Minimum mean-squared error transform coding and subband coding

Knowledge of the power spectrum of a stationary random sequence can be used for quantizing the signal efficiently and with minimum mean-squared error. A multichannel filter is used to transform the random sequence into an intermediate set of variables that are quantized using independent scalar quantizers, and then inverse-filtered, producing a quantized version of the original sequence. Equal word-length and optimal word-length quantization at high bit rates is considered. An analytical solution for the filter that minimizes the mean-squared quantization error is obtained in terms of its singular value decomposition. The performance is characterized by a set of invariants termed second-order modes, which are derived from the eigenvalue decomposition of the matrix-valued power spectrum. A more general rank-reduced model is used for decreasing distortion by introducing bias. The results are specialized to the case when the vector-valued time series is obtained from a scalar random sequence, which gives rise to a filter bank model for quantization. The asymptotic performance of such a subband coder is derived and shown to coincide with the asymptotic bound for transform coding. Quantization employing a single scalar pre- and postfilter, traditional transform coding using a square linear transformation, and subband coding in filter banks, arise as special cases of the structure analyzed here     

Predictive subband image coding with wavelet transform

Wavelet transform can decompose images into various multiresolution subbands. In these subbands the correlation exists. A novel technique for image coding by taking advantage of the correlation is addressed. It is based on predictive edge detection from the LL band of the lowest resolution level to predict the edge in the LH, HL and HH bands in the higher resolution level. If the coefficient is predicted as an edge it is preserved; otherwise, it is discarded. In the decoder, the location of the preserved coefficients can also be found as in the encoder. Therefore, no overhead is needed. Instead of complex vector quantization, which is commonly used in subband image coding for high compression ratio, simple scalar quantization is used to code the remaining coefficients and achieves very good results.     

Multi-channel overlapping rounding transform for HINT and subband lossless image compression

In this paper, an ORT-based (overlapping rounding transform-based) multi-channel filtering technique is proposed. We show that the proposed technique does not only unify the computations of the HINT (hierarchical interpolation) algorithms, but enables also multi-channel subband filter banks to be applied to lossless image compression. As examples, two efficient non-separable four-channel filter banks are newly presented.     

LINC: a common theory of transform and subband coding

A common theory of lapped orthogonal transforms (LOTs) and critically sampled filter banks, called L into N coding (LINC), is presented. The theory includes a unified analysis of both coding methods and identity relations between the transform, inverse transform, analysis filter bank, and synthesis filter bank. A design procedure for LINC analysis/synthesis systems, which satisfy the conditions for perfect reconstruction, is developed. The common LINC theory is used to define an ideal LINC system which is used, together with the power spectral density of the input signal, to calculate theoretical bounds for the coding gain. A generalized overlapping block transform (OBT) with time domain aliasing cancellation (TDAC) is used to approximate the ideal LINC. A generalization of the OBT includes multiple block overlap and additional windowing. A recursive design procedure for windows of arbitrary lengths is presented. The coding gain of the generalized OBT is higher than that of the Karhunen-Loeve transform (KLT) and close to the theoretical bounds for LINC. In the case of image coding, the generalized OBT reduces the blocking effects when compared with the DCT     

Generalized unequal length lapped orthogonal transform for subband image coding

Generalized linear phase lapped orthogonal transforms with unequal length basis functions (GULLOTs) are considered. The length of each basis of the proposed GULLOT can be different from each other, whereas all the bases of the conventional GenLOT are of equal length. In general, for image coding application, the long basis for a low-frequency band and the short basis for a high-frequency one are desirable to reduce the blocking and the ringing artifact simultaneously. Therefore, the GULLOT is suitable especially for a subband image coding. In order to apply the GULLOT to a subband image coding, we also investigate the size-limited structure to process the finite length signal, which is important in practice. Finally, some design and image coding examples are shown to confirm the validity of the proposed GULLOT.     

