4,611 research outputs found
MDL Denoising Revisited
We refine and extend an earlier MDL denoising criterion for wavelet-based
denoising. We start by showing that the denoising problem can be reformulated
as a clustering problem, where the goal is to obtain separate clusters for
informative and non-informative wavelet coefficients, respectively. This
suggests two refinements, adding a code-length for the model index, and
extending the model in order to account for subband-dependent coefficient
distributions. A third refinement is derivation of soft thresholding inspired
by predictive universal coding with weighted mixtures. We propose a practical
method incorporating all three refinements, which is shown to achieve good
performance and robustness in denoising both artificial and natural signals.Comment: Submitted to IEEE Transactions on Information Theory, June 200
Spherical deconvolution of multichannel diffusion MRI data with non-Gaussian noise models and spatial regularization
Spherical deconvolution (SD) methods are widely used to estimate the
intra-voxel white-matter fiber orientations from diffusion MRI data. However,
while some of these methods assume a zero-mean Gaussian distribution for the
underlying noise, its real distribution is known to be non-Gaussian and to
depend on the methodology used to combine multichannel signals. Indeed, the two
prevailing methods for multichannel signal combination lead to Rician and
noncentral Chi noise distributions. Here we develop a Robust and Unbiased
Model-BAsed Spherical Deconvolution (RUMBA-SD) technique, intended to deal with
realistic MRI noise, based on a Richardson-Lucy (RL) algorithm adapted to
Rician and noncentral Chi likelihood models. To quantify the benefits of using
proper noise models, RUMBA-SD was compared with dRL-SD, a well-established
method based on the RL algorithm for Gaussian noise. Another aim of the study
was to quantify the impact of including a total variation (TV) spatial
regularization term in the estimation framework. To do this, we developed TV
spatially-regularized versions of both RUMBA-SD and dRL-SD algorithms. The
evaluation was performed by comparing various quality metrics on 132
three-dimensional synthetic phantoms involving different inter-fiber angles and
volume fractions, which were contaminated with noise mimicking patterns
generated by data processing in multichannel scanners. The results demonstrate
that the inclusion of proper likelihood models leads to an increased ability to
resolve fiber crossings with smaller inter-fiber angles and to better detect
non-dominant fibers. The inclusion of TV regularization dramatically improved
the resolution power of both techniques. The above findings were also verified
in brain data
Isotropic inverse-problem approach for two-dimensional phase unwrapping
In this paper, we propose a new technique for two-dimensional phase
unwrapping. The unwrapped phase is found as the solution of an inverse problem
that consists in the minimization of an energy functional. The latter includes
a weighted data-fidelity term that favors sparsity in the error between the
true and wrapped phase differences, as well as a regularizer based on
higher-order total-variation. One desirable feature of our method is its
rotation invariance, which allows it to unwrap a much larger class of images
compared to the state of the art. We demonstrate the effectiveness of our
method through several experiments on simulated and real data obtained through
the tomographic phase microscope. The proposed method can enhance the
applicability and outreach of techniques that rely on quantitative phase
evaluation
- …