Probabilistic Modeling and Inference for Sequential Space-Varying Blur Identification

Abstract

The identification of parameters of spatially variant blurs given a clean image and its blurry noisy version is a challenging inverse problem of interest in many application fields, such as biological microscopy and astronomical imaging. In this paper, we consider a parametric model of the blur and introduce an 1D state-space model to describe the statistical dependence among the neighboring kernels. We apply a Bayesian approach to estimate the posterior distribution of the kernel parameters given the available data. Since this posterior is intractable for most realistic models, we propose to approximate it through a sequential Monte Carlo approach by processing all data in a sequential and efficient manner. Additionally, we propose a new sampling method to alleviate the particle degeneracy problem, which is present in approximate Bayesian filtering, particularly in challenging concentrated posterior distributions. The considered method allows us to process sequentially image patches at a reasonable computational and memory costs. Moreover, the probabilistic approach we adopt in this paper provides uncertainty quantification which is useful for image restoration. The practical experimental results illustrate the improved estimation performance of our novel approach, demonstrating also the benefits of exploiting the spatial structure the parametric blurs in the considered models.

A novel variational approach for multiphoton microscopy image restoration: from PSF estimation to 3D deconvolution

“…As figure 3 demonstrates, the estimated FWHM and angles are consistent across the four beads, validating the assumption of a stationary PSF in the observed field. Moreover, the average FWHM values are close to the theoretical expectations computed with (45) and (46), equal to 0.34 µm along the axial axes, and 1.43 µm in the depth direction, which validates our approach.…”

“…Another strategy is to break down the problem into two successive inverse problems. In this two-step approach, one first performs a calibration step [37,44,46,52,65], providing an estimate of the PSF h in a controlled situation where x is a known (i.e. calibrated) entity.…”

SABRINA: A Stochastic Subspace Majorization-Minimization Algorithm

“…The goal is to retrieve an estimation of x from the pair of images (z, y). This inverse problem typically arises in the calibration of optical instruments [5,43]. The observation model (110) can be expressed equivalently as…”