Publications by Emrah Bostan | EPFL Graph Search

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

Michaël Unser, Emrah Bostan, Ulugbek Kamilov

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-Inst Electrical Electronics Engineers Inc2014

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

Statistics of Wavelet Coefficients for Sparse Self-Similar Images

Michaël Unser, Julien René Pierre Fageot, Emrah Bostan

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

Bayesian Denoising: From MAP to MMSE Using Consistent Cycle Spinning

Michaël Unser, Emrah Bostan, Ulugbek Kamilov, 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-Inst Electrical Electronics Engineers Inc2013

Sparse Stochastic Processes and Discretization of Linear Inverse Problems

Michaël Unser, Emrah Bostan, Ulugbek Kamilov, 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

Benefits of consistency in image denoising with steerable wavelets

Michaël Unser, Emrah Bostan, Ulugbek Kamilov, 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

Benefits Of Consistency In Image Denoising With Steerable Wavelets

Michaël Unser, Emrah Bostan, Ulugbek Kamilov, 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 ...

Ieee2013

Bayesian Estimation for Continuous-Time Sparse Stochastic Processes

Michaël Unser, Arash Amini, Emrah Bostan, Ulugbek Kamilov

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

Spatio-Temporal Regularization Of Flow-Fields

Michaël Unser, Nikolaos Stergiopoulos, Emrah Bostan, Pouya Dehghani Tafti, Orestis Vardoulis, Davide Piccini

We introduce a novel variational framework for the regularized reconstruction of time-resolved volumetric flow fields. Our objective functional takes the physical characteristics of the underlying flow into account in both the spatial and the temporal doma ...

IEEE2013

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

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

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

Statistics of Wavelet Coefficients for Sparse Self-Similar Images

Bayesian Denoising: From MAP to MMSE Using Consistent Cycle Spinning

Sparse Stochastic Processes and Discretization of Linear Inverse Problems

Benefits of consistency in image denoising with steerable wavelets

Benefits Of Consistency In Image Denoising With Steerable Wavelets

Bayesian Estimation for Continuous-Time Sparse Stochastic Processes

Spatio-Temporal Regularization Of Flow-Fields

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

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

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

Bayesian Estimation for Continuous-Time Sparse Stochastic Processes

Bayesian Denoising: From MAP to MMSE Using Consistent Cycle Spinning

Statistics of Wavelet Coefficients for Sparse Self-Similar Images

Sparse Stochastic Processes and Discretization of Linear Inverse Problems

Benefits Of Consistency In Image Denoising With Steerable Wavelets

Benefits of consistency in image denoising with steerable wavelets

Spatio-Temporal Regularization Of Flow-Fields