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

Efficient low-complexity block entropy coding requires careful exploitation of specific data characteristics to circumvent the practical difficulties associated with large alphabets. Two recent image coding methods, alphabet and group partitioning (AGP) and set partitioning in hierarchical trees (SPIHT) can be viewed as block entropy coding methods, which are successful because of the manner in which they partition the alphabet into sets and encode these sets very efficiently. Here we present analysis and numerical results to show that AGP and SPIHT are indeed efficient block entropy coders.

Efficient block entropy coding with low complexity

Many scenarios require single frame random access and error resilience in coding, transmission, and decoding of image sequences We propose in this paper a SPIHT coder that encodes a sequence of images one frame at a time and uses two methods together to achieve strong error resilience The first method groups wavelet coefficients into a number of tree blocks and the second one encodes these tree blocks independently using SPIHT with progressive significance maps Because a substantial part of a progressive significance map contains a fixed-length code stream called the complementary significance map (comp-sigmap), transmission bit errors do not propagate within the compsig-map Furthermore, since the block trees are encoded independently, no error in a given bitstream propagates to another bitstream Simulations show that the two methods together show stronger error resilience than either one separately Furthermore, because the groups are formed by interleaved spatial orientation trees, faulty reconstruction from bit errors affecting a given treeblock can be concealed by estimating the true wavelet coefficients from neighboring coefficients in adjacent error-free spatial orien-

A Doubly Error Resilient Coder of Image Sequences.

There exists a transform trellis code that is optimal for stationary Gaussian sources and the squarederror distortion measure at all rates. In this paper we train an asymptotically optimal version of such a code to obtain one which is matched better to the statistics of real world data. The training algorithm uses the M-algorithm to search the trellis codebook and the LBG-algorithm to update the trellis codebook. To adapt the codebook for the varying input data we use two gain-adaptive methods. The gain-adaptive sheme 1 which normalizes input block data by its gain factor is applied to images at rate 0. 5 bits/pixel. When each block is encoded at the same rate the nonstationarity among the block variances leads to a variation in the resulting distortion from one block to another. To alleviate the non-uniformity among the encoded image we design four clusters from the block power in which each cluster has its own trellis codebook and different rates. The rate of each cluster is assigned through requiring a constant distortion per-letter. This gain-adaptive scheme 2 produces good visual and measurable quality at low rates.© (1990) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Gain-adaptive trained transform trellis code for images

We propose an elegant yet efficient adaptive subband coding scheme in which the rate allocation and structures of the quantizers are jointly optimized based on the time-varying rate-distortion characteristics of the input signals. By employing the tree-structured vector quantizers and the generalized BFOS pruning algorithm, the operations of the rate allocation and quantization are elegantly combined, whereby the adaptation is both convenient and optimal. The results on video coding have shown that the adaptive scheme can achieve substantial performance improvement over the non-adaptive scheme.

Adaptive joint rate allocation and quantization in subband signal coding

http://ieeexplore.ieee.org/iel4/557/4025/00695239.pdf

William A. Pearlman

Papers

Efficient block entropy coding with low complexity

A Doubly Error Resilient Coder of Image Sequences.

Gain-adaptive trained transform trellis code for images

Adaptive joint rate allocation and quantization in subband signal coding

Performance Gains Of Subband Coding