The wavelet dimension function for arbitrary real dilations is defined and used to address several questions involving the existence of MRA wavelets and well-localized wavelets for irrational dilations. The theory of quasi-affine frames for rational dilations and the existence of non-MSF wavelets for certain irrational dilations play an important role in this development. Expansive dilations ad...

In this paper, we present an image compression scheme based on the automatic segmentation of regions of interest (RoI) and a lossy wavelet compression algorithm adapted to this segmentation. Quasi-lossless compression is applied to the RoI while lossy compression is allowed outside the RoI, preserving at best the visual quality of the decoded image within a deened RoI. In fact, for diagnostic a...

We seek to demonstrate a connection between refinable quasi-affine systems and the discrete wavelet transform known as the à trous algorithm. We begin with an introduction of the bracket product, which is the major tool in our analysis. Using multiresolution operators, we then proceed to reinvestigate the equivalence of the duality of refinable affine frames and their quasiaffine counterparts a...

This article presents results of image enhancement for robot vision. Results are obtained by superresolution techniques in wavelet domain. The calculated motion of wavelet coefficients in stationary image can enhance image quality. It can be used as interpolation information for increasing resolution. This is basis for wavelet quasi-superresolution, where one low-resolution image is interpolate...

We present a new family of compactly supported and symmetric biorthogonal wavelet systems. Each refinement mask in this family has tension parameter ω. When ω = 0, it becomes the minimal length biorthogonal Coifman wavelet system [17]. Choosing ω away from zero, we can get better smoothness of the refinable functions at the expense of slightly larger support. Though the construction of the new ...

Here, we contribute to the continuing development of the quasi-wavelet (QW) model of turbulence that is currently being used in simulations of sound propagation and scattering in the turbulent atmosphere. We show that a QW model of temperature fluctuations exists for any physically reasonable temperature spectrum of isotropic homogeneous turbulence, including the widely used von Kármán spectrum...

This article gives an outline of the novel algorithm for image superresolution based on wavelets. In this algorithm morphological operations in low-resolution image are combined with approximation of high-resolution wavelet coefficients. Since it involves only a single original low-resolution image, we call it quasi-superresolution. The final result is high-resolution image obtained from a sing...