Publications by Aurélien Bourquard

Compressed imaging by sparse random convolution

Theo Lasser, Antonio Lopez, Aurélien Bourquard

The theory of compressed sensing (CS) shows that signals can be acquired at sub-Nyquist rates if they are sufficiently sparse or compressible. Since many images bear this property, several acquisition models have been proposed for optical CS. An interestin ...

Optical Society of America2016

Adaptive Image Resizing Based on Continuous-Domain Stochastic Modeling

Michaël Unser, Aurélien Bourquard, Hagay Kirshner, John Paul Ward

We introduce an adaptive continuous-domain modeling approach to texture and natural images. The continuous-domain image is assumed to be a smooth function, and we embed it in a parameterized Sobolev space. We point out a link between Sobolev spaces and sto ...

Ieee-Inst Electrical Electronics Engineers Inc2014

Anisotropic Interpolation of Sparse Generalized Image Samples

Michaël Unser, Aurélien Bourquard

Practical image-acquisition systems are often modeled as a continuous-domain prefilter followed by an ideal sampler, where generalized samples are obtained after convolution with the impulse response of the device. In this paper, our goal is to interpolate ...

Ieee-Inst Electrical Electronics Engineers Inc2013

Binary Compressed Imaging

Michaël Unser, Aurélien Bourquard

Compressed sensing can substantially reduce the number of samples required for conventional signal acquisition at the expense of an additional reconstruction procedure. It also provides robust reconstruction when using quantized measurements, including in ...

Ieee-Inst Electrical Electronics Engineers Inc2013

Linear Interpolation Of Biomedical Images Using A Data-Adaptive Kernel

Michaël Unser, Aurélien Bourquard, Hagay Kirshner, John Paul Ward

In this work, we propose a continuous-domain stochastic model that can be applied to image data. This model is autoregressive, and accounts for Gaussian-type as well as for non-Gaussian-type innovations. In order to estimate the corresponding parameters fr ...

IEEE2013

A Practical Inverse-Problem Approach to Digital Holographic Reconstruction

Christian Depeursinge, Michaël Unser, Nicolas Pavillon, Aurélien Bourquard, Emrah Bostan

In this paper, we propose a new technique for high-quality reconstruction from single digital holographic acquisitions. The unknown complex object field is found as the solution of a nonlinear inverse problem that consists in the minimization of an energy ...

OSA2013

Autocalibrated Signal Reconstruction From Linear Measurements Using Adaptive Gamp

Michaël Unser, Aurélien Bourquard, Ulugbek Kamilov, Emrah Bostan

In this paper, we reconstruct signals from underdetermined linear measurements where the componentwise gains of the measurement system are unknown a priori. The reconstruction is performed through an adaptation of the message-passing algorithm called adapt ...

Ieee2013

Compressed Optical Imaging

Aurélien Bourquard

We address the resolution of inverse problems where visual data must be recovered from incomplete information optically acquired in the spatial domain. The optical acquisition models that are involved share a common mathematical structure consisting of a l ...

EPFL2013

Hessian-Based Norm Regularization for Image Restoration With Biomedical Applications

Michaël Unser, Aurélien Bourquard, Stamatios Lefkimmiatis

We present nonquadratic Hessian-based regularization methods that can be effectively used for image restoration problems in a variational framework. Motivated by the great success of the total-variation (TV) functional, we extend it to also include second- ...

IEEE2012

Hessian-Based Regularization For 3-D Microscopy Image Restoration

Michaël Unser, Aurélien Bourquard, Stamatios Lefkimmiatis

We investigate a non quadratic regularizer that is based on the Hessian operator for dealing with the restoration of 3-D images in a variational framework. We show that the regularizer under study is a valid extension of the total-variation (TV) functional ...

Ieee2012

One-Bit Measurements With Adaptive Thresholds

Michaël Unser, Aurélien Bourquard, Ulugbek Kamilov, Arash Amini

We introduce a new method for adaptive one-bit quantization of linearmeasurements and propose an algorithm for the recovery of signals based on generalized approximate message passing (GAMP). Our method exploits the prior statistical information on the sig ...

IEEE Institute of Electrical and Electronics Engineers2012

Image Segmentation With Background Correction Using A Multiplicative Smoothing-Spline Model

Michaël Unser, Aurélien Bourquard, Ramtin Madani

This paper presents an image-segmentation method which compensates multiplicative distortions based on smooth regularity assumptions. In this work, we generalize the original Chan-Vese functional to handle a continuous multiplicative bias. In the derivatio ...

Ieee2012

Resolution-Invariant Separable Arma Modeling Of Images

Michaël Unser, Aurélien Bourquard, Hagay Kirshner

We suggest a continuous-domain stochastic modeling of images that is invariant to spatial resolution. Specifically, we are proposing an estimator that is calibrated with respect to the sampling step, and that can potentially handle aliased data. Motivated ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2011

A Second-Order Extension Of Tv Regularization For Image Deblurring

Michaël Unser, Aurélien Bourquard, Zafer Dogan, Stamatios Lefkimmiatis

In this paper, we propose a novel second-order regularizer based on the maximum response of the second-order directional derivative, assuming that the image under consideration belongs to the class of piecewise-linear signals. Compared to total-variation r ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2011

Optical Imaging Using Binary Sensors

Michaël Unser, François Aguet, Aurélien Bourquard

This paper addresses the problem of reconstructing an image from 1-bit-quantized measurements, considering a simple but nonconventional optical acquisition model. Following a compressed-sensing design, a known pseudo-random phase-shifting mask is introduce ...

OSA2010