. We then present an overview in the area of ultrasound, including computational anatomy with three-dimensional cardiac ultrasound. Next, wavelets in tomography are reviewed, including their relationship to the radon transform and applications in position emission tomography imaging. Finally, wavelet applications in digital mammography are reviewed, including computer-assisted diagnostic systems that support the detection and classification of small masses and methods of contrast enhancement.

Optimal bit allocation and best-basis selection for wavelet packets and TSVQ

To use wavelet packets for lossy data compression, the following issues must be addressed: quantization of the wavelet subbands, allocation of bits to each subband, and best-basis selection. We present an algorithm for wavelet packets that systematically identifies all bit allocations/best-basis selections on the lower convex hull of the rate-distortion curve. We demonstrate the algorithm on tree-structured vector quantizers used to code image subbands from the wavelet packet decomposition.

Complexity-constrained best-basis wavelet packet algorithm for image compression

The concept of adapted waveform analysis using a best-basis selection out of a predefined library of wavelet packet (WP) bases allows an efficient image representation for the purpose of compression. Image coding methods based on the best-basis WP representation have shown significant coding gains for some image classes compared with methods using a fixed dyadic structured wavelet basis, at the expense however, of considerably higher computational complexity. A modification of the best-basis method, the so-called complexity constrained best-basis algorithm (CCBB), is proposed which parameterises the complexity gap between the fast (standard) wavelet transform and the best wavelet packet basis of a maximal WP library. This new approach allows a ‘suboptimal’ best basis to be found with respect to a given budget of computational complexity or, in other words, it offers an instrument to control the trade-off between compression speed and coding efficiency. Experimental results are presented for image coding applications showing a highly nonlinear relationship between the rate-distortion (RD) performance and the computational complexity in such a way that a relatively small increase in complexity with respect to the standard wavelet basis results in a relatively high RD gain.

Wavelet packet transform applied to a set of signals: A new approach to the best-basis selection

A new approach to best-basis selection for a set of signals, enabling significant and uniform data compression in the time-frequency domain, is proposed. The high degree of data compression can be used as the first step of fast approximate principal component analysis (PCA) of data sets with high rank (∼ 10 4). The performance of the proposed approach is tested for two data sets and compared with Wickerhauser's approach of fast approximate PCA.