A Linear Systems Approach to Imaging Through Turbulence

Abstract

In this paper we address the problem of recovering an image from a sequence of distorted versions of it, where the distortion is caused by what is commonly referred to as ground-level turbulence. In mathematical terms, such distortion can be described as the cumulative effect of a blurring kernel and a time-dependent deformation of the image domain. We introduce a statistical dynamic model for the generation of turbulence based on linear dynamical systems (LDS). We expand the model to include the unknown image as part of the unobserved state and apply Kalman filtering to estimate such state. This operation yields a blurry image where the blurring kernel is effectively isoplanatic. Applying blind nonlocal Total Variation (NL-TV) deconvolution yields a sharp final result.

Implementation of the Centroid Method for the Correction of Turbulence

“…Analytically, this model can be inverted (i.e., find the image I from the sequence I i ) by different methods. A first method consists in computing the average of all the input images I i , which converges to the image I blurred by the positive kernel κ, and then de-convolve the average image [6,7,9,16]. A second method consists in inverting the deformation of one of the images I i to recover the image I [5,4,21,8,15].…”

STELLA MARIS: Stellar marine refractive imaging sensor

“…Random waves of the WAI greatly exacerbate the distortions. They are much more severe than distortions created by atmospheric turbulence [15,21,41,54], due to the sharp difference of water and air refractive indices. If the WAI shape can be estimated, distortions attributed to the waves can be countered.…”

Model-free prediction of atmospheric warp based on artificial neural network

“…There are a fairly large number of methods in the literature that address the problem of restoring nonuniformly warped images degraded by atmospheric turbulence [4][5][6][7][8][9][10][11]. These methods could further be enhanced if the turbulence-induced warping can be predicted ahead of time.…”

“…The state-space dimension of the pixel-oscillatory model is very large to be intractable [11]. In order to circumvent this issue, each pixel is assumed to oscillate independently of its neighbors, and also independently in the horizontal and vertical directions.…”