Blindly Deconvolving Super-noisy Blurry Image Sequences

TL;DR

This paper introduces two novel blind deconvolution methods for noisy, blurry image sequences that do not require estimating unknown filters, improving the recovery of original images from degraded observations.

Contribution

The paper presents two new methods for multi-frame blind deconvolution that avoid filter estimation, including an eigenvector-based approach with a pre-processing step to enhance performance.

Findings

Eigenvector method outperforms previous approaches in synthetic tests.

Pre-processing step effectively increases signal subspace dimension.

Proposed methods achieve better image recovery in noisy, blurry conditions.

Abstract

Image blur and image noise are imaging artifacts intrinsically arising in image acquisition. In this paper, we consider multi-frame blind deconvolution (MFBD), where image blur is described by the convolution of an unobservable, undeteriorated image and an unknown filter, and the objective is to recover the undeteriorated image from a sequence of its blurry and noisy observations. We present two new methods for MFBD, which, in contrast to previous work, do not require the estimation of the unknown filters. The first method is based on likelihood maximization and requires careful initialization to cope with the non-convexity of the loss function. The second method circumvents this requirement and exploits that the solution of likelihood maximization emerges as an eigenvector of a specifically constructed matrix, if the signal subspace spanned by the observations has a sufficiently large dimension. We describe a pre-processing step, which increases the dimension of the signal subspace by artificially generating additional observations. We also propose an extension of the eigenvector method, which copes with insufficient dimensions of the signal subspace by estimating a footprint of the unknown filters (that is a vector of the size of the filters, only one is required for the whole image sequence). We have applied the eigenvector method to synthetically generated image sequences and performed a quantitative comparison with a previous method, obtaining strongly improved results.