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 image coding system is proposed in which hexagonally sampled images are decomposed into subbands that are selective in both frequency and orientation. Nine high frequency bands each of one octave and 60 degrees of angular orientation are built on a pyramidal structure along with one low frequency band. Bits are then allocated optimally to the subbands under a mean-squared error distortion measure. Optimal quantizers are designed for each subband for entropy coding under a Laplacian distribution assumption. An adaptive version of the coding scheme is also implemented and the results are compared at rates of 0.5 and 1.0 bits per pixel.

Hexagonal sub-band coding for images m11.4

It has been proved recently that for Gaussian sources with memory an ideal subband split will produce a coding gain for scalar or vector quantization of the subbands. Following the methodology of the proofs, we outline a method for successively splitting the subbands of a source, one at a time to obtain the largest coding gain. The subband with the largest theoretical rate reduction (TRR) is determined and split at each step of the decomposition process. The TRR is the difference between the rate in optimal encoding of N-tuples from a Gaussian source (or subband) and the rate for the same encoding of its subband decomposition. The TRR is a monotone increasing function of a so-called spectral flatness ratio, which involves the products of the eigenvalues of the source (subband) and subband decomposition covariance matrices of order N. These eigenvalues are estimated by the variances of the Discrete Cosine Transform, which approximates those of the optimal Karhunen Loeve Transform. After the subband decomposition hierarchy or tree is determined through the criterion of maximal TRR, each subband is encoded with a variable rate entropy constrained vector quantizer. Optimal rate allocation to subbands is done with the BFOS algorithm which does not require any source modelling. We demonstrate the benefit of using the criterion by comparing coding results on a two-level low-pass pyramidal decomposition with coding results on a two-level decomposition obtained using the criterion. For 60 MCFD (Motion Compensated Frame Difference) frames of the Salesman sequence an average rate- distortion advantage of 0.73 dB and 0.02 bpp and for 30 FD (Frame Difference) frames of Caltrain image sequence an average rate-distortion advantage of 0.41 dB and 0.013 bpp are obtained with the optimal decomposition over low-pass pyramidal decomposition.© (1995) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Image subband coding using an information-theoretic subband splitting criterion

A tree code, asymptotically optimal for stationary Gaussian sources and squared error distortion [2], is used to encode transforms of image sub-blocks. The variance spectrum of each sub-block is estimated and specified uniquely by a set of one-dimensional auto-regressive parameters. The expected distortion is set to a constant for each block and the rate is allowed to vary to meet the given level of distortion. Since the spectrum and rate are different for every block, the code tree differs for every block. Coding simulations for target block distortion of 15 and average block rate of 0.99 bits per pel (bpp) show that very good results can be obtained at high search intensities at the expense of high computational complexity. The results at the higher search intensities outperform a parallel simulation with quantization replacing tree coding. Comparative coding simulations also show that the reproduced image with variable block rate and average rate of 0.99 bpp has 2.5 dB less distortion than a similarly reproduced image with a constant block rate equal to 1.0 bpp.

Variable Rate, Adaptive Transform Tree Coding Of Images

A transform trellis coding scheme for images is presented. A two dimensional discrete cosine transform is applied to the image followed by a search on a trellis structured code. This code is a sliding block code that utilizes a constrained size reproduction alphabet. The image is divided into blocks by the transform coding. The non-stationarity of the image is counteracted by grouping these blocks in clusters through a clustering algorithm, and then encoding the clusters separately. Mandela ordered sequences are formed from each cluster i.e identically indexed coefficients from each block are grouped together to form one dimensional sequences. A separate search ensues on each of these Mandela ordered sequences. Padding sequences are used to improve the trellis search fidelity. The padding sequences absorb the error caused by the building up of the trellis to full size. The simulations were carried out on a 256x256 image ('LENA'). The results are comparable to any existing scheme. The visual quality of the image is enhanced considerably by the padding and clustering.

Discrete Cosine Transform Image Coding With Sliding Block Codes

A new algorithm for nonorthogonal decomposition is proposed and applied to Gabor decomposition of image. The algorithm is iterative and its advantages are discussed. Also a modified version of the algorithm is considered which increases the rate of convergence. Image simulations show that this method gives much lower reconstruction error that the method using biorthogonal functions, at a cost of a greater amount of computer time. >

William A. Pearlman

Papers

Hexagonal sub-band coding for images m11.4

Image subband coding using an information-theoretic subband splitting criterion

Variable Rate, Adaptive Transform Tree Coding Of Images

Discrete Cosine Transform Image Coding With Sliding Block Codes

A new method for non-orthogonal decomposition