Subband Coding Research Articles

3D Scan-Based Wavelet Transform and Quality Control for Video Coding

Wavelet coding has been shown to achieve better compression than DCT coding and moreover allows scalability. 2D DWT can be easily extended to 3D and thus applied to video coding. However, 3D subband coding of video suffers from two drawbacks. The first is the amount of memory required for coding large 3D blocks; the second is the lack of temporal quality due to the sequence temporal splitting. In fact, 3D block-based video coders produce jerks. They appear at blocks temporal borders during video playback. In this paper, we propose a new temporal scan-based wavelet transform method for video coding combining the advantages of wavelet coding (performance, scalability) with acceptable reduced memory requirements, no additional CPU complexity, and avoiding jerks. We also propose an efficient quality allocation procedure to ensure a constant quality over time.

Reconstruction-Based Subband Image Coding for UDP Transmissions over the Internet

Quality-delay trade-offs can be made in transmitting subband-coded images in the Internet by using either the TCP or the UDP protocol. Delivery by TCP gives superior decoding quality but with very long delays when the network is unreliable, whereas delivery by UDP has negligible delays but with degraded quality when packets are lost. Although images are delivered primarily by TCP today, we study in this paper the use of UDP to deliver multi-description reconstruction-based subband-coded images and the reconstruction of missing information at the receiver based on information received. We first determine empirically the interleaving factors that should be used in order to keep the probability of unrecoverable packet losses sufficiently small. Next, we propose a joint sender-receiver approach for designing transforms in multi-description subband coding. In the receiver, we use a simple interpolation-based reconstruction algorithm, as sophisticated concealment techniques cannot be employed in practice. In the sender, we design an optimized reconstruction-based subband transform (ORB-ST), with an objective of minimizing the mean squared error, assuming that some of the descriptions are lost and that the missing information is reconstructed by simple averaging at the destination. Experimental results show that our proposed ORB-ST performs well in real Internet tests, and UDP delivery of MDC images is an attractive alternative to TCP delivery.

画像符号化用電力相補特性２チャネル直線位相偶数次ＩＩＲフィルタバンク

This paper presents a method for designing a 6th-order two-channel linear-phase IIR filter bank with quasi-power complementary characteristics for image subband coding. The lowpass filter is specified to have a double or quadruple zero at ω = π and is designed with weighted equiripple approximation based on the formulation of an eigen-value problem. A design example of an image subband coding system using a three-stage octave division filter bank with rounded integer analysis output signals has shown to have a pseudo perfect reconstruction image “Lena” with a PSNR as highas 55.8 dB. The coding performance (PSNR versus bit rate) using bit plane arithmetic coding was nearly equal to that of 5th-order IIR filter banks and superior to 9 / 7 FIR filter banks.

Subband coding of cyclostationary signals

Fig. 4. The control input using the boundary-layer technique. formed LTV system to retain the dynamical features of the original LTV system. The update law of the transformation matrix using a timevarying differential Sylvester equation has been developed to guarantee the uniformly exponential convergence of the closed-loop dynamics on the sliding mode. A robust sliding-mode output regulator using only the output measurements has been designed to drive the system output to converge to zero in a finite time. A simulation example has been carried out with the results that good convergence and robustness properties with respect to the bounded input disturbance are obtained. Further work is to extend the scheme to the control of general SISO and MIMO LTV systems with uncertainties. REFERENCES

Quantisation noise control in perceptual audio coding using low selectivity filter banks

The problem of computing, in a subband audio coder, the maximum quantisation noise power that can be injected in each band to ensure transparent coding when low selectivity filter banks are used, is addressed. A low complexity strategy, taking into account the frequency responses of the synthesis filter bank, is proposed for achieving an overall distortion due to quantisation noise always below the masking threshold (provided by a psycho-acoustic model) for any length prototype filters.

