Publications by Emrah Bostan | EPFL Graph Search

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, 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

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

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

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

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

Variational Decomposition of Vector Fields in the Presence of Noise

Michaël Unser, Emrah Bostan, Pouya Dehghani Tafti

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

Benefits of Consistency in Image Denoising with Steerable Wavelets

Michaël Unser, Emrah Bostan, Ulugbek Kamilov

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 ap ...

IEEE2013

Emrah Bostan

Graph Chatbot

Chat with Graph Search

Statistics of Wavelet Coefficients for Sparse Self-Similar Images

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

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

Bayesian Estimation for Continuous-Time Sparse Stochastic Processes

Sparse Stochastic Processes and Discretization of Linear Inverse Problems

Bayesian Denoising: From MAP to MMSE Using Consistent Cycle Spinning

Benefits of consistency in image denoising with steerable wavelets

Benefits Of Consistency In Image Denoising With Steerable Wavelets

Variational Decomposition of Vector Fields in the Presence of Noise

Benefits of Consistency in Image Denoising with Steerable Wavelets

Bayesian Estimation for Continuous-Time Sparse Stochastic Processes

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

Variational Decomposition of Vector Fields in the Presence of Noise

Benefits of Consistency in Image Denoising with Steerable Wavelets

Statistics of Wavelet Coefficients for Sparse Self-Similar Images

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

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

Bayesian Denoising: From MAP to MMSE Using Consistent Cycle Spinning