Showing papers by "William A. Pearlman published in 1996"

A new, fast, and efficient image codec based on set partitioning in hierarchical trees

Abstract: Embedded zerotree wavelet (EZW) coding, introduced by Shapiro (see IEEE Trans. Signal Processing, vol.41, no.12, p.3445, 1993), is a very effective and computationally simple technique for image compression. We offer an alternative explanation of the principles of its operation, so that the reasons for its excellent performance can be better understood. These principles are partial ordering by magnitude with a set partitioning sorting algorithm, ordered bit plane transmission, and exploitation of self-similarity across different scales of an image wavelet transform. Moreover, we present a new and different implementation based on set partitioning in hierarchical trees (SPIHT), which provides even better performance than our previously reported extension of EZW that surpassed the performance of the original EZW. The image coding results, calculated from actual file sizes and images reconstructed by the decoding algorithm, are either comparable to or surpass previous results obtained through much more sophisticated and computationally complex methods. In addition, the new coding and decoding procedures are extremely fast, and they can be made even faster, with only small loss in performance, by omitting entropy coding of the bit stream by the arithmetic code.

An image multiresolution representation for lossless and lossy compression

Abstract: We propose a new image multiresolution transform that is suited for both lossless (reversible) and lossy compression. The new transformation is similar to the subband decomposition, but can be computed with only integer addition and bit-shift operations. During its calculation, the number of bits required to represent the transformed image is kept small through careful scaling and truncations. Numerical results show that the entropy obtained with the new transform is smaller than that obtained with predictive coding of similar complexity. In addition, we propose entropy-coding methods that exploit the multiresolution structure, and can efficiently compress the transformed image for progressive transmission (up to exact recovery). The lossless compression ratios are among the best in the literature, and simultaneously the rate versus distortion performance is comparable to those of the most efficient lossy compression methods.

Analysis of linear prediction, coding, and spectral estimation from subbands

Abstract: Linear prediction schemes make a prediction x/spl circ//sub i/ of a data sample x/sub i/ using p previous samples. It has been shown by Woods and O'Neil (1986) as well as Pearlman (1991) that as the order of prediction p/spl rarr//spl infin/, there is no gain to be obtained by coding subband samples. This paper deals with the less well understood theory of finite-order prediction and optimal coding from subbands which are generated by ideal (brickwall) filtering of a stationary Gaussian source. We first prove that pth-order prediction from subbands is superior to pth-order prediction in the fullband, when p is finite. This fact adduces that optimal vector p-tuple coding in the subbands is shown to offer quantifiable gains over optimal fullband p-tuple coding, again when p is finite. The properties of subband spectra are analyzed using the spectral flatness measure. These results are used to prove that subband DPCM provides a coding gain over fullband DPCM, for finite orders of prediction. In addition, the proofs provide means of quantifying the subband advantages in linear prediction, optimal coding, and DPCM coding in the form of gain formulas. Subband decomposition of a source is shown to result in a whitening of the composite subband spectrum. This implies that, for any stationary source, a pth-order prediction error filter (PEF) can be found that is better than the pth-order PEF obtained by solving the Yule-Walker equations resulting from the fullband data. We demonstrate the existence of such a "super-optimal" PEF and provide algorithmic approaches to obtaining this PEF. The equivalence of linear prediction and AR spectral estimation is then exploited to show theoretically, and with simulations, that AR spectral estimation from subbands offers a gain over fullband AR spectral estimation.

Three-dimensional subband coding of video using the zero-tree method

Abstract: In this paper, a simple yet highly effective video compression technique is presented. The zerotree method by Said, which is an improved version of Shapiro's original one, is applied and expanded to three-dimension to encode image sequences. A three-dimensional subband transformation on the image sequences is first performed, and the transformed information is then encoded using the zerotree coding scheme. The algorithm achieves results comparable to MPEG-2, without the complexity of motion compensation. The reconstructed image sequences have no blocking effects at very low rates, and the transmission is progressive.© (1996) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Three-dimensional subband coding of video using the zero-tree method

Abstract: In this paper, a simple yet highly effective video compression technique is presented. The zerotree method by Said 3 , 4 which is an improved version of Shapiro's 1 2 original one, is applied and expanded to three-dimension to encode image sequences. A three-dimensional subband transformation on the image sequences is first performed, and the transformed information is then encoded using the zerotree coding scheme. The algorithm achieves results comparable to MPEG-2, without the complexity of motion compensation. The reconstructed image sequences have no blocking effects at very low rates, and the transmission is progressive.

Texture coding using a Wold decomposition model

Abstract: A novel approach for coding textured images is presented. The texture field is assumed to be a realization of a regular homogeneous random field, which can have a mixed spectral distribution. On the basis of a two-dimensional (2-D) Wold-like decomposition, the field is represented as a sum of a purely indeterministic, harmonic, and countable number of evanescent fields. We present an algorithm for estimating and coding the texture model parameters, and show that the suggested algorithm yields high-quality reconstructions at low bit rates. The model and the resulting coding algorithm are seen to be applicable to a wide variety of texture types found in natural images.

A closed form expression for an efficient class of quadrature mirror filters and its FIR approximation

Abstract: We find a simple closed form expression for an efficient class of Quadrature Mirror Filters (QMF's) by exploiting the inherent symmetry of the QMF property. We derive a simple rule of thumb to calculate the maximum feasible frequency selectivity of the filter for a given number N of filter taps. We show that, for even n, the frequency selectivity of a 2n+1 or 2n tap filter can be increased if and only if the number of taps is increased by at least 4. Most existing QMF's closely match the derived analytical expression as well as verify the results on frequency selectivity. We obtain FIR implementations of the aforementioned analytical expression by using the Remez allocation algorithm. We choose weighting functions that confine the error to the intersection of the transition band and the stop band of the filter, as well as force the magnitude of the passband ripple to be much lower than that of the stopband ripple. We make such a choice in order to optimally satisfy the power complementarity condition as well as to attain high stop band attenuation. Our implementations match existing designs in performance.

Variable-length tree-structured subvector quantization

Abstract: It is demonstrated in this paper that the encoding complexity advantage of a variable-length tree-structured vector quantizer (VLTSVQ) can be enhanced by encoding low dimensional subvectors of a source vector instead of the source vector itself at the nodes of the tree structure without significantly sacrificing coding performance. The greedy tree growing algorithm for the design of such a vector quantizer codebook is outlined. Different ways of partitioning the source vector into its subvectors and several criteria of interest for selecting the appropriate subvector for making the encoding decision at each node are discussed. Techniques of tree pruning and resolution reduction are applied to obtain improved coding performance at the same low encoding complexity. Application of an orthonormal transformation such as KLT or subband transformation to the source and the implication of defining the subvectors from orthogonal subspaces are also discussed. Finally simulation results on still images and AR(1) source are presented to confirm our propositions.© (1996) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.