Publication

Discretization of the radon transform and of its inverse by spline convolutions

Publications associées (63)

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Linear Interpolation Of Biomedical Images Using A Data-Adaptive Kernel

Michaël Unser, John Paul Ward, Aurélien Bourquard, Hagay Kirshner

In this work, we propose a continuous-domain stochastic model that can be applied to image data. This model is autoregressive, and accounts for Gaussian-type as well as for non-Gaussian-type innovations. In order to estimate the corresponding parameters fr ...

IEEE2013

Can Localization Microscopy Benefit From Approximation Theory?

Michaël Unser, Cédric René Jean Vonesch, Hagay Kirshner

We introduce a general and computationally efficient approach to 3-D localization microscopy. The main idea is to construct a continuous-domain representation of the PSF by expanding it in a polynomial B-spline basis. This allows us to fit the PSF to the d ...

IEEE2013

Anisotropic Interpolation of Sparse Generalized Image Samples

Michaël Unser, Aurélien Bourquard

Practical image-acquisition systems are often modeled as a continuous-domain prefilter followed by an ideal sampler, where generalized samples are obtained after convolution with the impulse response of the device. In this paper, our goal is to interpolate ...

Ieee-Inst Electrical Electronics Engineers Inc2013

Interpolating point spread function anisotropy

Frédéric Courbin, Georges Meylan, Marc Gentile

Planned wide-field weak lensing surveys are expected to reduce the statistical errors on the shear field to unprecedented levels. In contrast, systematic errors like those induced by the convolution with the point spread function (PSF) will not benefit fro ...

Edp Sciences S A2013

Wavelet-Based Reconstruction for Magnetic Resonance Imaging

Matthieu Guerquin-Kern

Magnetic resonance imaging (MRI) scanners produce raw measurements that are unfit to direct interpretation, unless an algorithmic step, called reconstruction, is introduced. Up to the last decade, this reconstruction was performed by algorithms of moderate ...

EPFL2012

A Box Spline Calculus for the Discretization of Computed Tomography Reconstruction Problems

Michaël Unser, Masih Nilchian

B-splines are attractive basis functions for the continuous-domain representation of biomedical images and volumes. In this paper, we prove that the extended family of box splines are closed under the Radon transform and derive explicit formulae for their ...

Institute of Electrical and Electronics Engineers2012

A novel sampling theorem on the sphere

Yves Wiaux, Jason Douglas McEwen

We develop a novel sampling theorem on the sphere and corresponding fast algorithms by associating the sphere with the torus through a periodic extension. The fundamental property of any sampling theorem is the number of samples required to represent a ban ...

Institute of Electrical and Electronics Engineers2011

Sensing and Recovery under Sparsity Constraints

Ali Hormati

Popular transforms, like the discrete cosine transform or the wavelet transform, owe their success to the fact that they promote sparsity. These transforms are capable of extracting the structure of a large class of signals and representing them by a few t ...

EPFL2010

A Box Spline Calculus for Computed Tomography

Michaël Unser

IEEE2010

Algorithms for the Computation of Continuous Transforms of Rectilinear Polygons from IC Layouts

Robin Scheibler

In this work, we present a novel way of computing the continuous Haar, Fourier and cosine series coefficients of rectilinear polygons. We derive algorithms to compute the inner products with the continuous basis functions directly from the vertices of the ...

2009