We study the non-parametric estimation of an unknown density f with support on R+ based i.i.d. sample multiplicative measurement errors. The proposed fully-data driven procedure is Mellin transform f, a regularisation inverse by spectral cut-off and data-driven model selection in order to deal upcoming bias-variance trade-off. introduce discuss further Mellin-Sobolev spaces which characterize r...

Space-variant sensing is the architectural basis of all higher vertebrate visual systems (Schwartz, 1994). One evident motivation for this is that the spacecomplexity of the human visual system is reduced by up to four orders of magnitude (Rojer and Schwartz, 1990) via the use of space-variant architecture (jar a given ratio of field width to maximum resolution). This observation has obvious pr...

Abstract. The purpose of this paper is to consider a new generalization of the Hurwitz zeta function. Generating functions, Mellin transform, and a series identity are obtained for this generalized class of functions. Some of the results are used to provide a further generalization of the Lambert transform. Relevance with various known results are depicted invariably. Multivariable extensions a...

A unitary signal transformation that is covariant by translation to scale changes (di-lations and compressions) in the signal is formulated and justiied. Unlike the Mellin transform, which is invariant to scale changes, this new transform is a true indicator of the scale content of a signal.

In this article we provide integral representations for the Dirichlet beta and Riemann zeta functions, which are obtained by combining Mellin transform with the fractional Fourier transform. As an application of these integral formulas we derive tractable expansions of these L-functions in the series of Meixner-Pollaczek polynomials and rising factorials.

Making use of inverse Mellin transform techniques for analytical continuation, an elegant proof and an extension of the zeta function regularization theorem is obtained. No series commutations are involved in the procedure; nevertheless the result is naturally split into the same three contributions of very different nature, i.e. the series of Riemann zeta functions and the power and negative e...

The paper presents a registration algorithm based on the Analytical Fourier-Mellin Transform (AFMT). In the Fourier Mellin registration algorithm, the estimation of the geometrical transformation is only done in the Fourier Transform phase domain which is known by containing the shape information. The proposed algorithm will be used to estimate homography since in the vicinity of key points, we...