Tanja Teuber

Deblurring Poissonian images by split Bregman techniques

The restoration of blurred images corrupted by Poisson noise is an important task in various applications such as astronomical imaging, electronic microscopy, single particle emission computed tomography (SPECT) and positron emission tomography (PET). In this paper, we focus on solving this task by minimizing an energy functional consisting of the I-divergence as similarity term and the TV regularization term. Our minimizing algorithm uses alternating split Bregman techniques (alternating direction method of multipliers) which can be reinterpreted as Douglas-Rachford splitting applied to the dual problem. In contrast to recently developed iterative algorithms, our algorithm contains no inner iterations and produces nonnegative images. The high efficiency of our algorithm in comparison to other recently developed algorithms to minimize the same functional is demonstrated by artificial and real-world numerical examples.

Removing Multiplicative Noise by Douglas-Rachford Splitting Methods

In this paper, we consider a variational restoration model consisting of the I-divergence as data fitting term and the total variation semi-norm or nonlocal means as regularizer for removing multiplicative Gamma noise. Although the I-divergence is the typical data fitting term when dealing with Poisson noise we substantiate why it is also appropriate for cleaning Gamma noise. We propose to compute the minimizers of our restoration functionals by applying Douglas-Rachford splitting techniques, resp. alternating direction methods of multipliers. For a particular splitting, we present a semi-implicit scheme to solve the involved nonlinear systems of equations and prove its Q-linear convergence. Finally, we demonstrate the performance of our methods by numerical examples.

Fast electrostatic halftoning

Electrostatic halftoning is a high-quality method for stippling, dithering, and sampling, but it suffers from a high runtime. This made the technique difficult to use for most real-world applications. A recently proposed minimisation scheme based on the non-equispaced fast Fourier transform (NFFT) lowers the complexity in the particle number M from

A new similarity measure for nonlocal filtering in the presence of multiplicative noise

\mathcal{O}(M^2)

Nonlocal filters for removing multiplicative noise

to

Anisotropic Smoothing Using Double Orientations

\mathcal{O}(M \log M).