Hybrid image compression model based on subband coding andedge-preserving regularisation

An edge-preserving image compression model is presented, based on subband coding and iterative constrained least square regularisation. The idea is to incorporate the technique of image restoration into the current lossy image compression schemes. The model utilises the edge information extracted from the source image as a priori knowledge for the subsequent reconstruction. Generally, the extracted edge information has a limited range of magnitudes and it can be lossily conveyed. Subband coding, one of the outstanding lossy image compression schemes, is incorporated to compress the source image. Vector quantisation, a block-based lossy compression technique, is employed to compromise the bit rate incurred by the additional edge information and the target bit rate. Experiments show that the approach could significantly improve both the objective and subjective quality of the reconstructed image by preserving more edge details. Specifically, the model incorporated with SPIHT (set partitioning in hierarchical trees) outperformed the original SPIHT with the “Baboon” continuous-tone test image. In general, the model may be applied to any lossy image compression systems     

Regularized subband coding scheme

Two enhanced subband coding schemes using a regularized image restoration technique are proposed: the first controls the global regularity of the decompressed image; the second extends the first approach at each decomposition level. The quantization scheme incorporates scalar quantization (SQ) and pyramidal lattice vector quantization (VQ) with both optimal bit and quantizer allocation. Experimental results show that both the block effect due to VQ and the quantization noise are significantly reduced.     

Rate-distortion-constrained subband video coding

This paper introduces a subband video coding algorithm for operation over a continuum of rates from very low to very high. The key elements of the system are statistical rate-distortion-constrained motion estimation and compensation, multistage residual quantization, high order statistical modeling, and arithmetic coding. The method is unique in that it provides an improved mechanism for dynamic spatial and temporal coding. Motion vectors are determined in a nontraditional way, using a rate-distortion cost criterion. This results in a smoother and more consistent motion field, relative to that produced by conventional block matching algorithms. Control over the system computational complexity and performance may be exercised easily     

Three-dimensional subband coding of video

We describe and show the results of video coding based on a three-dimensional (3-D) spatio-temporal subband decomposition. The results include a 1-Mbps coder based on a new adaptive differential pulse code modulation scheme (ADPCM) and adaptive bit allocation. This rate is useful for video storage on CD-ROM. Coding results are also shown for a 384-kbps rate that are based on ADPCM for the lowest frequency band and a new form of vector quantization (geometric vector quantization (GVQ)) for the data in the higher frequency bands. GVQ takes advantage of the inherent structure and sparseness of the data in the higher bands. Results are also shown for a 128-kbps coder that is based on an unbalanced tree-structured vector quantizer (UTSVQ) for the lowest frequency band and GVQ for the higher frequency bands. The results are competitive with traditional video coding techniques and provide the motivation for investigating the 3-D subband framework for different coding schemes and various applications.     

New directions in subband coding

Two very different subband coders are described. The first is a modified dynamic bit-allocation-subband coder (D-SBC) designed for variable rate coding situations and easily adaptable to noisy channel environments. It can operate at rates as low as 12 kb/s and still give good quality speech. The second coder is a 16-kb/s waveform coder, based on a combination of subband coding and vector quantization (VQ-SBC). The key feature of this coder is its short coding delay, which makes it suitable for real-time communication networks. The speech quality of both coders has been enhanced by adaptive postfiltering. The coders have been implemented on a single AT&T DSP32 signal processor     

Region adaptive subband image coding

We present a region adaptive subband image coding scheme using the statistical properties of image subbands for various subband decompositions. Motivated by analytical results obtained when the input signal to the subband decomposition is a unit step function, we analyze the energy packing properties toward the lower frequency subbands, edges, and the dependency of energy distribution on the orientation of the edges, in subband decomposed images. Based on these investigations and ideal analysis/synthesis filtering done in the frequency domain, the region adaptive subband image coding scheme extracts suitably shaped regions in each subband and then uses adaptive entropy-constrained quantizers for different regions under the assumption of a generalized Gaussian distribution for the image subbands. We also address the problem of determining an optimal subband decomposition among all possible decompositions. Experimental results show that visual degradations in the reconstructed image are negligible at a bit rate of 1.0 b/pel and reasonable quality images are obtainable at rates as low as 0.25 b/pel.     

Rate-distortion-optimal subband coding withoutperfect-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     

基于子带金字塔结构的彩色图像小波编码

本文改进了分层树集分割算法(SPIHT),重新设计了一种子带金字塔的数据结构来组织图像的二维小波变换系数,既减少了存储空间又加快了编码速度.在彩色图像的YUV空间按位平面的顺序依次对YUV三个分量编码,输出颜色分量完全嵌入式的码流.实验结果表明改进后算法对彩色图像的编码能获得很好的率失真性能,而且适用于高分辨率、不规则图像的编解码.     

