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/.

/pdf/image-quality-assessment-from-error-visibility-to-structural-1rlwcqe34t.pdf

Image quality assessment: from error visibility to structural similarity

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 …

I and i

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.

http://ahvazdownload.persiangig.com/document/article/39.pdf

A wavelet tour of signal processing

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.

http://dns2.asia.edu.tw/~ysho/YSHO-English/2000%20Engineering/PDF/IEE%20Tra%20Cir%20Sys%20Vid%20Tec6,%20243.pdf

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

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 >

http://dns2.asia.edu.tw/~ysho/YSHO-English/2000%20Engineering/PDF/IEE%20Tra%20Sig%20Pro41,%203445.pdf

Embedded image coding using zerotrees of wavelet coefficients

This paper proposes an efficient, low complexity audio coder based on the SPIHT (set partitioning in hierarchical trees) coding algorithm , which has achieved notable success in still image coding. A wavelet packet transform is used to decompose the audio signal into 29 frequency subbands corresponding roughly to the critical subbands of the human auditory system. A psychoacoustic model, which, for simplicity, is based on MPEG model I, is used to calculate the signal to mask ratio, and then calculate the bit rate allocation among subbands. We distinguish the subbands into two groups: the low frequency group which contains the first 17 subbands corresponding to 0-3.4 kHz, and the high frequency group which contains the remaining high frequency subbands. The SPIHT algorithm is used to encode and decode the low frequency group and a reverse sorting process plus arithmetic coding algorithm is used to encode and decode the high frequency group. The experiment shows that this coder yields nearly transparent quality at bit rates 55-66 kbits/sec, and degrades only gradually at lower rates. The low complexity of this coding system shows its potential for interactive applications with levels of quality from good to perceptually transparent.

An efficient, low-complexity audio coder delivering multiple levels of quality for interactive applications

With clear and easy-to-understand explanations, this book covers the fundamental concepts and coding methods of signal compression, whilst still retaining technical depth and rigor. It contains a wealth of illustrations, step-by-step descriptions of algorithms, examples and practice problems, which make it an ideal textbook for senior undergraduate and graduate students, as well as a useful self-study tool for researchers and professionals. Principles of lossless compression are covered, as are various entropy coding techniques, including Huffman coding, arithmetic coding and Lempel-Ziv coding. Scalar and vector quantization and trellis coding are thoroughly explained, and a full chapter is devoted to mathematical transformations including the KLT, DCT and wavelet transforms. The workings of transform and subband/wavelet coding systems, including JPEG2000 and SBHP image compression and H.264/AVC video compression, are explained and a unique chapter is provided on set partition coding, shedding new light on SPIHT, SPECK, EZW and related methods.

Digital Signal Compression: Principles and Practice

This paper focuses on lossless medical image compression methods for 3D volumetric medical images that operate on three-dimensional (3D) reversible integer wavelet transforms. We offer an application of the Set Partitioning in Hierarchical Trees (SPIHT) algorithm to volumetric medical images, using a 3D wavelet decomposition and a 3D spatial dependence tree. The wavelet decomposition is accomplished with integer wavelet filters implemented with the lifting method, where careful scaling and truncations keep the integer precision small and the transform unitary. We have tested our encoder on volumetric medical images using different integer filters and different coding unit sizes. The coding unit sizes of 16 and 8 slices save considerable memory and coding delay from full sequence coding units used in previous works. Results show that, even with these small coding units, our algorithm with certain filters performs as well and sometimes better in lossless coding than previously coding systems using 3D integer wavelet transforms on volumetric medical images.

Lossless volumetric medical image compression

An adaptation procedure is introduced for determining in real-time the extent on the analysis window in point estimation of signals corrupted by additive noise. In the tasks of restoring a noisy one-dimensional test signal and a two-dimensional noisy image, mean, median and minimum-mean-square-error filters are compared with fixed and adaptive window implementations. The visual results of the signal and image restorations exhibit superior preservation of edge and detail and suppression of noise for the filters with adaptive windows. >

Edge-preserving noise filtering based on adaptive windowing

In this paper, we investigate a two-stage near-lossless compression scheme. It is in the spirit of "lossy plus residual coding" and consists of a wavelet-based lossy layer followed by an arithmetic coding of the quantized residual to guarantee a given L/sup /spl infin// error bound in the pixel domain. Our focus is on the selection of the optimum bit rate for the lossy layer to achieve the minimum total bit rate. Unlike other similar lossy plus lossless approaches using a wavelet-based lossy layer, the proposed method does not require iteration of decoding and the IWT(Inverse Wavelet Transform) to locate the optimum bit rate. We propose a simple method to estimate the optimal bit rate and provide a theoretical justification for it. It is based on the 'critical rate' argument from the Rate-Distortion theory and 'whiteness' of the residual.

William A. Pearlman

Papers

An efficient, low-complexity audio coder delivering multiple levels of quality for interactive applications

Digital Signal Compression: Principles and Practice

Lossless volumetric medical image compression

Edge-preserving noise filtering based on adaptive windowing

A wavelet-based two-stage near-lossless coder