Bayesian Image Recovery for Dendritic Structures Under Low Signal-to-Noise Conditions

Abstract

Experimental research seeking to quantify neuronal structure constantly contends with restrictions on image resolution and variability. In particular, experimentalists often need to analyze images with very low signal-to-noise ratio (SNR). In many experiments dye toxicity scales with the light intensity; this leads experimentalists to reduce image SNR in order to preserve the viability of the specimen. In this work we present a Bayesian approach for estimating the neuronal shape given low-SNR observations. This Bayesian framework has two major advantages. First, the method effectively incorporates known facts about 1) the image formation process, including blur and the Poisson nature of image noise at low intensities, and 2) dendritic shape, including the fact that dendrites are simply-connected geometric structures with smooth boundaries. Second, we may employ standard Markov chain Monte Carlo (MCMC) techniques for quantifying the posterior uncertainty in our estimate of the dendritic shape. We describe an efficient computational implementation of these methods and demonstrate the algorithm's performance on simulated noisy two-photon laser-scanning microscopy images.

3D image reconstruction using Radon transform

“…For the reconstruction algorithms, a Bayesian approach can be used. In the Bayesian approach, an important role is played by the prior knowledge of some physiological parameters, for example in the CT tomography, the attenuation coefficients for the various organs [9,[13][14][15][16][17]. A reconstruction algorithm based on Bayesian approach is detailed in Sect.…”

“…(8) and (9). Many authors have contributed to develop useful image restoration methods using a maximum likelihood approach [9,[13][14][15][16][17][18][19].…”

“…Following Fudenberg and Paninski [9], we can introduce a limited maximum likelihood to simulate possible contribution of the Π unknown function, so that we have to compute an estimator aŝ (17) where λ and f (Π ) are a parameter and a function, respectively, taking in account the incidence of instrumental aberrations. Because λ and f (Π ) represents unknown contributions, we can quantify the uncertainty in the estimator Eq.…”

“…A Gibbs sampler can be used for doing this quantification. The idea is that, given the observed data I obs , we iteratively choose a pixel i randomly and a set of states of pixel reproducing the incidence of artifacts, for example, discontinuities for Shepp-Logan phantoms or suitable different extinction factor for real medical images [9,13,19]. The global procedure for image reconstruction from stacks is displayed in Fig.…”

“…In general, a dendritic model can accurately quantify both 3D topology (connectivity) and morphology (radius, length, branching angles, etc) of the dendritic structure. Recently, several algorithms were produced where the main emphasis is put on topology or morphology, or both [9]. Inferential methods have been largely used for the identification of vascular dendritic structures.…”