Time–frequency analysis

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Optimal Isotropic Wavelets for Localized Tight Frame Representations

Michaël Unser, John Paul Ward, Pedram Pad

In this letter, we aim to identify the optimal isotropic mother wavelet for a given spatial dimension based on a localization criterion. Within the framework of the calculus of variations, we specify an Euler-Lagrange equation for this problem, and we find ...

IEEE2015

FIR filters for hardware-based real-time multi-band image blending

Yusuf Leblebici, Vladan Popovic

Creating panoramic images has become a popular feature in modern smart phones, tablets, and digital cameras. A user can create a 360 degree field-of-view photograph from only several images. Quality of the resulting image is related to the number of source ...

Spie-Int Soc Optical Engineering2015

On multiscale methods in Petrov-Galerkin formulation

Patrick Henning

In this work we investigate the advantages of multiscale methods in Petrov-Galerkin (PG) formulation in a general framework. The framework is based on a localized orthogonal decomposition of a high dimensional solution space into a low dimensional multisca ...

Springer Heidelberg2015

Beyond Allan Variance - GMWM Framework For Sensor Calibration

Jan Skaloud, Stéphane Guerrier

Proposed 50 years ago for studying stability of oscillators, Allan Variance (AV) was accepted by IEEE as a standard for characterizing behavior of sensors. However, the inverse mapping, i.e. the estimation of noise-parameters from Allan Variance is less st ...

2015

Template-Free Wavelet-Based Detection of Local Symmetries

Michaël Unser, Zsuzsanna Püspöki

Our goal is to detect and group different kinds of local symmetries in images in a scale- and rotation-invariant way. We propose an efficient wavelet-based method to determine the order of local symmetry at each location. Our algorithm relies on circular h ...

IEEE2015

Sparsity-Driven Statistical Inference for Inverse Problems

Ulugbek Kamilov

This thesis addresses statistical inference for the resolution of inverse problems. Our work is motivated by the recent trend whereby classical linear methods are being replaced by nonlinear alternatives that rely on the sparsity of naturally occurring sig ...

EPFL2015

Automatic Identification and Calibration of Stochastic Parameters in Inertial Sensors

Jan Skaloud, Stéphane Guerrier

We present an algorithm for determining the nature of stochastic processes and their parameters based on the analysis of time series of inertial errors. The algorithm is suitable mainly (but not only) for situations where several stochastic processes are s ...

Wiley Periodicals, Inc2015

Divergence-Free Wavelet Frames

Michaël Unser, Emrah Bostan, John Paul Ward

We propose an efficient construction of wavelet frames in any number of dimensions that are divergence-free. Our approach is based on applying the Leray projector, which is scale-invariant, to a standard wavelet frame. We prove that the projected wavelets ...

Ieee-Inst Electrical Electronics Engineers Inc2015

Inference for Generalized Linear Models via Alternating Directions and Bethe Free Energy Minimization

Ulugbek Kamilov

Generalized Linear Models (GLMs), where a random vector x is observed through a noisy, possibly nonlinear, function of a linear transform z = A x arise in a range of applications in nonlinear filtering and regression. Approximate Message Passing (AMP) meth ...

IEEE2015

Interior Tomography Using 1D Generalized Total Variation. Part II: Multiscale Implementation

Michaël Unser, John Paul Ward

To address the classic interior tomography problem where projections at each view extend only to the shadow of a circular region completely interior to the subject being scanned, previously we showed that the exact recovery of two- and three-dimensional pi ...

Siam Publications2015