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

The purpose of this two-part monograph is to present a tutorial on set partition coding, with emphasis and examples on image wavelet transform coding systems, and describe their use in modern image coding systems. Set partition coding is a procedure that recursively splits groups of integer data or transform elements guided by a sequence of threshold tests, producing groups of elements whose magnitudes are between two known thresholds, therefore, setting the maximum number of bits required for their binary representation. It produces groups of elements whose magnitudes are less than a certain known threshold. Therefore, the number of bits for representing an element in a particular group is no more than the base-2 logarithm of its threshold rounded up to the nearest integer. SPIHT (Set Partitioning in Hierarchical Trees) and SPECK (Set Partitioning Embedded blocK) are popular state-of-the-art image coders that use set partition coding as the primary entropy coding method. JPEG2000 and EZW (Embedded Zerotree Wavelet) use it in an auxiliary manner. Part I elucidates the fundamentals of set partition coding and explains the setting of thresholds and the block and tree modes of partitioning. Algorithms are presented for the techniques of AGP (Amplitude and Group Partitioning), SPIHT, SPECK, and EZW. Numerical examples are worked out in detail for the latter three techniques. Part II describes various wavelet image coding systems that use set partitioning primarily, such as SBHP (Subband Block Hierarchical Partitioning), SPIHT, and EZBC (Embedded Zero-Block Coder). The basic JPEG2000 coder is also described. The coding procedures and the specific methods are presented both logically and in algorithmic form, where possible. Besides the obvious objective of obtaining small file sizes, much emphasis is placed on achieving low computational complexity and desirable output bitstream attributes, such as embeddedness, scalability in resolution, and random access decodability.

This monograph is extracted and adapted from the forthcoming textbook entitled Digital Signal Compression: Principles and Practice by William A. Pearlman and Amir Said, Cambridge University Press, 2009.

/pdf/set-partition-coding-part-i-of-set-partition-coding-and-2usmkg2raf.pdf

Set Partition Coding: Part I of Set Partition Coding and Image Wavelet Coding Systems

The purpose of this chapter is to present some tutorial material in information theory which is pertinent to the subject of subband coding and to develop this material further in order to gain insight into the superior performance realized in subband coding systems. Except for the well-known result that PCM coding of subbands outperforms direct PCM coding of the full-band original (see [7]), which is known to be generally inefficient, there have been hardly any theoretical analyses which have shown a mean-squared error improvement for subband coding. The superior results of subband coding systems are largely empirical in nature and they have indeed been impressive in coding of images. In this chapter these superior results are quantified in formulas, which have not yet appeared in print elsewhere.

Performance Bounds for Subband Coding

An adaptive block discrete-cosine transform (DCT) coding scheme is implemented with the same average distortion designated for each block. This constant distortion designation not only has perceptual advantages, but also allows the rate to vary, adjusting to the changing spectral characteristics among the blocks. The successful execution of this scheme requires a different spectral estimate for each block. To keep overhead and computation within limits, a novel technique is introduced by which a two-dimensional block spectrum is characterized by a one-dimensional autoregressive model. Simulations with images of natural scenes and medical radiology provide reconstructions with nearly uniform block distortion and very high visual and measurable quality at low rates. >

Adaptive cosine transform image coding with constant block distortion

We propose a new low-complexity entropy-coding method to be used for coding waveform signals. It is based on the combination of two schemes: (1) an alphabet partitioning method to reduce the complexity of the entropy-coding process; (2) a new recursive set partitioning entropy-coding process that achieves rates smaller than first order entropy even with fast Huffman adaptive codecs. Numerical results with its application for lossy and lossless image compression show the efficacy of the new method, comparable to the best known methods.© (1997) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Low-complexity waveform coding via alphabet and sample-set partitioning

In addition to high compression efficiency, future still and moving image coding systems will require many other features They include fidelity and resolution scalability, region of interest enhancement, random access decoding, resilience to errors due to channel noise or packet loss, fast encoding and/or decoding speed, and low computational and hardware complexity Moreover, there are emerging new venues for the application of image compression techniques to data associated with points of a two or three-dimensional grid that will demand these features and perhaps others We shall discuss these new venues along with the usual ones and show how tree-based, set-partitioning wavelet coding methods, such as SPIHT (Set Partitioning in Hierarchical Trees) and SPECK (Set Partitioning Embedded bloCK) will fulfill most of the demands of current and future applications We shall also discuss the emerging JPEG-2000 in this framework

/pdf/trends-of-tree-based-set-partitioning-compression-techniques-3q6ov1spte.pdf

William A. Pearlman

Papers

Set Partition Coding: Part I of Set Partition Coding and Image Wavelet Coding Systems

Performance Bounds for Subband Coding

Adaptive cosine transform image coding with constant block distortion

Low-complexity waveform coding via alphabet and sample-set partitioning

Trends of Tree-Based, Set-Partitioning Compression Techniques in Still and Moving Image Systems