Orthogonal moments are recognized as useful tools for object representation and image analysis. It has been shown that the recently developed discrete orthogonal moments have better performance than the conventional continuous orthogonal moments. In this paper, a new set of discrete orthogonal polynomials, namely Hahn polynomials, are introduced. The related Hahn moment functions defined on thi...

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...

A code over GF(qm) can be imaged or expanded into a code over GF(q) using a basis for the extension field over the base field. The properties of such an image depend on the original code and the basis chosen for imaging. Problems relating the properties of a code and its image with respect to a basis have been of great interest in the field of coding theory. In this work, a generalized version ...

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. ...

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...

Many systems of orthogonal polynomials and functions are bases of a variety of function spaces, such as the Hermite and Laguerre functions which are orthogonal bases of L2(−∞,∞) and L2(0,∞), and the Jacobi polynomials which are an orthogonal basis of a weighted L2(−1, 1). The associated Legendre functions, and more generally, the spheroidal wave functions are also an orthogonal basis of L2(−1, ...

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 paper, an integrated approach is proposed for non-recursive formulation of connection coefficients of different orthogonal functions in terms of a generic orthogonal function. The application of these coefficients arises when the product of two orthogonal basis functions are to be expressed in terms of single basis functions. Two significant advantages are achieved; one, the non-recursi...