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

Estimation Error of the Constrained Lasso

Volkan Cevher, Yen-Huan Li, Ya-Ping Hsieh, Nissim Zerbib

This paper presents a non-asymptotic upper bound for the estimation error of the constrained lasso, under the high-dimensional (

n \ll p

) setting. In contrast to existing results, the error bound in this paper is sharp, is valid when the parameter to be e ...

2016

Method and apparatus for low complexity spectral analysis of bio-signals

David Atienza Alonso, Andreas Peter Burg, Srinivasan Murali, Georgios Karakonstantis, Aviinaash Sankaranarayanan

A method and device for reducing the computational complexity of a processing algorithm, of a discrete signal, in particular of the spectral estimation and analysis of bio-signals, with minimum or no quality loss, which comprises steps of (a) choosing a do ...

2015

A Fast Hadamard Transform for Signals with Sub-linear Sparsity in the Transform Domain

Martin Vetterli, Robin Scheibler, Saeid Haghighatshoar

In this paper, we design a new iterative low-complexity algorithm for computing the Walsh-Hadamard transform (WHT) of an N dimensional signal with a K-sparse WHT. We suppose that N is a power of two and K = O(N^α), scales sub-linearly in N for some α ∈ (0, ...

Institute of Electrical and Electronics Engineers2015

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

Generalized Poisson Summation Formula for Tempered Distributions

Michaël Unser, Quy Ha Nguyen

The Poisson summation formula (PSF), which relates the sampling of an analog signal with the periodization of its Fourier transform, plays a key role in the classical sampling theory. In its current forms, the formula is only applicable to a limited class ...

IEEE2015

Extension of ultrasound Fourier slice Imaging theory to sectorial acquisition

Jean-Philippe Thiran, Rafael Eduardo Carrillo Rangel, Adrien Georges Jean Besson, Olivier Bernard

Ultrasound image reconstruction from the echoes received by an ultrasound probe after the transmission of diverging waves is an active area of research because of its capacity to insonify at ultra-high frame rate with large regions of interest using small ...

2015

Multiple phase estimation via signal separation using a windowed Fourier transform in digital holographic interferometry

Pramod Rastogi, Rishikesh Dilip Kulkarni

This paper proposes a novel method for the simultaneous estimation of multiple interference phases from a single recording of the interference field in a multi-wave digital holographic interferometry set-up. The method involves the separation of signal com ...

Institute of Physics2015

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

On the Continuity of Characteristic Functionals and Sparse Stochastic Modeling

Michaël Unser, Julien René Pierre Fageot, Arash Amini

The characteristic functional is the infinite-dimensional generalization of the Fourier transform for measures on function spaces. It characterizes the statistical law of the associated stochastic process in the same way as a characteristic function specif ...

Springer Birkhauser2014

Approximate Message Passing With Consistent Parameter Estimation and Applications to Sparse Learning

Michaël Unser, Ulugbek Kamilov

We consider the estimation of an independent and identically distributed (i.i.d.) (possibly non-Gaussian) vector x is an element of R-n from measurements y is an element of R-m obtained by a general cascade model consisting of a known linear transform foll ...

Ieee-Inst Electrical Electronics Engineers Inc2014

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

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Estimation Error of the Constrained Lasso

Method and apparatus for low complexity spectral analysis of bio-signals

A Fast Hadamard Transform for Signals with Sub-linear Sparsity in the Transform Domain

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

Generalized Poisson Summation Formula for Tempered Distributions

Extension of ultrasound Fourier slice Imaging theory to sectorial acquisition

Multiple phase estimation via signal separation using a windowed Fourier transform in digital holographic interferometry

Compressed Sensing of Memoryless Sources

On the Continuity of Characteristic Functionals and Sparse Stochastic Modeling

Approximate Message Passing With Consistent Parameter Estimation and Applications to Sparse Learning

A Fast Hadamard Transform for Signals with Sub-linear Sparsity in the Transform Domain

Approximate Message Passing With Consistent Parameter Estimation and Applications to Sparse Learning

Generalized Poisson Summation Formula for Tempered Distributions

Extension of ultrasound Fourier slice Imaging theory to sectorial acquisition

Compressed Sensing of Memoryless Sources

Method and apparatus for low complexity spectral analysis of bio-signals

Estimation Error of the Constrained Lasso

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

Multiple phase estimation via signal separation using a windowed Fourier transform in digital holographic interferometry

On the Continuity of Characteristic Functionals and Sparse Stochastic Modeling