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 study the performance of conditional entropy-constrained vector quantizers when used to quantize subbands of the displaced frame differences derived from video sequences. Chou and Lookabaugh (1990) originally suggested a locally optimal design of this new kind of vector quantizer which can be accomplished through a generalization of the well known entropy-constrained vector quantizer (ECVQ) algorithm. This generalization of the ECVQ algorithm to a conditional entropy-constrained is called CECVQ, i.e., conditional ECVQ. The non-memoryless quantization performed by the conditional entropy-constrained VQ is based on the current vector to be encoded and the previous encoded vector. A new algorithm for conditional entropy-constrained vector quantizer design is derived and it is based on the pairwise nearest neighbour technique presented by Equitz (1989). >

Conditional entropy-constrained vector quantization of displaced frame difference subband signals

In critical applications of image compression that are sensitive to information loss, lossless compression techniques are usually employed. The compression ratios obtained from lossless techniques are low. Hence we need different schemes that give quantitative guarantees about the type and amount of distortion incurred, viz. near-lossless compression methods. In this paper, we explore hybrid techniques for near-lossless image compression based on error bound per pixel and apply them to Digital Terrain Elevation Data (DTED).
We develop multi-stage quantization methods and other hybrid schemes using SPIHT as an embedded lossy coder. The methods developed are scalable with a control on maximum allowable deviation per pixel in the reconstruction. We compare the results obtained by these methods with JPEG-LS, the standard for lossless and near-lossless compression. Results show that these methods usually perform better than JPEG-LS in terms of compression performance and have additional features useful for progressive transmission.

Near-lossless compression of digital terrain elevation data

We find a simple closed form expression for an efficient class of Quadrature Mirror Filters (QMF's) by exploiting the inherent symmetry of the QMF property. We derive a simple rule of thumb to calculate the maximum feasible frequency selectivity of the filter for a given number N of filter taps. We show that, for even n, the frequency selectivity of a 2n+1 or 2n tap filter can be increased if and only if the number of taps is increased by at least 4. Most existing QMF's closely match the derived analytical expression as well as verify the results on frequency selectivity. We obtain FIR implementations of the aforementioned analytical expression by using the Remez allocation algorithm. We choose weighting functions that confine the error to the intersection of the transition band and the stop band of the filter, as well as force the magnitude of the passband ripple to be much lower than that of the stopband ripple. We make such a choice in order to optimally satisfy the power complementarity condition as well as to attain high stop band attenuation. Our implementations match existing designs in performance.

http://ieeexplore.ieee.org/iel4/82/10403/00486467.pdf

A closed form expression for an efficient class of quadrature mirror filters and its FIR approximation

A degree-k zero tree model is presented, in order to quantify the coding power of zerotrees in wavelet-based image coding. Based on the model, the coding behaviors of modern zerotree based image coders are clearly explained. Also, we explain why the well-known SPIHT algorithm can code a wider range of zerotrees than EZW. Experimental results support our idea that higher degree zerotree coder will have more coding power.

Quantifying the coding power of zerotrees of wavelet coefficients: a degree-k zerotree model

For faster random access of a target image block, a bi-section idea is
applied to link image blocks. Conventional methods configure the blocks in linearly linked way, for which the block seek time entirely depends on the location of the block on the compressed bitstream. The block linkage information is configured such that binary search is
possible, giving the worst case block seek time of log 2 (n),
for n blocks. Experimental results with 3D-SPIHT on video sequences show that the presented idea gives substantial speed improvement with minimal bit overhead.

William A. Pearlman

Papers

Conditional entropy-constrained vector quantization of displaced frame difference subband signals

Near-lossless compression of digital terrain elevation data

A closed form expression for an efficient class of quadrature mirror filters and its FIR approximation

Quantifying the coding power of zerotrees of wavelet coefficients: a degree-k zerotree model

Fast and constant time random access decoding with log2n block seek time