Publications related to Recovery of Compressible Signals in Unions of Subspaces

Sparse Recovery of Strong Reflectors With an Application to Non-Destructive Evaluation

Jean-Philippe Thiran, Martin Vetterli, Dimitris Perdios, Eric Bezzam, Adrien Besson, Hanjie Pan

In this paper we show that it is sufficient to recover the locations of K strong reflectors within an insonified medium from three receive elements and 2K+1 samples per element. The proposed approach leverages advances in sampling signals with a finite rat ...

IEEE2018

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

Compressive Sampling Using Annihilating Filter-Based Low-Rank Interpolation

Kyong Hwan Jin

While the recent theory of compressed sensing provides an opportunity to overcome the Nyquist limit in recovering sparse signals, a solution approach usually takes the form of an inverse problem of an unknown signal, which is crucially dependent on specifi ...

IEEE2017

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

A compressed-sensing approach for ultrasound imaging

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

Ultrasonography uses multiple piezo-electric element probes to image tissues. Current time-domain beamforming techniques require the signal at each transducer-element to be sampled at a rate higher than the Nyquist criterion, resulting in an extensive amou ...

2017

Learning Data Triage: Linear Decoding Works for Compressive MRI

Volkan Cevher, Yen-Huan Li

The standard approach to compressive sampling considers recovering an unknown deterministic signal with certain known structure, and designing the sub-sampling pattern and recovery algorithm based on the known structure. This approach requires looking for ...

Ieee2016

Non-linear Recovery of Sparse Signal Representations with Applications to Temporal and Spatial Localization

Zafer Dogan

Foundations of signal processing are heavily based on Shannon's sampling theorem for acquisition, representation and reconstruction. This theorem states that signals should not contain frequency components higher than the Nyquist rate, which is half of the ...

EPFL2015

Compressed Sensing of Memoryless Sources

Saeid Haghighatshoar

Compressed sensing is a new trend in signal processing for efficient sampling and signal acquisition. The idea is that most real-world signals have a sparse representation in an appropriate basis and this can be exploited to capture the sparse signal by ta ...

EPFL2014

Model-based Sketching and Recovery with Expanders

Volkan Cevher, Luca Baldassarre, Bubacarr Bah

Linear sketching and recovery of sparse vectors with randomly constructed sparse matrices has numerous applications in several areas, including compressive sensing, data stream computing, graph sketching, and combinatorial group testing. This paper conside ...

2014

Sparsity in tensor optimization for optical-interferometric imaging

Jean-Philippe Thiran, Yves Wiaux, Rafael Eduardo Carrillo Rangel, Anna Auria Rasclosa

Image recovery in optical interferometry is an ill-posed nonlinear inverse problem arising from incomplete power spectrum and bispectrum measurements. We review our previous work, which reformulates this nonlinear problem in the framework of tensor recover ...

IEEE2014

Recovery of Compressible Signals in Unions of Subspaces

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Sparse Recovery of Strong Reflectors With an Application to Non-Destructive Evaluation

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

Compressive Sampling Using Annihilating Filter-Based Low-Rank Interpolation

An Adaptive Sublinear-Time Block Sparse Fourier Transform

A compressed-sensing approach for ultrasound imaging

Learning Data Triage: Linear Decoding Works for Compressive MRI

Non-linear Recovery of Sparse Signal Representations with Applications to Temporal and Spatial Localization

Compressed Sensing of Memoryless Sources

Model-based Sketching and Recovery with Expanders

Sparsity in tensor optimization for optical-interferometric imaging

Compressed Sensing of Memoryless Sources

Compressive Sampling Using Annihilating Filter-Based Low-Rank Interpolation

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

Learning Data Triage: Linear Decoding Works for Compressive MRI

An Adaptive Sublinear-Time Block Sparse Fourier Transform

Sparse Recovery of Strong Reflectors With an Application to Non-Destructive Evaluation

Non-linear Recovery of Sparse Signal Representations with Applications to Temporal and Spatial Localization

Model-based Sketching and Recovery with Expanders

Sparsity in tensor optimization for optical-interferometric imaging

A compressed-sensing approach for ultrasound imaging