Designing lensless imaging systems to maximize information capture

Mask-based lensless imaging uses an optical encoder (e.g. a phase or amplitude mask) to capture measurements, then a computational decoding algorithm to reconstruct images. In this work, we evaluate and design lensless encoders based on the information content of their measurements using mutual information estimation. Our approach formalizes the object-dependent nature of lensless imaging and quantifies the interdependence between object sparsity, encoder multiplexing, and noise. Our analysis reveals that optimal encoder designs should tailor encoder multiplexing to object sparsity for maximum information capture, and that all optimally-encoded measurements share the same level of sparsity. Using mutual information-based optimization, we design information-optimal encoders for compressive imaging of fixed object distributions. Our designs demonstrate improved downstream reconstruction performance for objects in the distribution, without requiring joint optimization with a specific reconstruction algorithm. We validate our approach experimentally by evaluating lensless imaging systems directly from captured measurements, without the need for image formation models, reconstruction algorithms, or ground truth data. Our comprehensive analysis establishes design and engineering principles for lensless imaging systems, and offers a model for the study of general multiplexing systems, especially those with object-dependent performance.