Shift-orthogonal wavelets are a new type of multiresolution wavelet bases that are orthogonal with respect to translation (or shifts) within one level but not with respect to dilations across scales. In this paper, we characterize these wavelets and investigate their main properties by considering two general construction methods. In the first approach, we start by specifying the analysis and s...

Recent wavelet research has primarily focused on real-valued wavelet bases. However, complex wavelet bases offer a number of potential advantageous properties. For example, it has been recently suggested that the complex Daubechies wavelet can be made symmetric. However, these papers always imply that if the complex basis has a symmetry property, then it must exhibit linear phase as well. In th...

Recent wavelet research has primarily focused on real-valued wavelet bases. However, complex wavelet bases ooer a number of potential advantageous properties. For example, it has been recently suggested 1], 2] that the complex Daubechies wavelet can be made symmetric. However, these papers always imply that if the complex basis has a symmetry property then it must exhibit linear phase as well. ...

This paper introduces orthogonal bandlet bases to approximate images having some geometrical regularity. These bandlet bases are computed by applying parameterized Alpert transform operators over an orthogonal wavelet basis. These bandletization operators depend upon a multiscale geometric flow that is adapted to the image, at each wavelet scale. This bandlet construction has a hierarchical str...

This paper introduces orthogonal bandelet bases to approximate images having some geometrical regularity. These bandelet bases are computed by applying parametrized Alpert transform operators over an orthogonal wavelet basis. These bandeletization operators depend upon a multiscale geometric flow that is adapted to the image at each wavelet scale. This bandelet construction has a hierarchical s...

In this letter, the two wavelet families, biorthogonal and Riesz bases are introduced. Biorthogonality for two possible decompositions in these bases, The Riesz stability implies that there exist such that Biorthogonal wavelet bases are related to multiresolution approximations. The direct consequence of the above derivation is tradeoff made between the support size of a wavelet and its number ...

The stereographic projection determines a bijection between the two-sphere, minus the North Pole, and the tangent plane at the South Pole. This correspondence induces a unitary map between the corresponding L2 spaces. This map in turn leads to equivalence between the continuous wavelet transform formalisms on the plane and on the sphere. More precisely, any plane wavelet may be lifted, by inver...