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A method is proposed for designing apodized apertures with a transmission profile which follows a curve defined using a cubic spline interpolation. The method is applied in digital holographic microscopy to perform digitally the apodization of the aperture ...
We propose a new method for the intermodal registration of images using a criterion known as mutual information. Our main contribution is an optimizer that we specifically designed for this criterion. We show that this new optimizer is well adapted to a mu ...
Based on the theory of approximation, this paper presents a unified analysis of interpolation and resampling techniques. An important issue is the choice of adequate basis functions. We show that, contrary to the common belief, those that perform best are ...
In this note, we provide an analytical approximation to the exponential integral valid for all values of its argument. The approximation is constructed by interpolation between the exponential integral's small and large asymptotes.The interpolation contain ...
This chapter presents a survey of interpolation and resampling techniques in the context of exact, separable interpolation of regularly sampled data. In this context, the traditional view of interpolation is to represent an arbitrary continuous function as ...
Many important problems in pure and applied mathematics and engineering can be reduced to linear algebra on dense structured matrices. The structure of these dense matrices is understood in the sense that their n2 entries can be "compressed" to a smaller n ...
A framework for the construction of stable spectral methods on arbitrary domains with unstructured grids is presented. Although most of the developments are of a general nature, an emphasis is placed on schemes for the solution of partial differential equa ...
We propose a new technique to perform nonuniform to uniform grid conversion: first, interpolate using nonuniform splines, then project the resulting function onto a uniform spline space and finally, resample. We derive a closed form solution to the least-s ...
We present two digital image processing methods for image quality enhancement in Digital Holographic Microscopy (DHM). With the first method, the Fourier transform of an off-axis hologram is spatially filtered in order to eliminate the zero order of diffra ...
This thesis presents a new method for the numerical reconstruction of digital holograms recorded in the off-axis configuration using a CCD camera. The propagation of the reconstructed wave front, from the hologram plane to an observation plane, is achieved ...