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On Interpolation and Resampling of Discrete Data

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Shapes from pixels

Martin Vetterli, Arash Amini, Loïc Arnaud Baboulaz, Mitra Fatemi

Continuous-domain visual signals are usually captured as discrete (digital) images. This operation is not invertible in general, in the sense that the continuous-domain signal cannot be exactly reconstructed based on the discrete image, unless it satisfies ...

Institute of Electrical and Electronics Engineers2016

Dust grain coagulation modelling: From discrete to continuous

Paola Paruta

In molecular clouds, stars are formed from a mixture of gas, plasma and dust particles. The dynamics of this formation is still actively investigated and a study of dust coagulation can help to shed light on this process. Starting from a pre-existing discr ...

Elsevier Science Bv2016

Statistical Optimality of Hermite Splines

Michaël Unser, Julien René Pierre Fageot, Virginie Sophie Uhlmann, Harshit Gupta

Hermite splines are commonly used for interpolating data when samples of the derivative are available, in a scheme called Hermite interpolation. Assuming a suitable statistical model, we demonstrate that this method is actually optimal for reconstructing r ...

IEEE2015

Iterative Potts and Blake-Zisserman minimization for the recovery of functions with discontinuities from indirect measurements

Martin Kurt Storath

Signals with discontinuities appear in many problems in the applied sciences ranging from mechanics, electrical engineering to biology and medicine. The concrete data acquired are typically discrete, indirect and noisy measurements of some quantities descr ...

Royal Soc2015

Euclidean Distance Matrices

Reza Parhizkar

Euclidean distance matrices (EDMs) are central players in many diverse fields including psychometrics, NMR spectroscopy, machine learning and sensor networks. However, they are not often exploited in signal processing. In this thesis, we analyze attributes ...

EPFL2013

Meta Morphic Particle Swarm Optimization

Auke Ijspeert, Soha Pouya, Jesse van den Kieboom

Particle Swarm Optimization is a simple and elegant optimization algorithm used to solve a large variety of different real-valued problems. When it comes to solving combinations of continuous and discrete problems however, PSO by itself is not very well su ...

Springer2013

GPU Prefilter for Accurate Cubic B-spline Interpolation

Philippe Thévenaz

Achieving accurate interpolation is an important requirement for many signal-processing applications. While nearest-neighbor and linear interpolation methods are popular due to their native GPU support, they unfortunately result in severe undesirable artif ...

Oxford University Press2012

Signal Processing in Space and Time

Francisco Pereira Correia Pinto

Sound waves propagate through space and time by transference of energy between the particles in the medium, which vibrate according to the oscillation patterns of the waves. These vibrations can be captured by a microphone and translated into a digital sig ...

EPFL2010

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 Stochastic Minimum-Norm Approach to Image and Texture Interpolation

Michaël Unser, Hagay Kirshner

We introduce an exponential-based consistent approach to image scaling. Our model stems from Sobolev reproducing kernels, motivated by their role in continuous-domain stochastic autoregressive processes. The proposed approach imposes consistency and applie ...

EURASIP2010