Roberto H. Bamberger

Optimum classification in subband coding of images

This paper investigates the classification technique, applied to subband coding of images, as a way of exploiting the non-stationary nature of image subbands. An algorithm for maximizing the classification gain, is presented. Each subband is optimally classified and the classification map is sent as side information. After optimum rate allocation, the classes are encoded using arithmetic and trellis coded quantization (ACTCQ) system. We compare this approach with other approaches for classification proposed in the literature. We propose a method for reducing the side rate which exploits the dependence between subbands as well as the within band dependence.<<ETX>>

Generalized symmetric extension for size-limited multirate filter banks

A multirate (MR) filter bank is called size-limited if the total number of output samples equals the number of input samples. A method called symmetric extension improved performance in subband image compression systems compared to the earlier method of circular convolution. However, the symmetric extension method was developed only for two-band uniform filter banks, and required even-length linear phase analysis filters. The authors generalize the symmetric extension method to the M-band, possibly nonuniform filter banks, where M=/>2. The length restriction on the analysis filters is relaxed.

FIR principal component filter banks

Two-dimensional (2-D) principal component filter banks (PCFBs) of finite impulse response (FIR) are proposed. For 2-D signals, among all uniform paraunitary FIR analysis/synthesis filter banks, the FIR PCFBs have the most energy compaction and maximize the arithmetic mean to geometric mean ratio (AM/GM ratio) of subband variances, which is the theoretic coding gain (TCC) of the systems under proper assumptions. The theoretic proof and design techniques are provided. Several special cases are discussed. Experimental results show the potential power of the FIR PCFBs.

New results on two and three dimensional directional filter banks

Recently, a family of multidimensional, non-separable filter banks known as directional filter banks were introduced. In subsequent works, these filter banks were shown to be effective for the detection and enhancement of linear features in noisy environments, resolution enhancement, and in subband image coding. In this paper, simplifying the design and implementation of the directional filter bank and also extending the directional filter bank constructs to the decomposition of three dimensional data such as video is focused upon. These new decompositions are generated by applying the two-dimensional decompositions utilized in the directional filter bank family along the different planes of the three dimensional signal. The three dimensional subband decompositions may be useful in motion detection and compensation for video sequence analysis and compression as well as linear and planar motion detection in noisy environments.<<ETX>>

Rules for multidimensional multirate structures

Identifies a comprehensive set of compact rules and efficient algorithms for simplifying and rearranging structures common in multidimensional multirate signal processing. The authors extend the 1D rules reported by Crochiere and Rabiner (1983), especially the many equivalent forms of cascades of upsamplers and downsamplers. They also include rules reported by other authors for completeness. The extension to mD is based primarily on the Smith form decomposition of resampling (nonsingular integer square) matrices. The Smith form converts non-separable multidimensional operations into separable ones by means a shuffling of input samples and a reshuffling of the separable operations. Based on the Smith form, the authors have developed algorithms for 1) computing coset vectors 2) finding greatest common sublattices 3) simplifying cascades of up/downsampling operations. The algorithms and rules are put together in a form that can be implemented efficiently in a symbolic algebra package. The authors have encoded the knowledge in the commercially available Mathematica environment. >

Comparison of different methods of classification in subband coding of images

Spatially varying quantization schemes try to exploit the non-stationary nature of image subbands. One technique for spatially varying quantization is classification based on AC energy of blocks. Several different methods of subband classification have been proposed in the literature. One method is to optimally classify each subband and send the classification maps as side information. Although image subbands can be shown to be roughly uncorrelated, they are not independent. Naveen and Woods proposed a method in which classification is done based on the AC energy of the block corresponding to the same spatial location, but from the lower frequency band. In their method, inter-subband dependence is exploited to almost completely eliminate side information, albeit at the cost of decreasing classification gain. In this paper, we proposed a new method of classification based on vector quantization of AC energy n-tuples formed by energies of blocks which correspond to the same spatial location in the original image but belong to different subbands. This method allows us to reduce the side information at the same time maximizing classification gain for each band under the vector constraint. The performance of the new method is compared with the other two methods. The comparison is made based on conditional entropies as well as actual bit rates.

Combining subband decomposition and sigma delta modulation for wideband A/D conversion

This paper describes a method of digitizing a wide-band signal by performing subband decomposition via a bank of tuned bandpass sigma-delta modulators. Each modulator only converts a portion of the signal spectrum, increasing the effective oversampling ratio for the wide-band signal by the number of parallel modulators. A prototype bandpass /spl Sigma//spl Delta/ modulator with a programmable noise null was fabricated in a 2 /spl mu/m CMOS process and used to construct a four channel parallel A/D conversion system.<<ETX>>

H/sub /spl infin// deconvolution filter design and its application in image restoration

This paper addresses the use of H/sub /spl infin// filtering to deconvolution, in particular, to the problem of image restoration. The proposed H/sub /spl infin// deconvolution filter has some advantages in the image restoration such as it can deal with unknown boundary problem and spatially varying blurs. The H/sub /spl infin// filter is compared with the inverse Wiener filter and a regularized restoration. The experimental results show that the H/sub /spl infin// filter deals with the unknown boundary problem better than the Wiener filter. Compared with the regularization method, it gives a sharper restored image, especially, when the original image contains many details.

Size-limited filter banks for subband image compression

A size-limited filter bank (SLFB) is a maximally decimated filter bank operating on a finite length (duration) input signal resulting in subband components whose total number of independent samples is equal to the number of input samples. A theoretical framework for the design, analysis, and implementation of such filter banks resulting from applying FIR separable filter banks to finite length signals is presented. The concept of maximizing theoretical coding gain (TCG) using optimal bit allocation is generalized for this special case. Using TCG, the relative merits of various different SLFBs are addressed.

A theory of size-limited filter banks

A theoretical framework for the design, implementation, and analysis of size-limited filter banks was presented by the same authors (1992). Several properties of these size-limited filter banks are discussed in detail. Two classes of size-limited filter banks based on linear time-varying (LTV) filters are presented. The relative merits of the various size-limited filter banks are assessed. This is accomplished by generalizing the concepts of theoretical coding gain (TCG) and optimal bit allocation to the size-limited filter banks and then calculating the TCG for a variety of different size-limited filter banks and input signals. In particular, it is revealed that, for finite extent inputs which are derived by windowing first-order autoregressive (AR) random processes, the performance of the different size-limited filter banks is a function of the degree of correlation in the AR process.<<ETX>>