An analysis of spatial context conditioning and run-length coding in embedded progressive, wavelet-based image coding is presented. The analysis shows that run-length coding of certain context subsequences is superior to pure entropy coding, both in terms of coding performance and of execution speed. Based on these considerations, a novel, intuitive context conditioning scheme using a spatial distance model to describe the statistics of significant coefficients is proposed. The results for the proposed coding scheme are competitive to the best coding schemes found in the literature.

Run-length coding has attracted much attention in wavelet-based image compression because of its simplicity and potentially low complexity. The main drawback is the inferior RD-performance compared to the state-of-the-art-coder SPIHT. In this paper, we concentrate on the embedded progressive run-length code of Tian and Wells (1996, 1998). We consider significance sequences drawn from the scan in the dominant pass. It turns out that self-similar curves for scanning the dominant pass increase the compression efficiency significantly. This is a consequence of the correlation of direct neighbors in the wavelet domain. This dependence can be better exploited by using groups of coefficients, similar to the SPIHT algorithm. This results in a new and very fast coding algorithm, which shows performance similar to the state-of-the-art coder SPIHT, but with lower complexity and small and fixed memory overhead.

A new nonlinear noise reduction method is presented that uses the discrete wavelet transform. Similar to Donoho (1995) and Donohoe and Johnstone (1994, 1995), the authors employ thresholding in the wavelet transform domain but, following a suggestion by Coifman, they use an undecimated, shift-invariant, nonorthogonal wavelet transform instead of the usual orthogonal one. This new approach can be interpreted as a repeated application of the original Donoho and Johnstone method for different shifts. The main feature of the new algorithm is a significantly improved noise reduction compared to the original wavelet based approach. This holds for a large class of signals, both visually and in the l/sub 2/ sense, and is shown theoretically as well as by experimental results.

The problem of allpass filter design for phase approximation and equalization in the Chebyshev sense is solved by using a generalized Remez algorithm. Convergence to the unique optimum is guaranteed and is achieved rapidly in the actual implementation. The well-known numerical problems for higher degree filters are analyzed and solved by a simple approach. Possible applications are: design of filters with a desired phase response (e.g., a delay element), the design of phase equalizers, or the design of recursive filters with magnitude prescriptions using parallel allpass filters. For the latter the algorithm can be modified to allow arbitrary tolerance schemes for the magnitude response.

We consider the design of digital filters and discuss the inclusion of explicitly specified transition bands in the frequency domain design of FIR filters. We put forth the notion that explicitly specified transition bands have been introduced in the filter design literature as an indirect and sometimes inadequate approach for dealing with discontinuities in the desired frequency response. We also present a rapidly converging, robust, simple algorithm for the design of optimal peak constrained least square lowpass FIR filters that does not require the use of transition bands. This versatile algorithm will design linear and minimum phase FIR filters and gives the best L/sub 2/ filter and a continuum of Chebyshev filters as special cases.

We propose a novel method for simultaneous noise reduction and data compression based on shrinking, quantizing and coding the wavelet packet (WP) coefficients. A dynamic programming and fast pruning algorithm is used to efficiently choose the best basis from the entire library of admissible WP bases, and jointly optimize the bit allocation strategy and the quantization scheme in the rate-distortion framework. Soft-thresholding in the wavelet domain can significantly suppress noise, e.g., the speckles of the synthetic aperture radar images, while maintaining bright reflections for subsequent detection and recognition. Optimal bit allocation, quantization and entropy coding achieve the goal of compression while maintaining the fidelity of the image.

We propose a novel method based on wavelet thresholding for enhancement of decompressed transform coded images. Transform coding at low bit rates typically introduces artifacts associated with the basis functions of the transform. In particular, the method works remarkably well in "deblocking" of DCT compressed images. The method is nonlinear, computationally efficient, and spatially adaptive and has the distinct feature that it removes artifacts yet retain sharp features in the images. An important implication of this result is that images coded using the JPEG standard can efficiently be postprocessed to give significantly improved visual quality in the images. The algorithm can use a conventional JPEG encoder and decoder for which VLSI chips are available.>

The paper introduces a novel speckle reduction method based on thresholding the wavelet coefficients of the logarithmically transformed image. The method is computational efficient and can significantly reduce the speckle while preserving the resolution of the original image. Both soft and hard thresholding schemes are studied and the results are compared. When fully polarimetric SAR images are available, the authors propose several approaches to combine the data from different polarizations to achieve even better performance. Wavelet processed imagery is shown to provide better detection performance for the synthetic-aperture radar (SAR) based automatic target detection/recognition (ATD/R) problem.>

An approach for the design of limit-cycle-free digital fixed-point filters is proposed. By constraining the transfer function already in the design phase, it is guaranteed that the filter will be free from limit cycles and overflow oscillations in the direct form implementation. The design strategy also guarantees low roundoff noise. The proposed approach is illustrated with design examples. The examples show that typically a 50-100% increase in the filter order (as compared to standard elliptic design) is needed for the limit-cycle-free implementation of a lowpass filter with the direct form (DF) structure. Since the DF structure is very efficient to implement in signal processors, the proposed filters are very attractive for such environment, whereas dedicated filter structures (wave digital, state-space, etc.) easily result in a 3 to 4-fold implementation complexity.>

Finding polynomial roots rapidly and accurately is an important problem in many areas of signal processing. We present a program that is superior in speed and accuracy to the best methods to our knowledge, i.e., Jenkins/Traub (1975) program and the eigenvalue method. Based on this, we give a simple approach to improve the accuracy for spectral factorization in the case that there are double roots on the unit circle.>