Optical designing and case study of image restoration for space-based ultra-lightweight electro-optical telescopic systems with an optically-sparse non-uniform-sized segmented primary aperture mirror

This work is an extensive study of the efficiency of the image regularization (Alternating Directions Method of Multipliers <i>i.e.</i>, ADMM) procedure implemented in tandem with one of the popular denoising techniques (Total Variation or Block Matching and 3D Filtering or Convolutional Neural Networks) for reconstruction of remotely captured images in the electro-optical domain using telescopes with optically-sparse aperture (OSA) mirrors. A suite of thirty-four images taken by the Sentinel-2 telescope with a ground resolved distance (GRD) of 1m and circumscribing a multitude of features and scenes is considered as the ground truth images. These range from houses and roads in urban settlements to pastoral lands with houses and rivers in the same Field-of-View (FoV) to landscapes of rivers and their adjoining areas - thereby offering an ideal testbed to infer on the edge detection as well as texture, contrast and smoothness retention capabilities of the post-processing routines when observed by OSA mirrors. Such mirrors are already known to have constraints on their performance, albeit the compromised collecting area and Modulation Transfer Function (MTF). This situation is, further, complicated by incorporation of noise of various origins, for <i>e.g.</i>, gaussian, impulse and shot noise. In this work, the authors present a comparative analysis on the imaging performance of a Standard OSA primary mirror with sub-apertures having equal sizes relative to two Non-Uniform Sized (NUS)-OSA mirror configurations - the Taylor-ln and One-by-Three configurations. The latter designs promise a significant improvement in the overall mass budget of the imaging system, capable of good imaging performance, attributed to their significant sidelobe suppression. However, the quality of the reconstructed images, including identification of small features, edge detection and preserving the contrast and texture depend significantly on the choice of the regularization parameters (<i>&lambda;</i> and <i>&rho;</i>), based on the features of the ground truth images and the type of mirror under consideration. Hence, to design an efficient imaging system where a series of observed images, corrupted with noise, is fed spontaneously to the post-processing pipeline via the downlink channel, the pipeline should be automated with an optimized pair of values for <i>&lambda;</i> and <i>&rho;</i> which could result in high quality reconstructed images, irrespective of the features in the input images. This is to enable near-real time observations for remote-sensing purposes and security and surveillance purposes, by avoiding any human intervention for determining these values on a case-to-case basis. It is concluded that assigning very low values to the penalty parameter <i>&rho;</i> is of consequence for good quality reconstructed images, irrespective of the features in the input images. Furthermore, the One-by-Three mirror has a better imaging quality, nearly similar to that of the more conventional Standard mirror. It is also concluded that CNN is the least preferred denoiser when trying to process a series of images captured by the imaging system with the least human intervention for adjusting the regularization parameters. Therefore, with proper post-processing pipeline in place for such ultra-lightweight imaging systems, NUS-OSA mirrors could find an efficient application where very large monolithic mirrors (diameter <i>sim</i> few tens of m) would have been required, for example, in space-based remote-sensing and security and surveillance or even astronomical systems in the Longwave Infrared-Thermal Infrared (LWIR-TIR) range to achieve GRDs of a few tens of cm.