Approximation and Compression of Piecewise Smooth Functions
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Very low bit rate image coding is an important problem regarding applications such as storage on low memory devices or streaming data on the internet. The state of the art in image compression is to use 2-D wavelets. The advantages of wavelet bases lie in ...
We present an explicit formula for B-spline convolution kernels; these are defined as the convolution of several B-splines of variable widths hi and degrees ni. We apply our results to derive spline-convolution-based algorithms for two closely related prob ...
We present an optimal spline-based algorithm for the enlargement or reduction of digital images with arbitrary (noninteger) scaling factors. This projection-based approach can be realized thanks to a new finite difference method that allows the computation ...
The theory of high rate lossy source coding is well developed both with respect to the practice of quantization and its fundamental rate distortion limits. But many modern compression systems for natural signals such as audio and images operate at lower ra ...
High resolution multidimensional image data yield huge datasets. For compression and analysis, 2D approaches are often used, neglecting the information coherence in higher dimensions, which can be exploited for improved compression. We designed a wavelet c ...
The first part of this paper proposes an adaptive, data-driven threshold for image denoising via wavelet soft-thresh- olding. The threshold is derived in a Bayesian framework, and the prior used on the wavelet coefficients is the generalized Gaussian distr ...
The concept of stationarity is central to signal processing; it indeed guarantees that the deterministic spectral properties of linear time-invariant systems are also applicable to realizations of stationary random processes. In almost all practical settin ...
Digital images are becoming increasingly successful thanks to the development and the facilitated access to systems permitting their generation (i.e. camera, scanner, imaging software, etc). A digital image basically corresponds to a 2D discrete set of reg ...
In this paper, we briefly review the connection between subband coding, wavelet approximation and general compression problems. Wavelet or subband coding is successful in compression applications partly because of the good approximation properties of wavel ...
In recent years, wavelet-based algorithms have been successful in different signal processing tasks. The wavelet trans- form is a powerful tool because it manages to represent both tran- sient and stationary behaviors of a signal with few transform coeffi- ...