基于线预测及变换的帧内编码方法

提出一种以线为单位进行帧内预测编码的新方法,从预测及变换两方面提高帧内编码的性能。首先在宏块内部以水平或垂直方向的线为单位,分别参考相邻的行或列像素进行多个方向的帧内预测,减少了预测像素与参考像素间的距离,从而提高预测精度;其次,在原有的4×4离散余弦变换（DCT）基础上补充了1×16的一维DCT,并以宏块为基本单位灵...     

A subband coding, BCH coding, and 16-QAM system for mobile radiospeech communications

A combined subband speech coding (SBC), Bose-Chaudhuri-Hocquenghem (BCH) error-correction coding, and 16-level quadrature amplitude modulation (16-QAM) scheme with switched diversity and speech postenhancement is proposed. The system's performance is dramatically improved by deploying some degree of fade tracking capability over fading channels. Further quality enhancement accrues by using appropriate mapping between the SBC speech codec and the Gray coded QAM words. Various BCH codes are utilized to adequately match the error-correcting power to the perceptual importance of the SBC bits. One of the proposed systems operates at 7 kBd and yields good communications-quality speech for channel signal-to-noise ratios (SNRs) in excess of 20 dB and encounters a maximum overall system delay of 55.125 ms. A more complex arrangement uses second-order switched diversity to reduce the channel SNR required to around 16 dB and the transmission rate to 5 kBd when the vehicular speed is 30 mph while the system delay is unchanged at 55.125 ms     

Three-dimensional subband coding with motion compensation

Three-dimensional (3-D) frequency coding is an alternative approach to hybrid coding concepts used in today's standards. The first part of this paper presents a study on concepts for temporal-axis frequency decomposition along the motion trajectory in video sequences. It is shown that, if a two-band split is used, it is possible to overcome the problem of spatial inhomogeneity in the motion vector field (MVF), which occurs at the positions of uncovered and covered areas. In these cases, original pixel values from one frame are placed into the lowpass-band signal, while displaced-frame-difference values are embedded into the highpass band. This technique is applicable with arbitrary MVF's; examples with block-matching and interpolative motion compensation are given. Derivations are first performed for the example of two-tap quadrature mirror filters (QMF's), and then generalized to any linear-phase QMF's. With two-band analysis and synthesis stages arranged as cascade structures, higher resolution frequency decompositions are realizable. In the second part of the paper, encoding of the temporal-axis subband signals is discussed. A parallel filterbank scheme was used for spatial subband decomposition, and adaptive lattice vector quantization was employed to approach the entropy rate of the 3-D subband samples. Coding results suggest that high-motion video sequences can be encoded at significantly lower rates than those achievable with conventional hybrid coders. Main advantages are the high energy compaction capability and the nonrecursive decoder structure. In the conclusion, the scheme is interpreted more generally, viewed as a motion-compensated short-time spectral analysis of video sequences, which can adapt to the quickness of changes. Although a 3-D multiresolution representation of the picture information is produced, a true multiresolution representation of motion information, based on spatio-temporal decimation and interpolation of the MVF, is regarded as the still-missing part.     

Image data compression using subband coding

A general reversive subband coding system with 2-D infinite impulse response filters is proposed. The system considered guarantees perfect image reconstruction (free of phase distortions). Application of wave digital filters is considered. A new technique of high-frequency source encoding is proposed. The experiments with real images prove high efficiency of the technique proposed.     

Orientation adaptive subband coding of images

In the subband coding of images, directionality of image features has thus far been exploited very little. The proposed subband coding scheme utilizes orientation of local image features to avoid the highly objectionable Gibbs-like phenomena observed at reconstructed image edges with conventional subband schemes at low bit rates, At comparable bit rates, the subjective image quality obtained by our orientation adaptive scheme is considerably enhanced over a conventional separable subband coding scheme, as well as other separable approaches such as the JPEG compression standard.     

ECG compression based on wavelet transform and Golomb coding

A new wavelet-based ECG compression method is presented. Wavelet transform coefficients are quantised with a uniform scalar dead zone quantiser. The Exp-Golomb coding is used to code the lengths of runs of the zero coefficients. The Golomb-Rice coding is used to code the nonzero coefficients. Experiments on several records from the MIT-BIH arrhythmia database show that the proposed coding algorithm outperforms other recently developed ECG compression algorithms.