Publications de Ulugbek Kamilov

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

Generalized linear models, 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) methods, b ...

IEEE2017

Optical Tomography Based On A Nonlinear Model That Handles Multiple Scattering

Michaël Unser, Alexandre Goy, Ulugbek Kamilov, Demetri Psaltis, Joowon Lim

Learning Tomography (LT) is a nonlinear optimization algorithm for computationally imaging three-dimensional (3D) distribution of the refractive index in semi-transparent samples. Since the energy function in LT is generally non-convex, the solution it obt ...

Ieee2017

Optical Tomographic Image Reconstruction Based on Beam Propagation and Sparse Regularization

Michaël Unser, Cédric René Jean Vonesch, Ulugbek Kamilov, Demetri Psaltis

Optical tomographic imaging requires an accurate forward model as well as regularization to mitigate missing-data artifacts and to suppress noise. Nonlinear forward models can provide more accurate interpretation of the measured data than their linear coun ...

2016

Learning from Examples in Optical Imaging

Michaël Unser, Cédric René Jean Vonesch, Ulugbek Kamilov, Demetri Psaltis

Imaging systems can be designed using examples and methods similar to the techniques used in deep learning. We describe experimental results demonstrating optical tomography based on the learning approach. ...

OSA2016

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

Learning Approach to Optical Tomography

Michaël Unser, Alexandre Goy, Cédric René Jean Vonesch, Ulugbek Kamilov, Demetri Psaltis

Optical tomography has been widely investigated for biomedical imaging applications. In recent years optical tomography has been combined with digital holography and has been employed to produce high-quality images of phase objects such as cells. In this p ...

Optical Soc Amer2015

Isotropic Inverse-Problem Approach for Two-Dimensional Phase Unwrapping

Michaël Unser, Ulugbek Kamilov, Demetri Psaltis

We propose a new technique for two-dimensional phase unwrapping. The unwrapped phase is found as the solution of an inverse problem that consists in the minimization of an energy functional. The latter includes a weighted data fidelity term that favors spa ...

JOSA2015

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

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

Variational Justification of Cycle Spinning for Wavelet-Based Solutions of Inverse Problems

Michaël Unser, Ulugbek Kamilov, Emrah Bostan

Cycle spinning is a widely used approach for improving the performance of wavelet-based methods that solve linear inverse problems. Extensive numerical experiments have shown that it significantly improves the quality of the recovered signal without increa ...

IEEE Institute of Electrical and Electronics Engineers2014

MMSE Estimation of Sparse Levy Processes

Michaël Unser, Ulugbek Kamilov, Arash Amini, Pedram Pad

We investigate a stochastic signal-processing framework for signals with sparse derivatives, where the samples of a Levy process are corrupted by noise. The proposed signal model covers the well-known Brownian motion and piecewise-constant Poisson process; ...

Ieee-Inst Electrical Electronics Engineers Inc2013

Bayesian Estimation for Continuous-Time Sparse Stochastic Processes

Michaël Unser, Ulugbek Kamilov, Emrah Bostan, Arash Amini

We consider continuous-time sparse stochastic processes from which we have only a finite number of noisy/noiseless samples. Our goal is to estimate the noiseless samples (denoising) and the signal in-between (interpolation problem). By relying on tools fro ...

Ieee-Inst Electrical Electronics Engineers Inc2013

Sparse Stochastic Processes and Discretization of Linear Inverse Problems

Michaël Unser, Ulugbek Kamilov, Emrah Bostan, Masih Nilchian

We present a novel statistically-based discretization paradigm and derive a class of maximum a posteriori (MAP) estimators for solving ill-conditioned linear inverse problems. We are guided by the theory of sparse stochastic processes, which specifies cont ...

Ieee-Inst Electrical Electronics Engineers Inc2013

Bayesian Denoising: From MAP to MMSE Using Consistent Cycle Spinning

Michaël Unser, Ulugbek Kamilov, Emrah Bostan, Abbas Kazerouni

We introduce a new approach for the implementation of minimum mean-square error (MMSE) denoising for signals with decoupled derivatives. Our method casts the problem as a penalized least-squares regression in the redundant wavelet domain. It exploits the l ...

IEEE Institute of Electrical and Electronics Engineers2013

MAP Estimators for Self-Similar Sparse Stochastic Models

Michaël Unser, Ulugbek Kamilov, Emrah Bostan, Julien René Pierre Fageot

We consider the reconstruction of multi-dimensional signals from noisy samples. The problem is formulated within the framework of the theory of continuous-domain sparse stochastic processes. In particular, we study the fractional Laplacian as the whitening ...

SampTA2013

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

Benefits of consistency in image denoising with steerable wavelets

Michaël Unser, Ulugbek Kamilov, Emrah Bostan, Bugra Tekin

The steerable wavelet transform is a redundant image representation with the remarkable property that its basis functions can be adaptively rotated to a desired orientation. This makes the transform well-suited to the design of wavelet-based algorithms app ...

2013

Message-Passing De-Quantization with Applications to Compressed Sensing

Ulugbek Kamilov

Estimation of a vector from quantized linear measurements is a common problem for which simple linear techniques are suboptimal—sometimes greatly so. This paper develops message-passing de-quantization (MPDQ) algorithms for minimum mean-squared error estim ...

IEEE2012

The Analog Formulation of Sparsity Implies Infinite Divisibility and Rules Out Bernoulli-Gaussian Priors

Michaël Unser, Ulugbek Kamilov, Arash Amini

Motivated by the analog nature of real-world signals, we investigate continuous-time random processes. For this purpose, we consider the stochastic processes that can be whitened by linear transformations and we show that the distribution of their samples ...

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