Image coding with an L/sup ∞/ norm and confidence interval criteria

Abstract

A new image coding technique based on an Linfinity-norm criterion and exploiting statistical properties of the reconstruction error is investigated. The original image is preprocessed, quantized, encoded, and reconstructed within a given confidence interval. Two important classes of preprocessing, namely linear prediction and iterated filterbanks, are used. The approach is also shown to be compatible with previous techniques. The approach allows a great flexibility in that it can perform lossless coding as well as a controlled lossy one: specifications are typically that only p% the reconstructed pixels are different from the original ones.

Error Inhomogeneity in Wavelet-Based Compression

“…Note that similar expressions for error variances in even/odd locations have been derived by Karray et al [12] and Alecu et al [13], albeit in a somewhat different context (e.g., the authors used these expressions to model the reconstruction error distributions at even/odd locations in order to obtain a precise estimate of the probability that the infinity norm of the reconstruction error exceeds a certain predefined threshold). Different treatment of even/odd locations reflects the authors' implicit assumption that these variances might be different from each other in some cases.…”

Temporal filtering for restoration of wavelet-compressed motion imagery

“…1 Here, it is assumed that the coefficients are approximately uncorrelated, allowing the simplifying approximation that K y is diagonal. For relatively high-rate situations (rather small quantization bin sizes), it is well established that the quantization errors are also uncorrelated [11,27]. For lower-rate situations it is not immediately obvious that the quantization errors are uncorrelated, although empirical evidence has supported such an assumption: We have performed simulations with numerous test images (frames from the standard video test sequences football, mobile, bike, garden, and tennis at resolution 352 Â 240), and quantization errors for the wavelet coefficients show no noticeable covariance with other coefficients.…”

“…1 has been conducted in the area of L N -constrained image compression [11], where the objective is to limit the maximum pixel error (i.e., a local approach) rather than an overall global average error. However, not only are the errors induced by wavelet quantization distributed differently, but they are also correlated.…”

On the Optimality of Embedded Deadzone Scalar-Quantizers for Wavelet-Based L-Infinite-Constrained Image Coding

“…We consider the family of embedded deadzone uniform scalar quantizers in which every sample is quantized to [6] sign if otherwise (1) where , determines the width of the deadzone, and represents the number of discarded bit-planes. We restrict ourselves to midtread quantizers, respectively the range of interest , i.e., embedded deadzone quantizers possessing a deadzone bin size that is larger or equal to the other bin sizes [6].…”

“…The local reconstruction error is referred to as the maximum absolute difference (MAXAD) between the pixel values in the original and reconstructed images. Various methods for -distortion constrained compression have been proposed in literature, some operating in the transform domain [1] or in the image domain [2], while others propose a hybrid bit-stream between the two [3]. We have recently proposed in [4] and [5] a wavelet-based -constrained scalable image-coding technique that generates a fully embedded -oriented bit-stream, while retaining the coding performance and scalability options of state-of-the-art wavelet-based codecs [6].…”