John W. Woods

Subband coding of images

Subband coding has become quite popular for the source encoding of speech. This paper presents a simple yet efficient extension of this concept to the source coding of images. We specify the constraints for a set of two-dimensional quadrature mirror filters (QMFs) for a particular frequency-domain partition, and show that these constraints are satisfied by a separable combination of one-dimensional QMFs. Bits are then optimally allocated among the subbands to minimize the mean-squared error for DPCM coding of the subbands. Also, an adaptive technique is developed to allocate the bits within each subband by means of a local variance mask. Optimum quantization is employed with quantizers matched to the Laplacian distribution. Subband coded images are presented along with their signal-to-noise ratios (SNRs). The SNR performance of the subband coder is compared to that of the adaptive discrete cosine transform (DCT), vector quantization, and differential vector quantization for bit rates of 0.67, 1.0, and 2.0 bits per pixel for 256 × 256 monochrome images. The adaptive subband coder has the best SNR performance.

Motion-compensated 3-D subband coding of video

This paper describes a video coding system based on motion-compensated three-dimensional (3-D) subband/wavelet coding (MC-3DSBC), which can overcome the limits of both 3-D SBC and MC prediction-based coding. In this new system, spatio-temporal subbands are generated by MC temporal analysis and a spatial wavelet transform, and then encoded by 3-D subband-finite state scalar quantization (3DSB-FSSQ). The rate allocation from the GOP level to each class of subbands is optimized by utilizing the structural property of MC-3DSBC that additive superposition approximately holds for both rate and distortion. The proposed video coding system is applied to several test video clips. Its performance exceeds that of both a known MPEG-1 implementation and a similar subband MC predictive coder while maintaining modest computational complexity and memory size.

Two-dimensional discrete Markovian fields

A definition of discrete Markovian random fields is formulated analogously to a definition for the continuous case given by Levy. This definition in the homogeneous Gaussian case leads to a difference equation that sets forth the state of the field in terms of its values on a band of minimum width P , where P is the order of the process. The state of the field at position (i,j) is given by the set of values of the nearest neighbors within distance P of the point (i,j) . Conversely, given a difference equation satisfying certain conditions relating to stability, there corresponds a homogeneous discrete Markov random field. This theory is applied to the problem of obtaining spectral estimates of a two-dimensional field, given observation over a limited aperture.

Kalman filtering in two dimensions

The Kalman filtering method is extended to two dimensions. The resulting computational load is found to be excessive. Two new approximations are then introduced. One, called the strip processor, updates a line segment at a time; the other, called the reduced update Kalman filter, is a scalar processor. The reduced update Kalman filter is shown to be optimum in that it minimizes the post update mean-square error (mse) under the constraint of updating only the nearby previously processed neighbors. The resulting filter is a general two-dimensional recursive filter.

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.

Kalman filtering in two dimensions: Further results

The two-dimensional reduced update Kalman filter was recently introduced. The corresponding scalar filtering equations were derived for the case of estimating a Gaussian signal in white Gaussian noise and were shown to constitute a general nonsymmetric half-plane recursive filter. This paper extends the method to the deconvolution problem of image restoration. This paper also provides a more thorough treatment of the uniquely two-dimensional boundary condition problems. Numerical and subjective examples are presented.

Bidirectional MC-EZBC with lifting implementation

In conventional motion-compensated three-dimensional subband/wavelet coding, where the motion compensation is unidirectional, incorrect classification of connected and unconnected pixels caused by incorrect motion vectors (MVs) has resulted in some coding inefficiency and visual artifacts in the embedded low-frame-rate video. In this paper, we introduce bidirectional motion compensated temporal filtering with unconnected pixel detection and I blocks. We also incorporate a recently suggested lifting implementation of the subband/wavelet filter for improved MV accuracy in an MC-EZBC coder. Simulation results compare PSNR performance of this new version of MC-EZBC versus H.26L under the constraint of equal groups of pictures size, and show a general parity with this state-of-the-art nonscalable coder on several test clips.

Compound Gauss-Markov random fields for image estimation

Algorithms for obtaining approximations to statistically optimal estimates for images modeled as compound Gauss-Markov random fields are discussed. The authors consider both the maximum a posteriori probability (MAP) estimate and the minimum mean-squared error (MMSE) estimate for image estimation and image restoration. Compound image models consist of several submodels having different characteristics along with an underlying structure model which govern transitions between these image submodels. Two different compound random field models are employed, the doubly stochastic Gaussian (DSG) random field and a compound Gauss-Markov (CGM) random field. The authors present MAP estimators for DSG and CGM random fields using simulated annealing. A fast-converging algorithm called deterministic relaxation, which, however, converges to only a locally optimal MAP estimate, is also presented as an alternative for reducing computational loading on sequential machines. For comparison purposes, the authors include results on the fixed-lag smoothing MMSE estimator for the DSG field and its suboptimal M-algorithm approximation. >

Sub-band coding of images

This paper presents an extension of sub-band coding to two-dimensions with particular application to images. We employ a 16 band decomposition using a tree structure of separable quadrature mirror filters and decimators. The sub-bands are encoded using DPCM with bits allocated to approximately minimize the mean-square error. A block-adaptive variant is also presented. A limited SNR comparison shows adaptive sub-band coding to outperform the adaptive discrete cosine transform and two types of vector quantizers.

Embedded image coding using zeroblocks of subband/wavelet coefficients and context modeling

With fast computation and excellent compression efficiency, two embedded coding techniques, zero-tree/-block coding and context modeling of the subband/wavelet coefficients, have been widely utilized for image coding applications. In this research, we present a new embedded wavelet image coding algorithm with an attempt to combine advantages of these two successful coding schemes. The experimental results show that the proposed algorithm outperforms the respected zero-tree/-block coders, SPIHT and SPECK, in compression efficiency. It is also comparable to the state-of-art JPEG 2000 test coder in PSNR performance while retaining the attractive low-complexity feature of the zeroblock coders.