In this paper, we present a perceptual distortion measure that predicts image integrity far better than meansquared error. This perceptual distortion measure is based on a model of human visual processing that ts empirical measurements of the psychophysics of spatial pattern detection. The model of human visual processing proposed involves two major components: a steerable pyramid transform and contrast normalization. We also illustrate the usefulness of the model in predicting perceptual distortion in real images. 1.

Subband and wavelet decompositions are powerful tools in image coding, because of their decorrelating effects on image pixels, the concentration of energy in a few coefficients, their multirate/multiresolution framework, and their frequency splitting which allows for efficient coding matched to the statistics of each frequency band and to the characteristics of the human visual system. Vector quantization provides a means of converting the decomposed signal into bits in a manner that takes advantage of remaining inter- and intra-band correlation as well as of the more flexible partitions of higher dimensional vector spaces. Since 1988 a growing body of research has examined the use of vector quantization for subband/wavelet transform coefficients. We present a survey of these methods. 1 Introduction Image compression maps an original image into a bit stream suitable for communication over or storage in a digital medium. The number of bits required to represent the coded image should b...

The wavelet transform has become a cutting-edge technology in image compression research. This article explains what wavelets are and provides a practical, nuts-andbolts tutorial on wavelet-based compression that will help readers to understand and experiment with this important new technology. Keywords: image coding, signal compression, wavelet transform, image transforms 1 Introduction The advent of multimedia computing has lead to an increased demand for digital images. The storage and manipulation of these images in their raw form is very expensive; for example, a standard 35mm photograph digitized at 12 ¯m per pixel requires about 18 MBytes of storage and one second of NTSC-quality color video requires almost 23 MBytes of storage. To make widespread use of digital imagery practical, some form of data compression must be used. Digital images can be compressed by eliminating redundant information. There are three types of redundancy that can be exploited by image compression system...

this paper, the boxes H i #!# indicate circular convolution of a #nite input image of size N with a #lter with impulse response h i #n# and Fourier transform

ABSTRACT This paper presents an overview of wavelet-based image coding. We develop the basics of image coding with a discussion of vector quantization. We motivate the use of transform coding in practical settings,and describe the properties of various decorrelating transforms. We motivate the use of the wavelet transform in coding using rate-distortion considerations as well as approximation-theoretic considerations. Finally,we give an overview of current coders in the literature. 1

In this paper, we develop structures for FIR perfect-rec. nstruction QMF banks which cover a subclass of systems that yield linear-phase analysis filters for arbitrary M. The parameters of these structures can be optimized in order to design analysis filters with minimmu stopband energy which at the same time have linear-phase and satisfy the perfect-reconstruction property. If there are M subbands, then depending upon whether the coefficients h(n) of each analysis filter is symmetric or antlsymmetric, several combinations of filter banks are possible. Some of these permit perfect-reconstruction and some do not. For a given M, we develop a formula for the number of combinatiuns for a subclass of linear-phase perfect-reconstruction structures. As an example, we elaborate on a perfect-reconstruction linear-phase lattice structure for three channels and develop a lattice structure for this case. The lattice structure is such that, regardless of the parameter values, the QMF bank e10oys perfect-reconstruction property while at the same time the analysis filters have linear phase. These parameters can therefore be optimized to obtain analysis filters with good magnitude response, without losing lhe above two features.

In this paper, we present a new algorithm for the design of orthonormal two-band rational filter banks. Owing to the connection between iterated rational filter banks and rational wavelets, this is also a design algorithm for orthonormal rational wavelets. It is basically a simple iterative procedure, which explains its exponential convergence and adaptability under various linear constraints (e.g., regularity). Although the filters obtained from this algorithm are suboptimally designed, they show excellent frequency selectivity.

FPGAs provide an ideal template for run-time reconfigurable (RTR) designs. Only recently have RTR enabling design tools that bypass the traditional synthesis and bitstream generation process for FPGAs become available. The JBits tool suite is an environment that provides support for RTR designs on Xilinx Virtex and 4K devices. This research provides a comprehensive design process description of a two-dimensional discrete wavelet transform (DWT) core using the JBits run-time reconfigurable FPGA design tool suite. Several aspects of the design process are discussed, including implementation, simulation, debugging, and hardware interfacing to a reconfigurable computing platform. The DWT lends itself to a straightforward implementation in hardware, requiring relatively simple logic for control and address generation circuitry. Through the application of RTR techniques to the DWT, this research attempts to exploit certain advantages that are unobtainable with static implementations. Performance results of the DWT core are presented, including speed of operation, resource consumption, and reconfiguration overhead times.

Multidimensional multirate systems have been used widely in signal processing, communications, and computer vision. Traditional multidimensional multirate systems are tensor products of one-dimensional systems. While these systems are easy to implement and design, they are inadequate to represent multidimensional signals since they cannot capture the geometric structure. Therefore, “true” multidimensional systems are more suited to multidimensional signals, such as images and videos. This thesis focuses on the characterization, design, and applications of “true” multidimensional multirate systems. One key property of multidimensional multirate systems is perfect reconstruction, which guarantees the original input can be perfectly reconstructed from the outputs. The most popular multidimensional multirate systems are multidimensional filter banks, including critically sampled and oversampled ones. Characterizing and designing multidimensional perfect reconstruction filter banks have been challenging tasks. For critically sampled filter banks, previous one-dimensional theory cannot be extended to the multidimensional

ich radiate in many branches of mathematics. At ICM'90, Coifman and Meyer gave a harmonic analysis point view, followed at ICM'94 by Daubechies and Donoho who explained the impact of wavelet bases in numerical analysis and statistics. Signal processing is now a driving force that has regrouped a community of mathematicians and engineers sharing representation techniques. Applications to signal compression, noise removal, and stochastic modeling lead us through recent developments in approximation theory, harmonic analysis, operator theory, probability, and statistics. Documenta Mathematica \Delta Extra Volume ICM 1998 \Delta 1--4 2 St' ephane Mallat 2 Sparse Representations Sparse representations have direct applications to data compression, but are also necessary to reduce the complexity of classification and identification problems for large size signals. This section begins with an approximation theory point of view