Compressive imaging and deep learning based image reconstruction methods in the 'SURPRISE' EU project

The Horizon 2020-funded SURPRISE project targets the development and demonstration of a geostationary compressive optical imaging instrument in the visible, NIR and MIR spectral bands. The instrument leverages the compressed sensing paradigm in several ways: first, the aim is to perform native data compression and encryption, thereby avoiding the need of dedicated hardware; second, the instrument targets super-resolution reconstruction, achieving a number of spatially resolved pixels that is larger than the number of detectors; third, the instrument is intended to have the capability to perform onboard analysis of the acquired scenes in order to detect events of interest. This paper presents an overview of the SURPRISE instrument concept and the related demonstrator, and an in-depth analysis of the related reconstruction algorithms. Specifically, we focus on the super-resolution imaging approach, and leave the discussion of encryption and onboard analysis for subsequent papers. Indeed, while compressed sensing has traditionally employed sparsity-based methods to recover the images from a set of random projections, the performance of these methods has often been unsatisfactory. A new generation of deep learning methods has shown that it is possible to learn strong priors from training data, obtaining reconstruction accuracy far better than that exhibited by the conventional methods. This paper reports on the performance and the features of a deep learning method selected for image reconstruction. The method is based on the ISTA-NET+ neural network, which has suitably generalized in order to match the optical design of the SURPRISE instrument and the related functional requirements. ISTA-NET+ mimics a few unrolled iterations of an iterative shrinkage method. Opposite to traditional methods, which employ a given fixed prior for reconstruction, e.g. sparsity or total variation, the deep learning approach learns the domain that is more suitable for image reconstruction from a training set. We show results of image sensing and reconstruction in a variety of conditions, and discuss the impact of micro-mirror type, model noise, amount of super-resolution. Current results on Earth observation images indicate that deep learning methods largely outperform existing methods. We also discuss the ability of the deep learning model to reconstruct images whose type is different from those employed during the training stage. Moreover, while traditional methods are typically iterative and therefore computationally intensive, deep learning methods are much simpler and can be trained to be robust to noise. In the final paper we will also include results on simulated images having the same optical characteristics as those acquired via the demonstrator, which is currently in its advanced design stage.