Multiframe blind image deconvolution with space and time variant PSFs

Abstract

The study of images in scientific fields such as remote sensing, medical imaging, and astronomy is important not only because pictures mimic one of the main human sensory modalities, but also because, in the case of signals outside the visible wavelengths, they allow for the visualization of artefacts beyond the sensitive range of the human eye. However, accurate information can only be extracted if the data is free from noise, and perhaps more importantly – blur. An improper focal-length setting, insufficient light, or camera motion, can introduce additional filtering during the image capture process. Medical image that require long exposure time can, for instance, lose sharpness due to patient movement. In radio astronomy, interferometers with unprecedented sensitivity, large fields of view, and narrow angular resolutions, are being built. However, the finite set of baselines still makes the accurate rendering of sharp radio images difficult. Similarly, the larger the aperture of an optical telescope, the stronger the aberrations introduced by the lens. Apart from hardware limitations, biases also arise from phenomena beyond human control such as, for instance, turbulence in the atmospheric and the ionospheric columns that change on millisecond scales. Induced distortions in the images are defined by the Point Spread Function (PSF) that models how rays from a point source trace in the instrument. The deconvolution process attempts to undo these adverse effects and recover the actual intensity values from the measured signal. The blur filter varies in time depending on the astronomical ‘seeing’ conditions as well as on the wavelengths being recorded. While in certain cases expensive hardware such as adaptive optics can help to elevate the problem, a software-based approach is more common due to its wide-ranging adaptability and applicability. This study proposes techniques that render a sharp version of a scene using multiple blurred frames captured over the same area. Each image is assumed to have a different, but unknown PSF. Kolmogorov and Moffat kernel that model the atmospheric and ionospheric effects as well as the filtering due to the lens or interferometry, are used. Many current methods adopt a non-blind approach (in the sense that the PSF is known) or estimate the blur filter form edge regions. This restricts their applicability to specific types of images. For instance, cosmological frames that encode faint point sources or extended object with a complex morphology, cannot be processed. Moreover, the majority of existing multiframe algorithms work in batch mode and assume the availability of all frames in the pre-processing stage. The objective of this study is to propose methods for Multiframe and Blind Image Deconvolution (MBID) – with or without noise. The penultimate goal is to reverse the effects of convolution without knowledge of the PSF. Complementary information from multiple images is combined to estimate a single sharp version of the scene. The deconvolution problem is reduced to a series of iterations in which the blur kernel is initially estimated and subsequently used to deconvolve the input frame. The result is in turn used to update the latent image. Reversing the spreading introduced by the convolution operator is an ill-posed problem. Finding a solution for x from the measurement set y in the undermined linear system y = Ax + ɛ is challenging. Infinitely many correct answers remain possible even if the PSF (A), and noise level (ɛ) are known. The frameworks we present make use of novel theories developed in the field of Compressed Sensing. Sparse magnitude coefficients are obtained by converging towards the vector with the least quadratic error that minimizes the l2 norm, or by searching for the sparses solution through the minimization of the l1 norm. Various methods including genetic programming and subtractive minimization in different domain representations, are considered for the recovery of the non-sparse but constrained phase information. An evolutionary based strategy that allows the performance to be tested at various stages of the deblurring process is designed and followed. Quantification of the recovery accuracy is made possible through the computation of various error metrics. A comparison with the images recovered by the current state-of-the art methods when the same set of blurred frames are processed, is also put forward. This analysis also takes into account the robustness to various noise levels. Encouraging results that are comparable and, at times, even better than those achieved by the existing approaches, are obtained.