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.

Region-based wavelet coding methods for digital mammography

Abstract: Spatial resolution and contrast sensitivity requirements for some types of medical image techniques, including mammography, delay the implementation of new digital technologies, namely, computer-aided diagnosis, picture archiving and communications systems, or teleradiology. In order to reduce transmission time and storage cost, an efficient data-compression scheme to reduce digital data without significant degradation of medical image quality is needed. In this study, we have applied two region-based compression methods to digital mammograms. In both methods, after segmenting the breast region, a region-based discrete wavelet transform is applied, followed by an object-based extension of the set partitioning in hierarchical trees (OB-SPIHT) coding algorithm in one method, and an object-based extension of the set partitioned embedded block (OB-SPECK) coding algorithm in the other. We have compared these specific implementations against the original SPIHT and the new standard JPEG 2000, both using reversible and irreversible filters, on five digital mammograms compressed at rates ranging from 0.1 to 1.0 bit per pixel (bbp). Distortion was evaluated for all images and compression rates by the peak signal-to-noise ratio. For all images, OB-SPIHT and OB-SPECK performed substantially better than the traditional SPIHT and JPEG 2000, and a slight difference in performance was found between them. A comparison applying SPIHT and the standard JPEG 2000 to the same set of images with the background pixels fixed to zero was also carried out, obtaining similar implementation as region-based methods. For digital mammography, region-based compression methods represent an improvement in compression efficiency from full-image methods, also providing the possibility of encoding multiple regions of interest independently.

A full-featured, error-resilient, scalable wavelet video codec based on the set partitioning in hierarchical trees (SPIHT) algorithm

Abstract: Compressed video bitstreams require protection from channel errors in a wireless channel. The 3-D set partitioning in hierarchical trees (SPIHT) coder has proved its efficiency and its real-time capability in the compression of video. A forward-error-correcting (FEC) channel (RCPC) code combined with a single automatic-repeat request (ARQ) proved to be an effective means for protecting the bitstream. There were two problems with this scheme: (1) the noiseless reverse channel ARQ may not be feasible in practice and (2) in the absence of channel coding and ARQ, the decoded sequence was hopelessly corrupted even for relatively clean channels. We eliminate the need for ARQ by making the 3-D SPIHT bitstream more robust and resistant to channel errors. We first break the wavelet transform into a number of spatio-temporal tree blocks which can be encoded and decoded independently by the 3-D SPIHT algorithm. This procedure brings the added benefit of parallelization of the compression and decompression algorithms, and enables implementation of region-based coding. We demonstrate the packetization of the bitstream and the reorganization of these packets to achieve scalability in bit rate and/or resolution in addition to robustness. Then we encode each packet with a channel code. Not only does this protect the integrity of the packets in most cases, but it also allows detection of packet-decoding failures, so that only the cleanly recovered packets are reconstructed. In extensive comparative tests, the reconstructed video is shown to be superior to that of MPEG-2, with the margin of superiority growing substantially as the channel becomes noisier. Furthermore, the parallelization makes possible real-time implementation in hardware and software.

N-dimensional data compression using set partitioning in hierarchical trees

Abstract: A data structure in a computer memory for use in encoding and decoding an N-dimensional subband decomposition of data points includes, after initialization, three lists: a list of insignificant sets of points (LIS); a list of significant points (LSP); and a list of insignificant points (LIP). The LIS is populated with sets, each of the sets being designated by a root node within the N-dimensional subband decomposition and having a corresponding tree structure of points within the N-dimensional subband decomposition, which tree structure of points is organized as descendants and offspring of the root node but not including the root node, the LIP is populated with points from within the highest designated subband of the N-dimensional subband decomposition, while the LSP is initially empty. The data structure permits encoding and decoding of any N-dimensional data set, i.e., any data set where N is a positive integer. Method and software for employing this data structure are also described.

Hyperspectral Image Compression Using Three-Dimensional Wavelet Coding

Abstract: A Hyperspectral image is a sequence of images generated by collecting contiguously spaced spectral bands of data. One can view such an image sequence as a three-dimensional array of intensity values (pixels) within a rectangular prism. We present a Three-Dimensional Set Partitioned Embedded bloCK (3DSPECK) algorithm based on the observation that hyperspectral images are contiguous in the spectrum axis (this implies large inter-band correlations) and there is no motion between bands. Therefore, the three-dimensional discrete wavelet transform can fully exploit the inter-band correlations. A SPECK partitioning algorithm extended to three-dimensions is used to sort significant pixels. Rate distortion (Peak Signal-to-Noise Ratio (PSNR) vs. bit rate) performances were plotted by comparing 3DSPECK against 3DSPIHT on several sets of hyperspectral images. Results show that 3DSPECK is comparable to 3DSPIHT in hyperspectral image compression. 3DSPECK can achieve compression ratios in the approximate range of 16 to 27 while providing very high quality reconstructed images. It guarantees over 3 dB PSNR improvement at all rates or rate saving at least a factor of 2 over 2D coding of separate spectral bands without axial transformation.

Source coding of the discrete Fourier transform

Abstract: Distortion-rate theory is used to derive absolute performance bounds and encoding guidelines for direct fixed-rate minimum mean-square error data compression of the discrete Fourier transform (DFT) of a stationary real or circularly complex sequence. Both real-part-imaginary-part and magnitude-phase-angle encoding are treated. General source coding theorems are proved in order to justify using the optimal test channel transition probability distribution for allocating the information rate among the DFT coefficients and for calculating arbitrary performance measures on actual optimal codes. This technique has yielded a theoretical measure of the relative importance of phase angle over the magnitude in magnitude-phase-angle data compression. The result is that the phase angle must be encoded with 0.954 nats, or 1.37 bits, more rate than the magnitude for rates exceeding 3.0 nats per complex element. This result and the optimal error bounds are compared to empirical results for efficient quantization schemes.

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 >