Wavelet transforms have started to receive increasing attention due to their wide applications in image and signal processing, and due to the recent discovery of a fast sequential algorithm for discrete wavelet transforms by Mallat[Mal89]. In this paper we present a mapping of the wavelet operations onto the MasPar massively parallel single instruction multiple data (SIMD) computer [Bla90], [Ma...

In this paper, we introduce a unified theory of tight wavelet frames on non-flat domains in both continuum setting, i.e. on manifolds, and discrete setting, i.e. on graphs; discuss how fast tight wavelet frame transforms can be computed and how they can be effectively used to process graph data. We start from defining multiresolution analysis (MRA) generated by a single generator on manifolds, ...

In this paper, local cubic quasi-interpolating splines on non-uniform grids are described. The splines are computed by fast computational algorithms that utilize the relation between splines and cubic interpolation polynomials. These splines provide an efficient tool for real-time signal processing. As an input, they use either clean or noised arbitrarily-spaced samples. Exact estimations of th...

We present a functional framework for the design of tight steerable wavelet frames in any number of dimensions. The 2-D version of the method can be viewed as a generalization of Simoncelli’s steerable pyramid that gives access to a larger palette of steerable wavelets via a suitable parametrization. The backbone of our construction is a primal isotropic wavelet frame that provides the multires...

Watermarking is one of the best solutions for copyright protection and authentication of multimedia contents. In this paper a hybrid scheme is proposed using wavelet and shearlet transforms with singular value decomposition. For better security, Arnold map is used for encryption. Examining the results and comparing with other methods show that this hybrid proposed scheme with simultaneous utili...

We have designed an adaptive essentially nonoscillatory (ENO)-wavelet transform for approximating discontinuous functions without oscillations near the discontinuities. Our approach is to apply the main idea from ENO schemes for numerical shock capturing to standard wavelet transforms. The crucial point is that the wavelet coefficients are computed without differencing function values across ju...

Studied are numerous issues associated with wavelet transforms in the JPEG-2000 Part-1 standard (i.e., ISO/IEC 15444-1). The dynamic range of wavelet transform coefficients and computational complexity of wavelet transforms are examined. Also, the effect of wavelet transforms on coding efficiency is investigated. The information presented herein may prove beneficial to those developing JPEG-200...

This paper develops two new adaptive wavelet transforms based on the lifting scheme. The lifting construction exploits a spatialdomain, prediction-error interpretation of the wavelet transform and provides a powerful framework for designing customized transforms. We use the lifting construction to adaptively tune a wavelet transform to a desired signal by optimizing data-based prediction error ...