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

Compressed video bitstreams require protection from channel errors in a wireless channel and protection from packet loss in a wired ATM channel. The three-dimensional (3-D) SPIHT coder has proved its efficiency and its real-time capability in compression of video. A forward-error-correcting (FEC) channel (RCPC) code combined with a single ARQ (automatic- repeat-request) proved to be an effective means for protecting the bitstream. There were two problems with this scheme: the noiseless reverse channel ARQ may not be feasible in practice; and, in the absence of channel coding and ARQ, the decoded sequence was hopelessly corrupted even for relatively clean channels. In this paper, we first show how to make the 3-D SPIHT bitstream more robust to channel errors by breaking the wavelet transform into a number of spatio-temporal tree blocks which can be encoded and decoded independently. This procedure brings the added benefit of parallelization of the compression and decompression algorithms. Then we demonstrate the packetization of the bit stream and the reorganization of these packets to achieve scalability in bit rate and/or resolution in addition to robustness. Then we encode each packet with a channel code. Not only does this protect the integrity of the packets in most cases, but it also allows detection of packet decoding failures, so that only the cleanly recovered packets are reconstructed. This procedure obviates ARQ, because the performance is only about 1 dB worse than normal 3-D SPIHT with FEC and ARQ. Furthermore, the parallelization makes possible real-time implementation in hardware and software.

/pdf/error-resilient-compression-and-transmission-of-scalable-38m6nrm3c3.pdf

Error-resilient compression and transmission of scalable video

We extend the work of Sherwood and Zeger to progressive video coding for noisy channels. By utilizing a 3D extension of the set partitioning in hierarchical trees (SPIHT) algorithm, we cascade the resulting 3D SPIHT video coder with a rate-compatible punctured convolutional channel coder for transmission of video over a binary symmetric channel. Progressive coding is achieved by increasing the target rate of the 3D embedded SPIHT video coder as the channel condition improves. The performance of our proposed coding system is acceptable at low transmission rate and bad channel conditions. Its low complexity makes it suitable for emerging applications such as video over wireless channels.

Progressive video coding for noisy channels

Summary form only given. Hyperspectral images were generated through the collection of hundreds of narrow and contiguously spaced spectral bands of data producing a highly correlated long sequence of images. An investigation and comparison was made on the performance of several three-dimensional embedded wavelet algorithms for compression of hyperspectral images. These algorithms include 3D-SPIHT, AT-3DSPIHT, 3D-SPECK (three-dimensional set partitioned embedded block), and JPEG2000. 3D-SPIHT is the three-dimensional extension of the state-of-the-art SPIHT (set partitioning in hierarchical trees) image compression algorithm. AT-SPIHT uses the same coding algorithms as 3D-SPIHT, but utilizes a more efficient, asymmetric tree structure. 3D-SPECK is a version of two-dimensional SPECK modified to encode 3D subband blocks. For an image sequence, 3D-DWT was applied to obtain a wavelet coefficient prism. This prism is partitioned into small code blocks with different sizes, and each subband is treated as a code block. A block splitting algorithm is used on the individual code blocks to test their significance. Compression performance was conducted on the mentioned algorithms using several AVIRIS (Airborne Visible Infrared Imaging Spectrometer) image sequences. The rate distortion performances were compared by means of the peak signal-to noise ratio (PSNR). The visual effect is considered a primary concern of hyperspectral imagery so an analysis of every algorithm's visual effect is in order. Through experimentation, AT-3DSPIHT provided high quality reconstructed images even at very low bit rate such as 0.4 bpp. A comparison was also conducted on JPEG200 and other algorithms concerning JPEG2000's multi-component images. The results have shown that AT-3DSPIHT, 3D-SPIHT and 3D-SPECK outperform JPEG2000 by the approximate range of 1 to 2.5 dB PSNR, depending on the image sequence.

Comparison of 3D set partitioning methods in hyperspectral image compression featuring an improved 3D-SPIHT

A novel approach for coding textured images is presented. The texture field is assumed to be a realization of a regular homogeneous random field, which can have a mixed spectral distribution. On the basis of a two-dimensional (2-D) Wold-like decomposition, the field is represented as a sum of a purely indeterministic, harmonic, and countable number of evanescent fields. We present an algorithm for estimating and coding the texture model parameters, and show that the suggested algorithm yields high-quality reconstructions at low bit rates. The model and the resulting coding algorithm are seen to be applicable to a wide variety of texture types found in natural images.

Texture coding using a Wold decomposition model

End users of large volume image datasets are often interested only in certain features that can be identified as quickly as possible. For hyperspectral data, these features could reside only in certain ranges of spectral bands and certain spatial areas of the target. The same holds true for volume medical images for a certain volume region of the subject's anatomy. High spatial resolution may be the ultimate requirement, but in many cases a lower resolution would suffice, especially when rapid acquisition and browsing are essential. This paper presents a major extension of the 3D-SPIHT (set partitioning in hierarchical trees) image compression algorithm that enables random access decoding of any specified region of the image volume at a given spatial resolution and given bit rate from a single codestream. Final spatial and spectral (or axial) resolutions are chosen independently. Because the image wavelet transform is encoded in tree blocks and the bit rates of these tree blocks are minimized through a rate-distortion optimization procedure, the various resolutions and qualities of the images can be extracted while reading a minimum amount of bits from the coded data. The attributes and efficiency of this 3D-SPIHT extension are demonstrated for several medical and hyperspectral images in comparison to the JPEG2000 Multicomponent algorithm.

https://link.springer.com/content/pdf/10.1155%2F2008%2F248905.pdf

William A. Pearlman

Papers

Error-resilient compression and transmission of scalable video

Progressive video coding for noisy channels

Comparison of 3D set partitioning methods in hyperspectral image compression featuring an improved 3D-SPIHT

Texture coding using a Wold decomposition model

Three-dimensional SPIHT coding of volume images with random access and resolution scalability