Image compression using wavelets and JPEG2000: a tutorial

The demand for higher and higher quality images transmitted quickly over the Internet has led to a strong need to develop better algorithms for the filtering and coding of such images. The introduction of the JPEG2000 compression standard has meant that for the first time the discrete wavelet transform (DWT) is to be used for the decomposition and reconstruction of images together with an efficient coding scheme. The use of wavelets implies the use of subband coding in which the image is iteratively decomposed into high- and low-frequency bands. Thus there is a need for filter pairs at both the analysis and synthesis stages. This paper aims in tutorial form to introduce the DWT, to illustrate its link with filters and filterbanks and to illustrate how it may be used as part of an image coding algorithm. It concludes with a look at the qualitative differences between images coded using JPEG2000 and those coded using the existing JPEG standard.

Allpass delay chain-based IIR PR filterbank and its application to multiple description subband coding

A class of infinite impulse response (IIR) perfect reconstruction (PR) filterbank is obtained with an allpass delay chain and finite impulse response (FIR) matrices at the analysis side. Such a formulation leads to a filterbank that can be optimized to any desired response. For a first-order allpass, the synthesis bank becomes FIR. Design examples showing warping of the frequency scale and filters with unequal passband widths are presented. The latter part of the work deals with designing a filterbank for a multiple description coding scenario. This is achieved in two parts: by obtaining the MMSE synthesis bank for a given analysis bank and channel state and by optimizing the analysis response to minimize the average distortion in the presence of channel erasures and quantization. The proposed IIR filterbank, as well as the well-known FIR paraunitary filterbank, are optimized for various channels, and their performances for the two-channel case have been compared with the derived optimal performance.

Construction of optimal subband coders using optimized and optimal quantizers

A method is presented for the optimization of arbitrary quantizers by use of a compensating postfilter. It is shown that the resulting optimized quantizers fit the model of a linear time-invariant filter followed by additive noise uncorrelated with the input which also characterizes the optimal (Lloyd-Max) quantizers. On the basis of this model, an expression for the variance of the error of a subband coder using optimized quantizers is explicitly determined. Given analysis filters which statistically separate the subbands, it is shown that this variance is minimized if these synthesis filters are chosen, which would achieve perfect reconstruction in lossless coding. The globally optimum filter bank, minimizing the coder error variance, is further obtained by proper choice of its analysis filters. A novel method for the determination of optimal bit allocation to subbands of the filter banks with optimized quantizers is also developed. The results are evaluated experimentally by comparison of the optimum uniformly split subband image coding scheme to classical logarithmically-split filter bank (wavelet) coding methods.

A warped linear-prediction-based subband audio coding algorithm

A novel audio coding algorithm is proposed where the warped-linear prediction (WLP) technique is employed to construct a perceptual pre- and post-filter for subband audio coding. A modified signal-to-mask ratio (SMR) calculation is given for subband coding of the WLP residuals of audio signals. The concept of perceptual entropy (PE) is extended to subband coding, resulting in the subband perceptual entropy (SPE), which gives a short time estimate of the lowest possible bit rate for transparent subband audio coding. Two WLP models with frequency responses approximating the spectral shape of the masking threshold are investigated and it is found that the residual signals of both models contain less SPE compared with that of the original audio signals. Subjective tests show that the proposed audio codec operating at 56 kbps has a perceptual quality comparable to MPEG-1 audio Layer II operating at 64 kbps.

Speech transmission using rate-compatible trellis codes and embedded source coding

This paper presents bandwidth-efficient speech transmission systems using rate-compatible channel coders and variable bitrate embedded source coders. Rate-compatible punctured convolutional codes (RCPC) are often used to provide unequal error protection (UEP) via progressive bit puncturing. RCPC codes are well suited for constellations for which Euclidean and Hamming distances are equivalent (BPSK and 4-PSK). This paper introduces rate-compatible punctured trellis codes (RCPT) where rate compatibility and UEP are provided via progressive puncturing of symbols in a trellis. RCPT codes constitute a special class of codes designed to maximize residual Euclidean distances (RED) after symbol puncturing. They can be designed for any constellation, allowing for higher throughput than when restricted to using 4-PSK. We apply RCPC and RCPT to two embedded source coders: a perceptual subband coder and the ITU embedded ADPCM G.727 standard. Different operating modes with distinct source/channel bit allocation and UEP are defined. Each mode is optimal for a certain range of AWGN channel SNRs. Performance results using an 8-PSK constellation clearly illustrate the wide range of channel conditions at which the adaptive scheme using RCPT can operate. For an 8-PSK constellation, RCPT codes are compared to RCPC with bit interleaved coded modulation codes (RCPC-BICM). We also compare performance to RCPC codes used with a 4-PSK constellation.

