Efficient filter flow for space-variant multiframe blind deconvolution

Abstract

Ultimately being motivated by facilitating space-variant blind deconvolution, we present a class of linear transformations, that are expressive enough for space-variant filters, but at the same time especially designed for efficient matrix-vector-multiplications. Successful results on astronomical imaging through atmospheric turbulences and on noisy magnetic resonance images of constantly moving objects demonstrate the practical significance of our approach.

Distributed approach for deblurring large images with shift-variant blur

“…If blur varies smoothly in field-of-view, then PSF at any location in the field can be well approximated by linear combination (interpolation) of only few PSFs sampled on a regular grid points within the field. First-order 2D interpolation weights are sufficient to render smooth variation of the blur within the field while keeping the shift-variant blur operator computationally efficient [2,3]. This suggests us to split the acquired image into overlapping blocks, approximate the regularizer on the whole image by sum of the regularizers on the blocks, and then deblur the blocks locally while imposing consensus on overlapping pixels by weighted average using first-order 2D interpolation weights.…”

“…Blending is done using weighted averaging (5) with the same first-order 2D interpolation weights ω i as in the proposed method. Though the second method is not intended to solve either the original problem (2) or the distributed problem (3), it is a straightforward way to deblur a large image with minimal computational resources. Hereafter, we will refer to the second method as independent deblurring method.…”

“…Thus, an efficient distributed algorithm is the one which is computation intensive rather than communication intensive. For shift-variant image deblurring, a possible approach is to use the distributed array abstraction available on modern distributed system, and reimplement the existing centralized methods [2,3] using distributed arrays. However, the bottleneck of such approaches is extensive data communication among the nodes at each iteration of the optimization algorithm, e.g., each time H or H T is applied, the nodes need to exchange a large amount of data.…”

“…There does not exist any efficient and straight-forward way for shift-variant deblurring. However, there are some fast approximations proposed in [1,2]; see [3] for detailed comparison between the different approximations. If we approximate the noise in observed image by a non-stationary white Gaussian noise as considered in [4] (see [5] for more refined noise model), the discrete image formation model can be written as: y = H x + ε.…”

A Linear Systems Approach to Imaging Through Turbulence

“…They perform image registration via Large Deformation Diffeomorphic Metric Mapping (LDDMM), introduced by Miller et al [4,30,46] which is computationally very expensive; moreover the final results depend heavily on the choice of the parameters of the LD-DMM registration. Li et al [24] use Principal Component Analysis (PCA) to deblur a sequence of turbulent images, simply by taking the statistically most significant vector as their estimate for the original static image; instead, Hirsch et al [21] formulate a space-variant deblurring algorithm that is seemingly computationally treatable. However neither [24] nor [21] address the issue of domain deformation and thus are only suitable when the geometric distortion is reasonably small.…”