I am a Post Doctoral Associate at
Duke university
working with
Rebecca Willett in the
Network and Imaging Science Laboratory (NISLab) .
News
"Poisson Noise Reduction with Non-Local PCA",
J. Salmon,
C.-A. Deledalle , R. Willett and
Z. Harmany , ICASSP, 2012
[ pdf |
Abstract
| BibTeX
| Demo Matlab
| ZIP ]
Abstract
Photon limitations arise in spectral imaging, nuclear medicine, astronomy
and night vision. The Poisson distribution used to model
this noise has variance equal to its mean so blind application of standard
noise removals methods yields significant artifacts. Recently,
overcomplete dictionaries combined with sparse learning techniques
have become extremely popular in image reconstruction. The aim
of the present work is to demonstrate that for the task of image denoising,
nearly state-of-the-art results can be achieved using small
dictionaries only, provided that they are learned directly from the
noisy image. To this end, we introduce patch-based denoising algorithms
which perform an adaptation of PCA (Principal Component
Analysis) for Poisson noise. We carry out a comprehensive empirical
evaluation of the performance of our algorithms in terms of accuracy
when the photon count is really low. The results reveal that,
despite its simplicity, PCA-flavored denoising appears to be competitive
with other state-of-the-art denoising algorithms.
BibTeX
@inproceedings{Salmon_Deledalle_Willett_Harmany12,
author = { J. Salmon and C-A. Deledalle and R. Willett and Z. T. Harmany},
title = {Poisson Noise Reduction with Non-Local PCA},
booktitle = {ICASPP},
pages = {},
year = {2012},
}
"Oracle inequalities and minimax rates for non-local means and related adaptive kernel-based methods",
E. Arias-Castro
, J. Salmon, R. Willett
[ pdf |
Abstract
| BibTeX
| Demo Matlab
| ZIP ]
Abstract
This paper describes a novel theoretical characterization of the performance of non-local means (NLM) for noise removal. NLM has proven effective in a variety of empirical studies, but little is understood fundamentally about how it performs relative to classical methods based on wavelets or how various parameters (e.g., patch size) should be chosen. For cartoon images and images which may contain thin features and regular textures, the error decay rates of NLM are derived and compared with those of linear filtering, oracle estimators, variable-bandwidth kernel methods, Yaroslavsky's filter and wavelet thresholding estimators. The trade-off between global and local search for matching patches is examined, and the bias reduction associated with the local polynomial regression version of NLM is analyzed. The theoretical results are validated via simulations for 2D images corrupted by additive white Gaussian noise.
BibTeX
@article{AriasCastro_Salmon_Willett,
author = {E. Arias-Castro and J. Salmon and R. Willett},
title = {Oracle inequalities and minimax rates for non-local means and related adaptive kernel-based methods},
journal = {technical report},
volume = {},
number = {arXiv:1112.4434v1 [math.ST]},
pages = {},
year = {2011},
doi = {}
}
Resume
In 2010, I finished my PHD in Statistics under the supervision of
Dominique Picard and
Erwan Le Pennec at the Laboratoire de Probabilités et de Modélisation Aléatoire (LPMA ) in Université Paris Diderot.
My thesis is about the denoising of digital images combining patch-based method and
statistical aggregation. The full manuscript can be found in my papers section. I am especially interested in topics such as:
aggregation of estimators, Patch based denoising methods, Non-parametric regression, On-line learning.