Audio decoding with frequency and complexity scalability

The paper describes a technique to design a complexity-scalable audio codec based on the partial reconstruction of the spectrum of a signal. The technique can be applied to any subband coding system based on cosine-modulated filterbanks. In the decoder, only a part of the subband is reconstructed, achieving an output signal with a lower sampling rate. The new synthesis filterbank, with a reduced number of channels and low computational cost, must be suitably designed. Hence, computational saving is traded for lower quality in the reconstructed signal. The technique can be used to design low-complexity decoders compatible with the MPEG audio standard, i.e. able to decode only a part of an MPEG bit stream. In this way, a single MPEG-coded audio can be decoded by different receivers, i.e. standard and low-complexity ones. The problem of having fixed bit rate streams for all the decoders will be discussed.

Optimality in Multi Carrier Communication, Multiple Description Coding and the Subband Coding of Cyclostationary Signals

This paper considers three different problems in signal processing/communications. The first involves Multiuser Discrete Multitone Transmission (DMT). The other two problems concerns variants of subband coding, specifically subband coding of cyclostationary signals and the multiple description coding. We show that underlying each is the same optimization problem that can be solved using the theory of majorization.

Design of low‐delay perfect‐reconstruction filter banks using linear programming

AbstractIn many applications of filter banks, a low‐delay filter bank in which the system delay is small is desirable. In this paper, two new design methods are proposed for low‐delay perfect‐reconstruction filter banks. First, a design method is described for a two‐channel perfect‐reconstruction filter bank suitable for subband coding. In this method, a high‐pass filter for perfect reconstruction is designed for an arbitrary low‐pass filter. Next, a design method is described for an oversampling perfect‐reconstruction DFT filter bank suitable for subband adaptive filter. In this method, a prototype filter for a perfect‐reconstruction synthesizer is designed for the prototype filter for an arbitrary analyzer. The effectiveness of the present method is demonstrated by design examples. © 2001 Scripta Technica, Electron Comm Jpn Pt 2, 84(6): 30–39, 2001

Three-Dimensional Embedded Subband Coding with Optimized Truncation (3-D ESCOT)

This paper presents an efficient video coding algorithm: Three-dimensional embedded subband coding with optimized truncation (3-D ESCOT), in which coefficients in different subbands are independently coded using fractional bit-plane coding and candidate truncation points are formed at the end of each fractional bit-plane. A rate-distortion optimized truncation scheme is used to multiplex all subband bitstreams together into a layered one. A novel motion threading technique is proposed to form threads along the motion trajectories in a scene. For efficient coding of motion threads, memory-constrained temporal wavelet transforms are applied along entire motion threads. Block-based motion threading is implemented in conjunction with 3-D ESCOT in a real video coder. Extension of 3-D ESCOT to object-based coding is also addressed. Experiments demonstrate that 3-D ESCOT outperforms MPEG-4 for most test sequences at the same bit rate.

Edge enhancement for subband-coded images

Subband coding is a well-established technique. Coding algorithms, however, rarely try to exploit residual similarities between subbands in order to get both coding gain and improvement in visual appearance. In this work we propose a simple postprocessing technique for edge enhancement and ringing-artifact reduction in subband-coded images. The proposed technique employs morphological filtering for preliminary image simplification and uses a novel dual-window nonlinear operator for subsequent edge enhancement. Visual appearance and numerical results confirm the validity of the approach. A simple coding scheme, designed to test the efficiency of the approach, gives good results.

Embedded video coding using invertible motion compensated 3-D subband/wavelet filter bank

Abstract In this paper, we present a new embedded video coding system with local motion compensation. An invertible motion compensated 3-D subband filter bank is utilized for video analysis/synthesis. The efficient embedded image coding scheme EZBC is extended to 3-D coding of video subbands. The coded bitstream is rate scalable and fully embedded thus meeting the increasing need for fine granular scalability in video streaming applications. Our experimental results show the new algorithm outperforms nonscalable standard MPEG-2 by 0.8– 3.3 dB (luminance component) over a broad range of bitrates, while providing an embedded video bitstream. Unlike conventional SNR hybrid coders, this multirate property is achieved without a loss in compression efficiency. Comparisons are also made to two other competing embedded video coders, LZC and 3D-SPIHT, both based on 3-D subband coding as well. The new coder demonstrates a significant advantage for encoding video with high local motion content, thanks to the efficient inclusion of local motion information in the temporal filter bank of our proposed system.

