Wavelet compression of ECG signals by the set partitioning in hierarchical trees algorithm.

A wavelet electrocardiogram (ECG) data codec based on the set partitioning in hierarchical trees (SPIHT) compression algorithm is proposed in this paper. The SPIHT algorithm [1] has achieved notable success in still image coding. We modified the algorithm for the one-dimensional case and applied it to compression of ECG data. Experiments on selected records from the MIT-BIH arrhythmia database revealed that the proposed codec is significantly more efficient in compression and in computation than previously proposed ECG compression schemes. The coder also attains exact bit rate control and generates a bit stream progressive in quality or rate.

Variable-length constrained-storage tree-structured vector quantization.

Constrained storage vector quantization, (CSVQ), introduced by Chan and Gersho (1990, 1991) allows for the stagewise design of balanced tree-structured residual vector quantization codebooks with low encoding and storage complexities. On the other hand, it has been established by Makhoul et al. (1985), Riskin et al. (1991), and by Mahesh et al. (see IEEE Trans. Inform. Theory, vol.41, p.917-30, 1995) that variable-length tree-structured vector quantizer (VLTSVQ) yields better coding performance than a balanced tree-structured vector quantizer and may even outperform a full-search vector quantizer due to the nonuniform distribution of rate among the subsets of its input space. The variable-length constrained storage tree-structured vector quantization (VLCS-TSVQ) algorithm presented in this paper utilizes the codebook sharing by multiple vector sources concept as in CSVQ to greedily grow an unbalanced tree structured residual vector quantizer with constrained storage. It is demonstrated by simulations on test sets from various synthetic one dimensional (1-D) sources and real-world images that the performance of VLCS-TSVQ, whose codebook storage complexity varies linearly with rate, can come very close to the performance of greedy growth VLTSVQ of Riskin et al. and Mahesh et al. The dramatically reduced size of the overall codebook allows the transmission of the code vector probabilities as side information for source adaptive entropy coding.

An image multiresolution representation for lossless and lossy compression.

We propose a new image multiresolution transform that is suited for both lossless (reversible) and lossy compression. The new transformation is similar to the subband decomposition, but can be computed with only integer addition and bit-shift operations. During its calculation, the number of bits required to represent the transformed image is kept small through careful scaling and truncations. Numerical results show that the entropy obtained with the new transform is smaller than that obtained with predictive coding of similar complexity. In addition, we propose entropy-coding methods that exploit the multiresolution structure, and can efficiently compress the transformed image for progressive transmission (up to exact recovery). The lossless compression ratios are among the best in the literature, and simultaneously the rate versus distortion performance is comparable to those of the most efficient lossy compression methods.

Texture coding using a Wold decomposition model.

A novel approach for coding textured images is presented. The texture field is assumed to be a realization of a regular homogeneous random field, which can have a mixed spectral distribution. On the basis of a two-dimensional (2-D) Wold-like decomposition, the field is represented as a sum of a purely indeterministic, harmonic, and countable number of evanescent fields. We present an algorithm for estimating and coding the texture model parameters, and show that the suggested algorithm yields high-quality reconstructions at low bit rates. The model and the resulting coding algorithm are seen to be applicable to a wide variety of texture types found in natural images.

Tree coding of image subbands.

The authors consider the encoding of image subbands with a tree code that is asymptotically optimal for Gaussian sources and the mean squared error (MSE) distortion measure. They first prove that optimal encoding of ideally filtered subbands of a Gaussian image source achieves the rate distortion bound for the MSE distortion measure. The optimal rate and distortion allocation among the subbands is a by-product of this proof. A bound is derived which shows that subband coding is closer than full-band coding to the rate distortion bound for a finite length sequence. The tree codes are then applied to encode the image subbands, both nonadaptively and adaptively. Since the tree codes are stochastic and the search of the code tree is selective, a relatively few reproduction symbols may have an associated squared error a hundred times larger than the target for the subband. Correcting these symbols through a postcoding procedure improves the signal-to-noise ratio and visual quality significantly, with a marginal increase in total rate.

A visual system model and a new distortion measure in the context of image processing.

Underlying many techniques of image restortation, quantization, and enhancement is the mathematically convenient, but visually unsuitable distortion measure of squared difference in intensity. Squared-intensity differences has an indirect phenomenological correspondence in a model of the visual system. We have undertaken, therefore, an experiment that derives a new distortion measure from an acceptable visual system model and compares it in a fair test against squared difference in intensity in an image restoration task. We start with an eye-brain system model inferred from the works of current vision researchers, which consists of a bank of paralles spatial frequency channels and image detectors. From this model we derive a new distortion criterion that is related to changes in the per-channel detection probability and phase angle. The optimal linear (Wiener) filters for each distortion measure operate in turn on the same noisy incoherent images. The results show that the filter for the new distortion measures yields a superior restoration. It is more visually agrreable, more sharply detailed, and truer in contrast compared to the squared-difference filter, and impressive in its own right. Its mathematical properties suggest that significantly increased efficeincy in the storage or communication of images my be gained by its use.