An LPC Excitation Model Using Wavelets

This paper presents a new model of linear predictive coding (LPC) excitation using wavelets for speech signals. The LPC excitation becomes a linear combination of a set of self- similar, orthonormal, band-pass signals with time localization and constant bandwidth in a logarithmic scale. Thus, the set of the coefficients in the linear combination represents the LPC excitation. The discrete wavelet transform (DWT) obtains the coefficients, having several asymmetrical and non-uniform distribution properties that are attractive for speech processing and compression. The properties include magnitude dependent sensitivity, scale dependent sensitivity, and limited frame length, which can be used for having low bit-rate speech. We show that eliminating 8.97% highest magnitude coefficients degrades speech quality down to 1.49dB SNR, while eliminating 27.51% lowest magnitude coefficient maintain speech quality at a level of 27.42 dB SNR. Furthermore eliminating 6.25% coefficients located at a scale associated with 175-630 Hz band severely degrades speech quality down to 4.20 dB SNR. Finally, our results show that optimal frame length for telephony applications is among 32, 64, or 128 samples

An LPC Excitation Model using Wavelets

This  paper  presents  a  new  model  of  linear  predictive  coding  (LPC) excitation  using  wavelets  for  speech  signals.   The  LPC  excitation   becomes  a linear combination of a set of self-  similar, orthonormal, band-pass signals with time localization and constant bandwidth in a logarithmic scale. Thus, the set of the  coefficients  in  the  linear  combination  represents  the  LPC  excitation.  The discrete  wavelet  transform  (DWT)  obtains  the  coefficients,  having  several asymmetrical  and  non-uniform  distribution  properties  that  are  attractive  for speech processing and compression. The properties include magnitude dependent sensitivity, scale dependent sensitivity, and limited frame length, which can be used  for  having  low  bit-rate  speech.  We  show  that  eliminating  8.97%  highest magnitude  coefficients  degrades  speech  quality  down  to  1.49dB  SNR,  while eliminating  27.51%  lowest  magnitude  coefficient  maintain  speech  quality  at  a level of 27.42 dB SNR. Furthermore eliminating 6.25% coefficients located at a scale associated with 175-630 Hz band severely degrades speech quality down to 4.20 dB SNR. Finally, our results show that optimal frame length for telephony applications is among 32, 64, or 128 samples

Hyperspectral image compression : adapting SPIHT and EZW to Anisotropic 3-D Wavelet Coding

Hyperspectral images present some specific characteristics that should be used by an efficient compression system. In compression, wavelets have shown a good adaptability to a wide range of data, while being of reasonable complexity. Some wavelet-based compression algorithms have been successfully used for some hyperspectral space missions. This paper focuses on the optimization of a full wavelet compression system for hyperspectral images. Each step of the compression algorithm is studied and optimized. First, an algorithm to find the optimal 3-D wavelet decomposition in a rate-distortion sense is defined. Then, it is shown that a specific fixed decomposition has almost the same performance, while being more useful in terms of complexity issues. It is shown that this decomposition significantly improves the classical isotropic decomposition. One of the most useful properties of this fixed decomposition is that it allows the use of zero tree algorithms. Various tree structures, creating a relationship between coefficients, are compared. Two efficient compression methods based on zerotree coding (EZW and SPIHT) are adapted on this near-optimal decomposition with the best tree structure found. Performances are compared with the adaptation of JPEG 2000 for hyperspectral images on six different areas presenting different statistical properties

Coding gain in paraunitary analysis/synthesis systems

A formal proof that bit allocation results hold for the entire class of paraunitary subband coders is presented. The problem of finding an optimal paraunitary subband coder, so as to maximize the coding gain of the system, is discussed. The bit allocation problem is analyzed for the case of the paraunitary tree-structured filter banks, such as those used for generating orthonormal wavelets. The even more general case of nonuniform filter banks is also considered. In all cases it is shown that under optimal bit allocation, the variances of the errors introduced by each of the quantizers have to be equal. Expressions for coding gains for these systems are derived

Graph Spectral Image Processing

Recent advent of graph signal processing (GSP) has spurred intensive studies of signals that live naturally on irregular data kernels described by graphs (e.g., social networks, wireless sensor networks). Though a digital image contains pixels that reside on a regularly sampled 2D grid, if one can design an appropriate underlying graph connecting pixels with weights that reflect the image structure, then one can interpret the image (or image patch) as a signal on a graph, and apply GSP tools for processing and analysis of the signal in graph spectral domain. In this article, we overview recent graph spectral techniques in GSP specifically for image / video processing. The topics covered include image compression, image restoration, image filtering and image segmentation

Regularity scalable image coding based on wavelet singularity detection

In this paper, we propose an adaptive algorithm for scalable wavelet image coding, which is based on the general feature, the regularity, of images. In pattern recognition or computer vision, regularity of images is estimated from the oriented wavelet coefficients and quantified by the Lipschitz exponents. To estimate the Lipschitz exponents, evaluating the interscale evolution of the wavelet transform modulus sum (WTMS) over the directional cone of influence was proven to be a better approach than tracing the wavelet transform modulus maxima (WTMM). This is because the irregular sampling nature of the WTMM complicates the reconstruction process. Moreover, examples were found to show that the WTMM representation cannot uniquely characterize a signal. It implies that the reconstruction of signal from its WTMM may not be consistently stable. Furthermore, the WTMM approach requires much more computational effort. Therefore, we use the WTMS approach to estimate the regularity of images from the separable wavelet transformed coefficients. Since we do not concern about the localization issue, we allow the decimation to occur when we evaluate the interscale evolution. After the regularity is estimated, this information is utilized in our proposed adaptive regularity scalable wavelet image coding algorithm. This algorithm can be simply embedded into any wavelet image coders, so it is compatible with the existing scalable coding techniques, such as the resolution scalable and signal-to-noise ratio (SNR) scalable coding techniques, without changing the bitstream format, but provides more scalable levels with higher peak signal-to-noise ratios (PSNRs) and lower bit rates. In comparison to the other feature-based wavelet scalable coding algorithms, the proposed algorithm outperforms them in terms of visual perception, computational complexity and coding efficienc

Steerable Discrete Cosine Transform

In image compression, classical block-based separable transforms tend to be inefficient when image blocks contain arbitrarily shaped discontinuities. For this reason, transforms incorporating directional information are an appealing alternative. In this paper, we propose a new approach to this problem, namely a discrete cosine transform (DCT) that can be steered in any chosen direction. Such transform, called steerable DCT (SDCT), allows to rotate in a flexible way pairs of basis vectors, and enables precise matching of directionality in each image block, achieving improved coding efficiency. The optimal rotation angles for SDCT can be represented as solution of a suitable rate-distortion (RD) problem. We propose iterative methods to search such solution, and we develop a fully fledged image encoder to practically compare our techniques with other competing transforms. Analytical and numerical results prove that SDCT outperforms both DCT and state-of-the-art directional transforms