Diapositivo 1

1
The Prox-it-Ans is a deconvolution algorithm for
data blurred and degraded by Poisson noise where
the Anscombe transform is used explicitly in the
problem formulation, resulting in a
nonlinear convex, AWGN deconvolution problem in
the Bayesian framework with a non-smooth
sparsity-promoting penalty over the
representation coefficients in a dictionary of
transforms (curvelets, wavelets) of the image to
be restored. The solution is obtained using a
fast proximal backward-forward splitting iteration
algorithm. The prior parameter is selected using
the generalized cross validation (GCV) criterion.
Denoising of Fluorescence Confocal Image
Sequences a Comparison Study
1,2Isabel Rodrigues (irodrigues_at_isr.ist.utl.pt)
and 1,3João Sanches (jmrs_at_isr.ist.utl.pt)
1Institute for Systems and Robotics2Instituto
Superior de Engenharia de Lisboa 3Instituto
Superior Técnico Lisbon, Portugal
Abstract Fluorescence laser scanning confocal
microscopy (FLSCM) imaging is now a common
biomedical tool that researchers make used in the
study of dynamic processes occurring inside the
living cells. Although fluorescent confocal
microscopes are reliable instruments, the
acquired images are usually corrupted by a severe
type of Poisson noise due to the small amount of
acquired radiation (low photon-count images) and
to the huge optico-electronics amplification.
These effects are even more pernicious when very
low intensity incident radiation is used to avoid
phototoxicity. In this work a convex, Bayesian
denoising algorithm, using a log-Euclidean total
variation regularization prior in space and a
log-Euclidean regularization prior in time is
described to remove the Poisson multiplicative
noise corrupting the FLSCM images. Since model
validation is a very important step, a comparison
with five state-of-the-art algorithms is
presented. Synthetic data were generated and
denoised with the described algorithm and with
each one of the other five. Results using the
Csiszár I-divergence and the SNR figures-of-merit
are presented.
Comparison Algorithms
Prox-it-Ans deconvolution algorithm for data
blurred and degraded by Poisson noise. The
Anscombe transform is used explicitly in the
problem formulation, resulting in a nonlinear
convex, AWGN deconvolution problem in the
Bayesian framework with a non-smooth
sparsity-promoting penalty over the
representation coefficients in a dictionary of
transforms (curvelets, wavelets) of the image to
be restored. The solution is obtained using a
fast proximal backward-forward splitting
iteration algorithm.
Prox-it-Gauss naive version of the Prox-it-Ans
where the Anscombe transform is performed first.
The Non-local Means algorithm (NLM) non-local
averaging technique, operating on all pixels in
the image with the same characteristic.
Problem Formulation
The BiShrink locally adaptive 3-D image
denoising algorithm using dual-tree complex
wavelet transforms with the bivariate shrinkage
thresholding function.

• The data exhibit a severe type of
  signal-dependent noise, assumed to obey a Poisson
  distribution
• Blur is neglected
• Independence of the observations assumed
• Bayesian framework MAP estimate
• X as Markov Random Field (MRF) - Gibbs
  distribution for X
• Anisotropic prior terms
• log-Euclidean TV edge preserving priors in space
• log-Euclidean priors in time

The BLF 2-D algorithm that smoothes images but
preserves edges by means of a nonlinear
combination of nearby image values.
The data LSFCM image sequences
The optimization problem
Signal to noise ratio (SNR) results
Csiszaer I-divergence results
The energy function
A comparison of the performance of the proposed
denoising algorithm with five state-of-the-art
algorithms is presented. Results with synthetic
data shows that the proposed algorithm
outperforms all the others when the SNR and
I-Divergence are used as figures-of-merit. The
CPU time outperforms all but one algorithms.
The data fidelity term
Non-convex optimization
CPU time to process the synthetic sequence
64x64x64 pixels
Example with real data (Hela cell)
Experimental Results
Synthetic Data

• A 64 64 pixels base image with a cell nucleus
  shape was generated.
• To each pixel of the base images, an exponential
  decay along the time (t 1, ..., 64) was applied
  to simulate the intensity decrease due to the
  photobleaching effect in a FLIP experiment, with
  rates equal to 0.07 for every pixel in the range
  of 10 (in pixel units) from the center
  coordinates of the hole (dark circle) and equal
  to 0.02 for the rest of the image.
• The true sequence was corrupted with Poisson
  noise.
• SNR range 3 dB to 9 dB.

Data provided by the Instituto de Medicina
Molecular de Lisboa