Recursive time-varying filter banks for subband image coding

Filter banks and wavelet decompositions that employ recursive filters have been considered previously and are recognized for their efficiency in partitioning the frequency spectrum. This paper presents an analysis of a new infinite impulse response (IIR) filter bank in which these computationally efficient filters may be changed adaptively in response to the input. The filter bank is presented and discussed in the context of finite-support signals with the intended application in subband image coding. In the absence of quantization errors, exact reconstruction can be achieved and by the proper choice of an adaptation scheme, it is shown that IIR time-varying filter banks can yield improvement over conventional ones

Role of anticausal inverses in multirate filter-banks. I. System-theoretic fundamentals

In a maximally decimated filter bank with identical decimation ratios for all channels, the perfect reconstructibility property and the nature of reconstruction filters (causality, stability, FIR property, and so on) depend on the properties of the polyphase matrix. Various properties and capabilities of the filter bank depend on the properties of the polyphase matrix as well as the nature of its inverse. In this paper we undertake a study of the types of inverses and characterize them according to their system theoretic properties (i.e., properties of state-space descriptions, McMillan degree, degree of determinant, and so forth). We find in particular that causal polyphase matrices with anticausal inverses have an important role in filter bank theory. We study their properties both for the FIR and IIR cases. Techniques for implementing anticausal IIR inverses based on state space descriptions are outlined. It is found that causal FIR matrices with anticausal FIR inverses (cafacafi) have a key role in the characterization of FIR filter banks. In a companion paper, these results are applied for the factorization of biorthogonal FIR filter banks, and a generalization of the lapped orthogonal transform called the biorthogonal lapped transform (BOLT) developed

Theory and design of uniform DFT, parallel, quadrature mirror filter banks

In this paper, the theory of uniform DFT, parallel, quadrature mirror filter (QMF) banks is developed. The QMF equations, i.e., equations that need to be satisfied for exact reconstruction of the input signal, are derived. The concept of decimated filters is introduced, and structures for both analysis and synthesis banks are derived using this concept. The QMF equations, as well as closed-form expressions for the synthesis filters needed for exact reconstruction of the input signalx(n), are also derived using this concept. In general, the reconstructed. signalhat{x}(n)suffers from three errors: aliasing, amplitude distortion, and phase distortion. Conditions for exact reconstruction (i.e., all three distortions are zero, andhat{x}(n)is equal to a delayed version ofx(n))of the input signal are derived in terms of the decimated filters. Aliasing distortion can always be completely canceled. Once aliasing is canceled, it is possible to completely eliminate amplitude distortion (if suitable IIR filters are employed) and completely eliminate phase distortion (if suitable FIR filters are employed). However, complete elimination of all three errors is possible only with some simple, pathalogical stable filter transfer functions. In general, once aliasing is canceled, the other distortions can be minimized rather than completely eliminated. Algorithms for this are presented. The properties of FIR filter banks are then investigated. Several aspects of IIR filter banks are also studied using the same framework

Sub-band/transform compression of video sequences

The progress on compression of video sequences is discussed. The overall goal of the research was the development of data compression algorithms for high-definition television (HDTV) sequences, but most of our research is general enough to be applicable to much more general problems. We have concentrated on coding algorithms based on both sub-band and transform approaches. Two very fundamental issues arise in designing a sub-band coder. First, the form of the signal decomposition must be chosen to yield band-pass images with characteristics favorable to efficient coding. A second basic consideration, whether coding is to be done in two or three dimensions, is the form of the coders to be applied to each sub-band. Computational simplicity is of essence. We review the first portion of the year, during which we improved and extended some of the previous grant period's results. The pyramid nonrectangular sub-band coder limited to intra-frame application is discussed. Perhaps the most critical component of the sub-band structure is the design of bandsplitting filters. We apply very simple recursive filters, which operate at alternating levels on rectangularly sampled, and quincunx sampled images. We will also cover the techniques we have studied for the coding of the resulting bandpass signals. We discuss adaptive three-dimensional coding which takes advantage of the detection algorithm developed last year. To this point, all the work on this project has been done without the benefit of motion compensation (MC). Motion compensation is included in many proposed codecs, but adds significant computational burden and hardware expense. We have sought to find a lower-cost alternative featuring a simple adaptation to motion in the form of the codec. In sequences of high spatial detail and zooming or panning, it appears that MC will likely be necessary for the proposed quality and bit rates

