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

In general, growth algorithms for optimal tree-structured vector quantizers do not exist. In this paper we show that if the source satisfies certain conditions; namely, that of diminishing marginal returns; optimal growth algorithms do exist. We present such an algorithm and compare its performance with that of other tree growth algorithms. Even for sources that do not meet the necessary conditions for the growth algorithm to be optimal, such as for speech with unknown statistics, it is seen by simulation that the algorithm outperforms other known growth algorithms, For sources that do not satisfy the required conditions, the algorithm presented here can also be used to grow the initial tree for the pruning process. The performance of such pruned trees is superior to that of trees pruned from full trees of the same rate. >

Variable-rate tree-structured vector quantizers

A coder for use in encoding and decoding a data set representing an image includes a first device which partitions the subband transformation into first and second sets, which adds the first set into a list of insignificant sets (LIS), and which initializes a list of significant pixels (LSP), a second device which tests the first and second sets for significance with respect to a threshold value, which partitions significant members of the first and second sets in accordance with first and second partitioning functions, respectively, and which adds significant pixels to the LSP, a third device which refines the quantization of the pixels in the LSP In operation, the threshold value is decrement as the second and third devices are operation in seriatim until the coding endpoint has been reached An optional fourth device entropy codes a significance map cooperatively generated by the second and third devices Methods for encoding and decoding the subband transformation of a data set and a computer program for converting a general purpose computer into a hierarchical image coder are also described

Embedded and efficient low-complexity hierarchical image coder and corresponding methods therefor

An embedded, block-based, wavelet transform coding algorithm of low complexity is proposed. Three-dimensional set partitioned embedded block (3D-SPECK) efficiently encodes, hyperspectral volumetric image data by exploiting the dependencies in all dimensions. Integer wavelet transform is applied to enable lossy and lossless decompression from the same bit stream. We demonstrate that 3D-SPECK, a wavelet domain algorithm, like other time domain algorithms, can preserve spectral profiles well. Airborne visible infrared imaging spectrometer (AVIRIS) imagery is used to test the proposed algorithm. Results show that 3D-SPECK, in addition to being very flexible, retains all the desirable features of compared state-of-the-art algorithms and is highly competitive to 3D-SPIHT and better than JPEG2000 multi-component in compression efficiency.

/pdf/lossy-to-lossless-block-based-compression-of-hyperspectral-aojxo00w4j.pdf

Lossy-to-lossless block-based compression of hyperspectral volumetric data

The SPIHT image compression algorithm is modified for application to large images with limited processor memory. The subband decomposition coefficients are partitioned into small tree-preserving spatial blocks which are each independently coded using the SPIHT algorithm. The bitstreams for each spatial block are assembled into a single final bitstream through one of two packetization schemes. The final bitstream can be embedded in fidelity with a small expense in rate, SPIHT encoding and decoding of the spatial blocks can be done in parallel for real-time video compression.

http://www.cipr.rpi.edu/people/faculty/pearlman.html/papers/asil99_wp.pdf

Low-memory packetized SPIHT image compression

This paper presents a low memory implementation of efficient lossy volumetric medical image compression using the set partitioning in hierarchical trees (SPIHT) algorithm. The coding units in this three-dimensional wavelet transform and compression method are short sequences of horizontal stripes cut from the sequence of slices in the volumetric image. As the compression degree increases, the boundaries between adjacent coding units became increasingly visible. Unlike video, where image frames are viewed under dynamic conditions, the volume image is examined under static conditions and must not exhibit such boundary artifacts. In order to eliminate them, we utilize overlapping and averaging both at the intra-slice and inter-slice boundaries between adjacent and successive stripe sequences. Our low memory implementation smooths out considerably the variation in mean squared error among different slices and suffers only an insignificant loss in performance from that of a full memory implementation.

William A. Pearlman

Papers

Variable-rate tree-structured vector quantizers

Embedded and efficient low-complexity hierarchical image coder and corresponding methods therefor

Lossy-to-lossless block-based compression of hyperspectral volumetric data

Low-memory packetized SPIHT image compression

Stripe-based SPHIT lossy compression of volumetric medical images for low memory usage and uniform reconstruction quality