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

An algorithm given by R.P. Rao (see Proc. IEEE Inter. Telecomm. Symp., Sept. 1990) for multirate vector quantization is used for coding image pyramids. The algorithm, called alphabet- and entropy-constrained vector quantization (AECVQ), operates by optimally choosing sub-codebooks from a large generic codebook. In terms of performance and complexity, AECVQ equals the best single-rate VQ. Excellent results at 1 b/p and below, judged both visually and using a peak-to-peak SNR criterion, have been obtained by coding image pyramids using the AECVQ algorithm. these results demonstrate significant improvements over existing schemes. Although an AECVQ based image coding scheme is considerably complex, it can be implemented in real time using current VLSI technology. >

Multirate vector quantization of image pyramids

Transform coding has been the focus of the research for image compression. In previous research, the Amplitude and Group Partitioning (AGP) coding scheme is proved to be a low complexity algorithm with higher performance, clearly one of the state-of-art transform coding techniques. However, the previous AGP is used along with the Discrete Cosine Transform (DCT) and the discrete wavelet transform. In this paper, a different transform, the Lapped Orthogonal Transform (LOT), replaces the DCT in conjunction with the AGP. This is the first time LOT and AGP have been combined in a coding method. The definition and design of the LOT are discussed. An objective metric to measure the performance of transform, coding gain, is calculated for both the DCT and the LOT. The LOT has slightly higher coding gain than the DCT. The principles of the LOT based AGP image codec (LOT-AGP) are presented and a complete codec, encoder and decoder, is implemented in software. The performance of the LOT-AGP is compared with other block transform coding schemes: the baseline JPEG codec and the DCT based AGP image codec (DCT- AGP) by both objective evaluation and subjective evaluation. The Peak Signal to Noise Ratio (PSNR) is calculated for these three coding schemes. The two AGP codecs are much better than the JPEG codec on PSNR, from about 1.7 dB to 3 dB depending on bit rate. The two AGP schemes have PSNR differences only to a small degree. Visually, the LOT-AGP has the best-reconstructed images among these three at all bit rates. In addition, the coding results of two other state-of-art progressive image codecs are cited for further comparison. One is the Set Partitioning in Hierarchical Trees (SPIHT) algorithm with a dyadic wavelet transform, and the other is Tran and Nguyen's method with the generalized LOT transform. The AGP coding and the adaptive Huffman entropy coding of LOT-AGP are less complex and the memory usage is smaller than in these two progressive codecs. Comparing these three codecs, i.e. the LOT-AGP and the two progressive codecs in PSNR small only small differences in PSNR. SPIHT has about 1 dB higher PSNR than the LOT-AGP and Tran and Nguyen's method for the test image Lena. For the test image Barbara, the PSNR of the LOT- AGP is about 0.5 dB higher than that of the SPIHT and 0.5 dB lower than that of Tran and Nguyen's method. This low- complexity and high performance codec may provide a new direction for the implementation of image compression.

Lapped orthogonal transform coding by amplitude and group partitioning

A new estimation criterion called the minimum-error minimum correlation
(MEMC) criterion is implemented in conjunction with an adaptive
windowing technique. The image statistics are calculated within the
window, the dimensions of which vary depending on the local statistics.
The MEMC estimator produces sharper and hence visually more pleasing
restorations, while the adaptive windows tend to isolate regions of the
image that are locally stationary. Since most of the error after restoration
is in the vicinity of edges, a postprocessing step of filtering along the
edges is applied. These image restorations are compared to both fixed
and adaptive minimum mean squared error estimators.

Adaptive estimators for filtering noisy images

Restoration of Noisy Images With Adaptive Windowing and Nonlinear Filtering*Woo -Jin Song and William A. PearlmanRensselaer Polytechnic InstituteElectrical, Computer, and Systems Engineering DepartmentTroy, New York 12180AbstractA general problem with statistically -based estimators for images degraded by additivenoise is their dependence on average quatities when image intensities vary rapidly andwidely. The Wiener estimator, for example, given the stationary power spectrum on the ob-ject image and the noise, is known to produce a noisy effect in the flat intensity regionsand a blurring or fuzzy effect in the edge regions on the restored image. The power spectraare usually estimated over regions containing both edges and flat regions and therefore arenot truly representative of either regional type. In this work, we accept a nonstationaryimage model and utilize a novel adaptive windowing technique in conjunction with a nonlinearestimator to overcome the cited defects of other estimators. This technique is appliedsuccessively to simulated noisy one -dimensional feature waveforms, an arbitrarily selectednoisy image scan line,noisy images with one -dimensional windowing, and noisy images withtwo -dimensional windowing. In each case, features of the edge and flat regions both arefaithfully reconstructed. In fact, the restored images are remarkably sharp and clean.They appear far superior to the comparable Wiener restorations despite the fact that theirmean -squared error is about the same or slightly larger.IntroductionParameter or spectral estimates required for image estimators are usually derived fromfixed regions of the image. The object image, however, is nonstationary or, at best, quasi -or locally stationary. Hence an image estimate based on such regional averages can not fol-low rapid statistical changes within a region. For example, the Wiener (minimum mean -squarelinear) estimator requires the image power spectrum, which averages quantities belonging tobusy and flat contrast areas of the image. The effect of averaging between these two re-gional types is manifested in restorations which are noisy in the flat areas due to insuf-ficient smoothing and fuzzy in the edge regions due to oversmoothing. If the analysis win -dow for parameter or spectral estimates contains elements truly representative of the sta-tistical class of the current picture element, then the desired estimate of the true objectintensity at that point would be obtained. Here we shall present a scheme for adaptivelychanging the analysis window so that it embraces elementsof the current pixel's statistical

Restoration Of Noisy Images With Adaptive Windowing And Nonlinear Filtering

A simple yet effective image sequence coding technique based on the zero-tree method is studied. The frames of the image sequence are decomposed hierarchically into 5 levels and motion compensation is performed on each subband separately. The displaced frame difference (DFD) is then encoded using the zero-tree method. Simulations done on the first 60 frames of the Miss America sequence using backward motion compensation with pel recursive motion estimation technique have yielded an average PSNR of 40.52 dB at a rate of 0.3 bpp and 43.68 dB at 1.0 bpp. This technique has the advantage that it works well with most images as no training set is required. There is precise control of the coding rate and the transmission is progressive.© (1993) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

William A. Pearlman

Papers

Multirate vector quantization of image pyramids

Lapped orthogonal transform coding by amplitude and group partitioning

Adaptive estimators for filtering noisy images

Restoration Of Noisy Images With Adaptive Windowing And Nonlinear Filtering

Image sequence coding using the zero-tree method