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

A low-complexity three-dimensional image compression algorithm based on wavelet transforms and set-partitioning strategy 
is presented. The Subband Block Hierarchial Partitioning (SBHP) algorithm is modified and extended to three dimensions,
and applied to every code block independently. The resultant algorithm, 3D-SBHP, efficiently encodes 3D image data
by the exploitation of the dependencies in all dimensions, while enabling progressive SNR and resolution decompression
and Region-of-Interest (ROI) access from the same bit stream. The code-block selection method by which random access
decoding can be achieved is outlined.The resolution scalable and random access performances are empirically investigated.
The results show 3D-SBHP is a good candidate to compress 3D image data sets for multimedia applications.

Scalable three-dimensional sbhp algorithm with region of interest access and low-complexity

We investigate and compare the performance of several three-dimensional (3D) embedded wavelet algorithms on lossless 3D
image compression. The algorithms are Asymmetric Tree Three-Dimensional Set Partitioning In Hierarchical Trees (AT-3DSPIHT), Three-Dimensional Set Partitioned Embedded bloCK (3D-SPECK), Three-Dimensional Context-Based Embedded Zerotrees of Wavelet coefficients (3D-CB-EZW), and JPEG2000 Part II for multi-component images. Two kinds of images are investigated in our study -- 8-bit CT and MR medical images and 16-bit AVIRIS hyperspectral images. First, the performances by using different size of coding units are compared. It shows that increasing the size of coding unit improves the performance somewhat. Second, the performances by using different integer wavelet transforms are compared for AT-3DSPIHT, 3D-SPECK and
3D-CB-EZW. None of the considered filters always performs the best for
all data sets and algorithms. At last, we compare the different lossless compression algorithms by applying integer wavelet transform on the entire image volumes. For 8-bit medical image volumes, AT-3DSPIHT performs the best almost all the time, achieving average of 12% decreases in file size compared with JPEG2000 multi-component, the second performer. For 16-bit hyperspectral images, AT-3DSPIHT always performs the best, yielding average 5.8% and 8.9% decreases in file size compared with 3D-SPECK and JPEG2000 multi-component, respectively. Two 2D compression algorithms, JPEG2000 and UNIX zip, are also included for reference, and all 3D algorithms perform much better than 2D algorithms.

Lossless compression for three-dimensional images

Motion differential set partition coding for image sequence and video compression

The error resilient and error concealment 3-D SPIHT (ERC-SPIHT) are introduced, which are encoded with an asymmetric tree structure. Next, error resilient video transmission is presented using the ERC-SPHITC algorithm with rate-compatible punctured convolutional (RCPC) code and Reed-Solomon code.

Improved error resilient embedded video coding

We present a wavelet-based near-lossless coder with L∞-error scalability. The method presented consists of a wavelet-based lossy layer encoder followed by multiple stages of residual refinements for L∞-error scalability. We introduce a successive refinement scheme in L∞-error sense for residual layers reminiscent of popular set-partitioning algorithms for embedded coding. The initial near-lossless error bound is attained by our previously proposed two-stage scheme which determines the bit-rate for the lossy layer 'on-the-fly' without any iteration. The resulting residual which is defined by the difference between the original and the initial near-lossless reconstruction is then further refined in L∞-error sense up to lossless reconstruction. This scheme provides a combination of L 2 -error embedded lossy reconstruction up to an automatically determined high-fidelity plus optional layers of scalable L∞-error. This may turn out to be particularly useful for scalable archival applications where the fidelity of reconstructions on the high-bit end needs to be strictly controlled.

William A. Pearlman

Papers

Scalable three-dimensional sbhp algorithm with region of interest access and low-complexity

Lossless compression for three-dimensional images

Motion differential set partition coding for image sequence and video compression

Improved error resilient embedded video coding

A wavelet-based two-stage near-lossless coder with L∞- error scalability