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

We have utilized for image coding a transform tree coding technique that is theoretically optimal for Gaussian sources and the squared error criterion at all nonzero rates. In the interest of affordable computation, we used a suboptimal discrete cosine transform to encode image sub-blocks and a selective search through the code tree. Coding simulations of a woman's face image at rates of 1.0 and 0.25 bits/pel gave good to excellent results. The rate 1.0 results were superior to previous ones using another tree coding method. Until now there have been no reported results with searched codes for images using a rate under 1.0 bit/pel. Encoding a computer-generated image source indicated SNR performance about 2dB less than the optimal SNR of the rate-distortion bound.

An optimal transform tree coding method applied to images

In this paper, we present a new image sequence coding scheme which employs backward motion compensation, quadtree segmentation, and pruned tree-structured vector quantization. Based only on the previous reconstructed frames, the backward motion compensation technique eliminates the necessity to transmit the motion displacement vectors as side information, and thus achieves a bit rate saving. Quadtree segmentation is used to exploit the regional characteristics of the signal. To take the advantage of the fact that many large areas of the motion compensated frame difference contain only low activity, the motion compensated frame difference is decomposed into large, low activity blocks and small, high activity blocks. The large blocks are encoded by their means while the small blocks are encoded by pruned tree-structured vector quantization (PTSVQ) at different rates. PTSVQ is both a multi-rate and variable rate coding technique and has the fast codebook search property due to its tree structure. It has been shown recently that PTSVQ may outperform full search unstructured VQ in the low bit rate range. Excellent results have been obtained in the computer simulation of this new scheme. When tested on the Salesman sequence, this interframe coding technique has achieved an average peak signal-to-noise ratio of 40.55 dB at an average bit rate of 0.43 bits per pixel, which indicates that the proposed scheme is suitable for low rate video applications.© (1992) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Multirate image sequence coding with quadtree segmentation and backward motion compensation

A robust method for restoration of photon- limited, blurred imagesWilliam A. Pearlman and Woo -Jin SongElectrical, Computer, and Systems Engineering DepartmentRensselaer Polytechnic InstituteTroy, N.Y. 12180AbstractA two -step procedure is developed for restoring low light level images degraded by alinear space- invariant blur. The first step uses a linear minimum mean square point esti-mate of the blurred image. The second removes the blur through a constrained linear leastsquares technique where the error of the first step is treated as additive noise. No priorknowledge of the object is required, as the procedure utilizes sample statistics in an anal-ysis window around each received image element to develop the estimators. The size of thewindow is adaptive, as it is adjusted for the next image element according to an activityindex computed for the current window. In experiments with simulated photon- noise -degraded,lineal- motion -blurred images, the efficacy of the procedure is demonstrated visually andmeasured by signal -to -noise ratio improvements.IntroductionA fundamental limitation in restoring images at low light levels is the photon noisearising from the random number of photoelectron counts during the observation interval foreach detector in the image detector array. Moreover, the image may also have suffered de-gradation in transmission through the atmosphere and in reception by a diffraction -limitedoptical system which may be moving relative to the object (image source). Here these atmos-pheric and optical system degradations shall be represented as a linear and spatially invar-iant filtering of the object. This paper addresses the problem of obtaining object estimatesfrom predominantly photon -limited images which have undergone lineal motion blur. These es-timates are obtained without prior knowledge of object or image statistics, as sample sta-tistics are generated upon reception and adaptively updated for different regions of the

A Robust Method For Restoration Of Photon-Limited, Blurred Images

Modern wavelet-based image compression methods provide not only higher compression performance, but also the capability to support various features, such as quality (SNR) scalability, resolution scalability, and region-of-interest encoding and decoding. Quality scalability is commonly achieved via bit-plane coding, which also helps to improve compression, since neighboring bits provide convenient and powerful contexts for entropy coding. However, on many important applications (e.g. digital camera), the images always need to have a pre-defined high quality, and any extra effort required for quality scalability is wasted. Furthermore, for compressing a very large size image source, a low time complexity is often the most desirable characteristic of an image coding algorithm. 
In this thesis, a resolution scalable and random accessible image coding algorithm, PROGRES (Progressive Resolution Decompression), is designed based on predictive dynamic range coding of wavelet coefficients and without bit-plane coding. Avoiding bit-plane coding leads to considerable speed improvement without compromising coding efficiency. The algorithm is designed and implemented for both 2D and 3D image sources. Experiments show that our suggested coding model lessens the computational burden of bit-plane based image coding, both in encoding and decoding time. 
The PROGRES algorithm combined with the presented fast random access decoding method having O(log2 n) block seek time is suitable for browsing a very large image bitstream. It can seek the requested part in the code-stream very quickly, and then decode them upto desired resolution at high speed. 
In related work, we introduce the concept of higher order zerotrees in modern wavelet-based coders and quantify their relative coding power. By analyzing two famous zerotree-based image coders, EZW and SPIHT, we are able to explain the superior coding efficiency of SPIHT through its ability to code higher order zerotrees than EZW. We are also able to calculate the bit savings of SPIHT compared to EZW within this framework.

Resolution scalable and random access decodable image coding with low time complexity

A method, computer system, and a computer program product is disclosed for encoding a sequence of color frames. The method includes a processor obtaining a sequence of color frames and rendering a first frame of the sequence in at least three components, each component representing a different color value. For each of the at least three components, the processor performs a wavelet transform on the first frame, initializes a significant points list and a list of insignificant sets to create an individual spatial tree of the list of insignificant sets for each component, searches all of the at least three components to identify a most significant bit in the first frame, and creates a consolidated significance map with all the color components for the first frame by searching the individual spatial tree for each component. The processor then obtains this significance map and utilizes the significance map to encode the first frame. The processor retains the significance map in memory as a key frame significance map and retains the first frame, or a color transform of the first frame, in memory, as a key frame.

William A. Pearlman

Papers

An optimal transform tree coding method applied to images

Multirate image sequence coding with quadtree segmentation and backward motion compensation

A Robust Method For Restoration Of Photon-Limited, Blurred Images

Resolution scalable and random access decodable image coding with low time complexity

Motion differential set partition coding for color image sequence compression