A 2D DWT architecture suitable for the Embedded Zerotree Wavelet Algorithm

Digital Imaging has had an enormous impact on industrial applications such as the Internet and video-phone systems. However, demand for industrial applications is growing enormously. In particular, internet application users are, growing at a near exponential rate. The sharp increase in applications using digital images has caused much emphasis on the fields of image coding, storage, processing and communications. New techniques are continuously developed with the main aim of increasing efficiency. Image coding is in particular a field of great commercial interest. A digital image requires a large amount of data to be created. This large amount of data causes many problems when storing, transmitting or processing the image. Reducing the amount of data that can be used to represent an image is the main objective of image coding. Since the main objective is to reduce the amount of data that represents an image, various techniques have been developed and are continuously developed to increase efficiency. The JPEG image coding standard has enjoyed widespread acceptance, and the industry continues to explore its various implementation issues. However, recent research indicates multiresolution based image coding is a far superior alternative. A recent development in the field of image coding is the use of Embedded Zerotree Wavelet (EZW) as the technique to achieve image compression. One of The aims of this theses is to explain how this technique is superior to other current coding standards. It will be seen that an essential part orthis method of image coding is the use of multi resolution analysis, a subband system whereby the subbands arc logarithmically spaced in frequency and represent an octave band decomposition. The block structure that implements this function is termed the two dimensional Discrete Wavelet Transform (2D-DWT). The 20 DWT is achieved by several architectures and these are analysed in order to choose the best suitable architecture for the EZW coder. Finally, this architecture is implemented and verified using the Synopsys Behavioural Compiler and recommendations are made based on experimental findings

A hybrid low bit-rate video codec using subbands and statistical modeling

A hybrid low bit-rate video codes using subbands and statistical modeling is proposed in this thesis. The redundancy within adjacent video frames is exploited by motion estimation and compensation. The Motion Compensated Frame Difference (MCFD) signals are decomposed into 7 subbands using 2-D dyadic tree structure and separable filters. Some of the subband signals are statistically modeled by using the 2-D AR(1) technique. The model parameters provide a representation of these subbands at the receiver side with a. certain level of error. The remaining subbands are compressed employing a classical waveform coding technique, namely vector quantization (VQ). It is shown that the statistical modeling is a viable representation approach for low-correlated subbands of MCFD signal.The subbands with higher correlation are better represented with waveform coding techniques

Multirate digital filters, filter banks, polyphase networks, and applications: a tutorial

Multirate digital filters and filter banks find application in communications, speech processing, image compression, antenna systems, analog voice privacy systems, and in the digital audio industry. During the last several years there has been substantial progress in multirate system research. This includes design of decimation and interpolation filters, analysis/synthesis filter banks (also called quadrature mirror filters, or QMFJ, and the development of new sampling theorems. First, the basic concepts and building blocks in multirate digital signal processing (DSPJ, including the digital polyphase representation, are reviewed. Next, recent progress as reported by several authors in this area is discussed. Several applications are described, including the following: subband coding of waveforms, voice privacy systems, integral and fractional sampling rate conversion (such as in digital audio), digital crossover networks, and multirate coding of narrow-band filter coefficients. The M-band QMF bank is discussed in considerable detail, including an analysis of various errors and imperfections. Recent techniques for perfect signal reconstruction in such systems are reviewed. The connection between QMF banks and other related topics, such as block digital filtering and periodically time-varying systems, based on a pseudo-circulant matrix framework, is covered. Unconventional applications of the polyphase concept are discussed

Localized temporal decorrelation for video compression

Many of the current video compression algorithms perform analysis and coding operations in a block-wise manner. Most of them use a motion compensated DCT algorithm as the basis. Many other codecs, mostly academic and in their infancy and known as Second Generation techniques, utilize region and contour based and model based techniques. Unfortunately, these second-generation methods have not been successful in gaining widespread acceptance in both the standards and the consumer world. Many of them require specialized computationally intensive software and/or hardware. Due to these shortcomings, current block based methods have been finetuned to get better performance at even very low bit rates (sub 64 kbps). Block based motion estimation is the principal mechanism used to compensate for motion between frames in an image sequence. Although current algorithms are fast and quite effective, they fail in compensating for uncovered background areas in a frame. Solutions such as hierarchical motion estimation schemes do not work very well since there is no reference in past, and in some cases, future frames for an uncovered background resulting in the block being transmitted as an intra frame (which requires the most bandwidth among all type of blocks). This thesis intro duces an intermediate stage, which compensates for these isolated uncovered areas. The intermediate stage uses a localized decorrelation technique to reduce frame to frame temporal redundancies. The algorithm can be easily incorporated into exist ing systems to achieve an even better performance and can be easily extended as a scalable video coding architecture. Experimental results show that the algorithm, used in conjunction with motion estimation, is quite effective in reducing temporal redundancies