William A. Pearlman

Bio: William A. Pearlman is an academic researcher from Rensselaer Polytechnic Institute. The author has contributed to research in topics: Data compression & Set partitioning in hierarchical trees. The author has an hindex of 36, co-authored 202 publications receiving 12924 citations. Previous affiliations of William A. Pearlman include Texas A&M University & University of Wisconsin-Madison.

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.

3D set partitioning coding methods in hyperspectral image compression

Abstract: Hyperspectral images are generated by collecting hundreds of narrow and contiguously spaced spectral bands of data producing a highly correlated long sequence of images. Some application specific data compression techniques may be applied advantageously before we process, store or transmit hyperspectral images. This paper applies asymmetric tree 3DSPIHT (AT-3DSPIHT) for hyperspectral image compression; it also investigates and compares the performance of the AT-3DSPIHT, 3DSPIHT and 3DSPECK on hyperspectral image compression. Results show that the AT-3DSPIHT outperforms the other two by the approximate range of 0.2 to 0.9 dB PSNR. It guarantees over 4 dB PSNR improvement at all rates or rate savings at least a factor of 2.5 over 2D coding of separate spectral bands without axial transformation.

Optimal encoding of discrete-time continuous-amplitude memoryless sources with finite output alphabets

Abstract: A rate-distortion theory is introduced for the optimal encoding of stationary memoryless continuous-amplitude sources with a single-letter distortion measure and reproduction alphabets of a given finite size. The theory arises from a judicious approximation of the original continuous-input discrete-output problem by one with discrete input and output. A size-constrained output alphabet rate-distortion function is defined, its coding significance is established by coding theorems, and a convergent algorithm is presented for its evaluation. The theory is applied to Gaussian sources with squared-error distortion measure. Using the algorithm for the calculation of the new rate-distortion function in this case establishes the existence of codes which attain almost any desired rate between the rate-distortion bound and the optimum entropy-coded quantizer. Furthermore, one can closely approach the rate-distortion limit with a surprisingly small number of output levels. The calculation furnishes optimal output levels, output level probabilities, and other parameters necessary for a trellis coding simulation. The search algorithm represents the first use for asymmetric sources and distortion measures of a variation of a single stack algorithm proposed by Gallager. Carrying out the simulation at a rate of 1 bit per source symbol, codes are found with 4 and 64 output levels which attain distortions smaller than that of an optimum quantizer and close to the rate-distortion bound. Furthermore, these codes attain comparable or better performance with far less search effort than previous attempts with a continuous output alphabet.

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.

SBHP-a low complexity wavelet coder

Abstract: We present a low-complexity entropy coder originally designed to work in the JPEG2000 image compression standard framework. The algorithm is meant for embedded and non-embedded coding of wavelet coefficients inside a subband, and is called subband-block hierarchical partitioning (SBHP). It was extensively tested following the standard experiment procedures, and it was shown to yield a significant reduction in the complexity of entropy coding, with small loss in compression performance. Furthermore, it is able to seamlessly support all JPEG2000 features. We present a description of the algorithm, an analysis of its complexity, and a summary of the results obtained after its integration into the verification model (VM).

Image quality assessment: from error visibility to structural similarity

Abstract: Objective methods for assessing perceptual image quality traditionally attempted to quantify the visibility of errors (differences) between a distorted image and a reference image using a variety of known properties of the human visual system. Under the assumption that human visual perception is highly adapted for extracting structural information from a scene, we introduce an alternative complementary framework for quality assessment based on the degradation of structural information. As a specific example of this concept, we develop a structural similarity index and demonstrate its promise through a set of intuitive examples, as well as comparison to both subjective ratings and state-of-the-art objective methods on a database of images compressed with JPEG and JPEG2000. A MATLAB implementation of the proposed algorithm is available online at http://www.cns.nyu.edu//spl sim/lcv/ssim/.

I and i

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

A wavelet tour of signal processing

Abstract: Introduction to a Transient World. Fourier Kingdom. Discrete Revolution. Time Meets Frequency. Frames. Wavelet Zoom. Wavelet Bases. Wavelet Packet and Local Cosine Bases. An Approximation Tour. Estimations are Approximations. Transform Coding. Appendix A: Mathematical Complements. Appendix B: Software Toolboxes.

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.

Embedded image coding using zerotrees of wavelet coefficients

Abstract: The embedded zerotree wavelet algorithm (EZW) is a simple, yet remarkably effective, image compression algorithm, having the property that the bits in the bit stream are generated in order of importance, yielding a fully embedded code The embedded code represents a sequence of binary decisions that distinguish an image from the "null" image Using an embedded coding algorithm, an encoder can terminate the encoding at any point thereby allowing a target rate or target distortion metric to be met exactly Also, given a bit stream, the decoder can cease decoding at any point in the bit stream and still produce exactly the same image that would have been encoded at the bit rate corresponding to the truncated bit stream In addition to producing a fully embedded bit stream, the EZW consistently produces compression results that are competitive with virtually all known compression algorithms on standard test images Yet this performance is achieved with a technique that requires absolutely no training, no pre-stored tables or codebooks, and requires no prior knowledge of the image source The EZW algorithm is based on four key concepts: (1) a discrete wavelet transform or hierarchical subband decomposition, (2) prediction of the absence of significant information across scales by exploiting the self-similarity inherent in images, (3) entropy-coded successive-approximation quantization, and (4) universal lossless data compression which is achieved via adaptive arithmetic coding >