32nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society Denoising of LSFCM images with compensation for the Photoblinking/Photobleaching effects Isabel Rodrigues1,2, J. Miguel Sanches1,3 1Institute for Systems and Robotics 2Instituto Superior de Engenharia de Lisboa 3Instituto Superior Técnico, Lisbon, Portugal 32nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society

The Problem Fluorescence confocal microscopy images are affected by fading effects, called photoblinking/ photobleaching (PBPB), that lead to image intensity decreasing along the time, preventing long time experiments. Images present low signal to noise ratio (SNR). Images are corrupted by non-additive noise mainly due to the strong amplification performed by the photomultiplier needed to detect the small fluorescent radiation emitted by the fluorophore. The SNR increases with the amount of incident radiation as well as the PBPB effect and the Toxicity 32nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society

Real data sequences 32nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society

Goal Design a reconstruction algorithm for this type of 2D + t image sequences in a Bayesian framework where the non- additive noise is modeled by a Poisson distribution and the spatio-temporal correlation among pixels is taken into account and a theoretical model to describe the intensity decay due to the PBPB effect is also included 32nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society

PBPB MODEL Fluorescent tagging molecules assumed in three main states: ON-state - able to fluoresce and be observed (nON), OFF-state - not able to fluoresce (not visible ) (nOFF), BLEACHED-state - permanently OFF. mean intensity of the image at the instant t The time intervals at each state are governed by Levy Statistics - statistical aging - leads to a constant increasing on the time intervals at each state along the time. 32nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society

PBPB MODEL -- parameters associated with the concentrations and state transition dynamics of the molecules; I – amount of incident radiation. and are constants computed using the initial conditions. Given the physical constraints of the problem it can be proved that are always positive real constants. 32nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society

Reconstruction Optimization criterion: MAP – maximum a posteriori Data fidelity term Prior term : pixel morphology intensity : pixel noiseless intensity, : pixel noisy intensity : PBPB model estimated parameters 32nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society

Prior The morphology is assumed to be a MRF  P(F) is a Gibbs distribution : log-Euclidean potential functions  edge preserving neighbors of f in a 2nd order clique 32nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society

Regularization parameters Optimization Non convex Energy function to minimize By changing the variable , , a convex function is obtained. The function is computed directly from the data. Regularization parameters 32nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society

EXPERIMENTAL RESULTS Synthetic Data Original F : Intensity layers: 10, 30, 60. Two-exponentials decay : Regularization parameters : 32nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society

EXPERIMENTAL RESULTS Synthetic Data Reconstructed sequence and estimated morphology. Images 2, 21, 63 32nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society

EXPERIMENTAL RESULTS Synthetic Data Monte Carlo test: 500 runs Estimated morphology relative error per iteration SNR morphology MSE morphology 32nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society

EXPERIMENTAL RESULTS Synthetic Data Model Validation (147.9s) (2.2s) (1319.2s) (17.2s) 32nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society

EXPERIMENTAL RESULTS Real Data Noisy data, estimated morphology and respective profile plots 32nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society

THANKS 32nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society