Progressive compressive sensing of large images with multiscale deep learning reconstruction

Compressive sensing (CS) is a sub-Nyquist sampling framework that has been employed to improve the performance of numerous imaging applications during the last 15 years. Yet, its application for large and high-resolution imaging remains challenging in terms of the computation and acquisition effort involved. Often, low-resolution imaging is sufficient for most of the considered tasks and only a fraction of cases demand high resolution, but the problem is that the user does not know in advance when high-resolution acquisition is required. To address this, we propose a multiscale progressive CS method for the high-resolution imaging. The progressive sampling refines the resolution of the image, while incorporating the already sampled low-resolution information, making the process highly efficient. Moreover, the multiscale property of the progressively sensed samples is capitalized for a fast, deep learning (DL) reconstruction, otherwise infeasible due to practical limitations of training on high-resolution images. The progressive CS and the multiscale reconstruction method are analyzed numerically and demonstrated experimentally with a single pixel camera imaging system. We demonstrate 4-megapixel size progressive compressive imaging with about half the overall number of samples, more than an order of magnitude faster reconstruction, and improved reconstruction quality compared to alternative conventional CS approaches.