Publications related to Solving Continuous-Domain Problems Exactly with Multiresolution B-Splines

A time-reversible integrator for the time-dependent Schrödinger equation on an adaptive grid

One of the most accurate methods for solving the time-dependent Schrödinger equation uses a combination of the dynamic Fourier method with the split-operator algorithm on a tensor-product grid. To reduce the number of required grid points, we let the grid ...

2019

Looking beyond Pixels

Hanjie Pan

Sparse recovery is a powerful tool that plays a central role in many applications, including source estimation in radio astronomy, direction of arrival estimation in acoustics or radar, super-resolution microscopy, and X-ray crystallography. Conventional a ...

EPFL2018

Unified Theory for Recovery of Sparse Signals in a General Transform Domain

Kyong Hwan Jin

Compressed sensing is provided a data-acquisition paradigm for sparse signals. Remarkably, it has been shown that the practical algorithms provide robust recovery from noisy linear measurements acquired at a near optimal sampling rate. In many real-world a ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2018

Super Resolution Phase Retrieval for Sparse Signals

Martin Vetterli, Juri Ranieri, Gilles Baechler, Amina Chebira, Miranda Krekovic

In a variety of fields, in particular those involving imaging and optics, we often measure signals whose phase is missing or has been irremediably distorted. Phase retrieval attempts to recover the phase information of a signal from the magnitude of its Fo ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2018

Sampling Continuous-time Sparse Signals: A Frequency-domain Perspective

Martin Vetterli, Benjamin Bejar Haro

We address the problem of sampling and reconstruction of sparse signals with finite rate of innovation. We derive general conditions under which perfect reconstruction is possible for sampling kernels satisfying Strang-Fix conditions. Previous results on t ...

2018

Sparse inverse problems for Fourier imaging

Anna Auria Rasclosa

Many natural images have low intrinsic dimension (a.k.a. sparse), meaning that they can be represented with very few coefficients when expressed in an adequate domain. The recent theory of Compressed Sensing exploits this property offering a powerful frame ...

EPFL2017

An Adaptive Sublinear-Time Block Sparse Fourier Transform

Volkan Cevher, Mikhail Kapralov, Jonathan Mark Scarlett, Amir Zandieh

The problem of approximately computing the

k

dominant Fourier coefficients of a vector

X

quickly, and using few samples in time domain, is known as the Sparse Fourier Transform (sparse FFT) problem. A long line of work on the sparse FFT has resulted in ...

2017

Sparsity-Based Data Reconstruction Models for Biomedical Imaging

Emrah Bostan

We propose new regularization models to solve inverse problems encountered in biomedical imaging applications. In formulating mathematical schemes, we base our approach on the sparse signal processing principles that have emerged as a central paradigm in t ...

EPFL2016

Representer Theorems for Sparsity-Promoting $ ℓ _{ 1 } $ Regularization

Michaël Unser, Julien René Pierre Fageot, Harshit Gupta

We present a theoretical analysis and comparison of the effect of

ℓ _{ 1 }

versus

ℓ _{ 2 }

regularization for the resolution of ill-posed linear inverse and/or compressed sensing problems. Our formulation covers the most general setting where the s ...

IEEE2016

Morphological component analysis for sparse regularization in plane wave imaging

Jean-Philippe Thiran, Yves Wiaux, Dimitris Perdios, Eric Bezzam, Rafael Eduardo Carrillo Rangel, Marcel Arditi, Adrien Georges Jean Besson

Classical ultrasound image reconstruction mainly relies on the well-known delay-and-sum (DAS) beamforming for its simplicity and real-time capability. Sparse regularization methods propose an alternative to DAS which lead to a better inversion of the ill-p ...

Ieee2016

Solving Continuous-Domain Problems Exactly with Multiresolution B-Splines

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A time-reversible integrator for the time-dependent Schrödinger equation on an adaptive grid

Looking beyond Pixels

Unified Theory for Recovery of Sparse Signals in a General Transform Domain

Super Resolution Phase Retrieval for Sparse Signals

Sampling Continuous-time Sparse Signals: A Frequency-domain Perspective

Sparse inverse problems for Fourier imaging

An Adaptive Sublinear-Time Block Sparse Fourier Transform

Sparsity-Based Data Reconstruction Models for Biomedical Imaging

Representer Theorems for Sparsity-Promoting $ ℓ _{ 1 } $ Regularization

Morphological component analysis for sparse regularization in plane wave imaging

Unified Theory for Recovery of Sparse Signals in a General Transform Domain

Super Resolution Phase Retrieval for Sparse Signals

Sampling Continuous-time Sparse Signals: A Frequency-domain Perspective

Looking beyond Pixels

An Adaptive Sublinear-Time Block Sparse Fourier Transform

Sparsity-Based Data Reconstruction Models for Biomedical Imaging

Sparse inverse problems for Fourier imaging

A time-reversible integrator for the time-dependent Schrödinger equation on an adaptive grid

Morphological component analysis for sparse regularization in plane wave imaging

Representer Theorems for Sparsity-Promoting $ ℓ _{ 1 } $ Regularization