A Review of the Theory and Applications of Optimal Subband and Transform Coders

The problem of optimizing digital filter banks based on input statistics was perhaps first addressed nearly four decades ago by Huang and Schultheiss. These authors actually considered a special case, namely transform coder optimization. Many of the subband coder optimization problems considered in recent years have close similarities to this work, though there are fundamental differences as well. Filter banks are used today not only for signal compression, but have found applications in signal denoising and in digital communications. A recent result is that principal component filter banks (PCFBs) offer an optimal solution to many problems under certain theoretical assumptions. While this result is quite powerful and includes several earlier results as special cases, there still remain some open problems in the area of filter bank optimization. We first give a review of the older classical methods to place the ideas in the right perspective. We then review recent results on PCFBs. The generality of these results is demonstrated by showing an application in digital communications (the discrete multitone channel). We show, for example, that the PCFB minimizes transmitted power for a given probability of error and bit rate. Future directions and open problems are discussed as well.

Rate-distortion-optimal subband coding without perfect-reconstruction constraints

We investigate the design of subband coders without the traditional perfect-reconstruction constraint on the filters. The coder uses scalar quantizers, and its filters and bit allocation are designed to optimize a rate-distortion criterion. Using convexity analysis, we show that optimality can be achieved using filterbanks that are the cascade of a (paraunitary) principal component filterbank for the input spectral process and a set of pre and postfilters surrounding each quantizer. Analytical expressions for the pre and postfilters are then derived. An algorithm for computing the globally optimal filters and bit allocation is given. We also develop closed-form solutions for the special case of two-channel coders under an exponential rate-distortion model. Finally, we investigate a constrained-length version of the filter design problem, which is applicable to practical coding scenarios. While the optimal filterbanks are nearly perfect-reconstruction at high rates, we demonstrate an apparently surprising advantage of optimal FIR filterbanks; they significantly outperform optimal perfect-reconstruction FIR filterbanks at all bit rates.

Noise reduction in oversampled filter banks using predictive quantization

We introduce two methods for quantization noise reduction in oversampled filter banks. These methods are based on predictive quantization (noise shaping or linear prediction). It is demonstrated that oversampled noise shaping or linear predictive subband coders are well suited for subband coding applications where, for technological or other reasons, low-resolution quantizers have to be used. In this case, oversampling combined with noise shaping or linear prediction improves the effective resolution of the subband coder at the expense of increased rate. Simulation results are provided to assess the achievable quantization noise reduction and resolution enhancement, and to investigate the rate-distortion properties of the proposed methods.

A tutorial on modern lossy wavelet image compression: foundations of JPEG 2000

One of the purposes of this article is to give a general audience sufficient background into the details and techniques of wavelet coding to better understand the JPEG 2000 standard. The focus is on the fundamental principles of wavelet coding and not the actual standard itself. Some of the confusing design choices made in wavelet coders are explained. There are two types of filter choices: orthogonal and biorthogonal. Orthogonal filters have the property that there are energy or norm preserving. Nevertheless, modern wavelet coders use biorthogonal filters which do not preserve energy. Reasons for these specific design choices are explained. Another purpose of this article is to compare and contrast "early" wavelet coding with "modern" wavelet coding. This article compares the techniques of the modern wavelet coders to the subband coding techniques so that the reader can appreciate how different modern wavelet coding is from early wavelet coding. It discusses basic properties of the wavelet transform which are pertinent to image compression. It builds on the background material in generic transform coding given, shows that boundary effects motivate the use of biorthogonal wavelets, and introduces the symmetric wavelet transform. Subband coding or "early" wavelet coding method is discussed followed by an explanation of the EZW coding algorithm. Other modern wavelet coders that extend the ideas found in the EZW algorithm are also described.