Emrah Bostan

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Related publications (26)

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Bayesian Denoising: From MAP to MMSE Using Consistent Cycle Spinning

Michaël Unser, Ulugbek Kamilov, Emrah Bostan

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

Generalized Total Variation Denoising Via Augmented Lagrangian Cycle Spinning With Haar Wavelets

Michaël Unser, Emrah Bostan, Ulugbek Kamilov

We consider the denoising of signals and images using regularized least-squares method. In particular, we propose a simple minimization algorithm for regularizers that are functions of the discrete gradient. By exploiting the connection of the discrete gra ...

Ieee2012

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

Benefits of consistency in image denoising with steerable wavelets

Michaël Unser, Emrah Bostan, Bugra Tekin, 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 app ...

2013

Wavelet Statistics of Sparse and Self-Similar Images

Michaël Unser, Julien René Fageot, Emrah Bostan

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

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