Publications de Emrah Bostan | EPFL Graph Search

Variations of intracellular density during the cell cycle arise from tip-growth regulation in fission yeast

Intracellular density impacts the physical nature of the cytoplasm and can globally affect cellular processes, yet density regulation remains poorly understood. Here, using a new quantitative phase imaging method, we determined that dry-mass density in fis ...

ELIFE SCIENCES PUBLICATIONS LTD2021

Combined Multi-Plane Tomographic Phase Retrieval and Stochastic Optical Fluctuation Imaging for 4D Cell Microscopy

Marcel Leutenegger, Theo Lasser, Hilal Lashuel, Adrien Charles-François Raymond Descloux, Emrah Bostan, Arno Pino Bouwens, Anne-Laure Mahul Mellier, Tomas Lukes

Super-resolution fluorescence microscopy provides unprecedented insight into cellular and subcellular structures. However, going beyond the diffraction barrier comes at a price since most far-field super-resolution imaging techniques trade temporal for spa ...

Nature Publishing Group2018

Learning Convex Regularizers for Optimal Bayesian Denoising

Michaël Unser, Emrah Bostan, Quy Ha Nguyen

2018

MMSE Denoising of Sparse and Non-Gaussian AR(1) Processes

Michaël Unser, Emrah Bostan, Pedram Pad, Pouria Tohidi

We propose two minimum-mean-square-error (MMSE) estimation methods for denoising non-Gaussian first-order autoregressive (AR(1)) processes. The first one is based on the message passing framework and gives the exact theoretic MMSE estimator. The second is ...

IEEE2016

Variational Phase Imaging Using the Transport-of-Intensity Equation

Michaël Unser, Daniel Sage, Emrah Bostan, Masih Nilchian, Emmanuel Augustin Julien Froustey

We introduce a variational phase retrieval algorithm for the imaging of transparent objects. Our formalism is based on the transport-of-intensity equation (TIE), which relates the phase of an optical field to the variation of its intensity along the direct ...

IEEE2016

Joint absorption and phase retrieval in grating-based x-ray radiography

Michaël Unser, Emrah Bostan, Masih Nilchian, Mohammad Reza Nilchiyan, Marco Stampanoni

Given the raw absorption and differential phase-contrast images obtained from a grating-based x-ray radiography, we formulate the joint denoising of the absorption image and retrieval of the non-differential phase image as a regularized inverse problem. Th ...

Optical Society of America2016

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

Divergence-Free Wavelet Frames

Michaël Unser, Emrah Bostan, John Paul Ward

We propose an efficient construction of wavelet frames in any number of dimensions that are divergence-free. Our approach is based on applying the Leray projector, which is scale-invariant, to a standard wavelet frame. We prove that the projected wavelets ...

IEEE Institute of Electrical and Electronics Engineers2015

Wavelet Statistics of Sparse and Self-Similar Images

Michaël Unser, Emrah Bostan, Julien René Pierre Fageot

It is well documented that natural images are compressible in wavelet bases and tend to exhibit fractal properties. In this paper, we investigate statistical models that mimic these behaviors. We then use our models to make predictions on the statistics of ...

Siam Publications2015

Improved Variational Denoising of Flow Fields with Application to Phase-Contrast MRI Data

Nikolaos Stergiopoulos, Michaël Unser, Emrah Bostan, Orestis Vardoulis, Stamatios Lefkimmiatis

We propose a new variational framework for the problem of reconstructing flow fields from noisy measurements. The formalism is based on regularizers penalizing the singular values of the Jacobian of the field. Specifically, we rely on the nuclear norm. Our ...

IEEE Institute of Electrical and Electronics Engineers2015

Statistics of Wavelet Coefficients for Sparse Self-Similar Images

Michaël Unser, Emrah Bostan, Julien René Pierre Fageot

We study the statistics of wavelet coefficients of non-Gaussian images, focusing mainly on the behaviour at coarse scales. We assume that an image can be whitened by a fractional Laplacian operator, which is consistent with an

∥ω∥ ^{ -\gamma }

spectral ...

IEEE2014

Phase Retrieval by Using Transport-of-Intensity Equation and Differential Interference Contrast Microscopy

Michaël Unser, Daniel Sage, Benjamin Rappaz, Emrah Bostan, Emmanuel Augustin Julien Froustey

We present a variational reconstruction algorithm for the phase-retrieval problem by using the differential interference contrast microscopy. Principally, we rely on the transport-of-intensity equation that specifies the sought phase as the solution of a p ...

IEEE2014

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

Digital Phase Reconstruction via Iterative Solutions of Transport-of-Intensity Equation

Michaël Unser, Emrah Bostan, Stamatios Lefkimmiatis, Emmanuel Augustin Julien Froustey

We develop a variational algorithm for reconstructing phase objects from a series of bright field micrographs. Our mathematical model is based on the transport-of-intensity equation (TIE), which links the phase of a complex field to the axial derivative of ...

Ieee2014

Variational Decomposition of Vector Fields in the Presence of Noise

Michaël Unser, Pouya Dehghani Tafti, Emrah Bostan

We present a variational framework, and an algorithm based on the alternating method of multipliers (ADMM), for the problem of decomposing a vector field into its curl- and divergence-free components (Helmholtz decomposition) in the presence of noise. We p ...

IEEE2013

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

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

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

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

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