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

In this paper, we elaborate on denoising schemes based on lossy compression. First, we provide an alternative interpretation of the so-called Occam filter and relate it with the complexity-regularized denoising schemes in the literature. Next, we discuss about the 'critical distortion' of a noisy source and argue that optimal denoising is achieved at the corresponding critical encoding rate rather than at the encoding rates suggested by other compression-based denoisers. Finally, we discuss the so-called 'indirect rate distortion problem'. We focus particularly on the high bit-rate encoding of noisy sources and show lossless compression of a denoised source is often very wasteful of bits, and suggest a simple way of determining an appropriate bit-rate for compressing a denoised source economically while retaining its initial denoised quality.

Critical encoding rate in combined denoising and compression

Optimal performance in a data compression scheme is very hard to obtain without inordinate computational complexity. However, there are possibilities of obtaining high performance with low complexity by proper exploitation of the characteristics of the data. Here, we shall concentrate on two recent low complexity algorithms for image compression which exploit data characteristics very efficiently. We shall try to discover principals for realizing high performance with low complexity and explain how these recent algorithms utilize these principles We shall also present image compression result with actual codecs which realize the promise of high compression with low complexity.© (1997) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

High-performance low-complexity image compression

One interesting feature of image compression is support of region of interest (ROI) access, in which an image sequence can be encoded only once and then the decoder can directly extract a subset of the bitstream to reconstruct a chosen ROI of required quality. In this paper, we apply Three-dimensional Subband Block Hierarchical Partitioning (3-D SBHP), a highly scalable wavelet transform based algorithm, for volumetric medical image compression to support ROI access. The codeblock selection method by which random access decoding can be achieved is outlined and the performance empirically
investigated. The experimental results show that there are a number of parameters that affect the effectiveness of ROI access, the most important being the size of the ROI size, code-block size, wavelet composition level, number of filter taps and target bit rate. Finally, one possible way to optimize ROI access performance is addressed.

Region of interest access with three-dimensional SBHP algorithm

We propose two approaches to scalable lossless coding of motion video. They achieve SNR-scalable bitstream up to lossless reconstruction based upon the subpixel-accurate MCTF-based wavelet video coding. The first approach is based upon a two-stage encoding strategy where a lossy reconstruction layer is augmented by a following residual layer in order to obtain (nearly) lossless reconstruction. The key advantages of our approach include an 'on-the-fly' determination of bit budget distribution between the lossy and the residual layers, freedom to use almost any progressive lossy video coding scheme as the first layer and an added feature of near-lossless compression. The second approach capitalizes on the fact that we can maintain the invertibility of MCTF with an arbitrary sub-pixel accuracy even in the presence of an extra truncation step for lossless reconstruction thanks to the lifting implementation. Experimental results show that the proposed schemes achieve compression ratios not obtainable by intra-frame coders such as Motion JPEG-2000 thanks to their inter-frame coding nature. Also they are shown to outperform the state-of-the-art non-scalable inter-frame coder H.264 (JM) lossless mode, with the added benefit of bitstream embeddedness.

William A. Pearlman

Papers

Hexagonal sub-band coding for images

Critical encoding rate in combined denoising and compression

High-performance low-complexity image compression

Region of interest access with three-dimensional SBHP algorithm

On scalable lossless video coding based on sub-pixel accurate MCTF