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 encoders based on the information content of their measurements using mutual information estimation. With this approach, we formalize the object-dependent nature of lensless imaging and study 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 with improved downstream reconstruction performance. We validate the benefits of reduced multiplexing for dense, natural images by evaluating experimental lensless imaging systems directly from captured measurements, without the need for image formation models, reconstruction algorithms, or ground truth images. Our comprehensive analysis establishes design and engineering principles for improving lensless imaging systems, and offers a model for the study of general multiplexing systems, especially those with object-dependent performance.

Universal evaluation and design of imaging systems using information estimation

Information theory, which describes the transmission of signals in the presence of noise, has enabled the development of reliable communication systems that underlie the modern world. Imaging systems can also be viewed as a form of communication, in which information about the object is "transmitted" through images. However, the application of information theory to imaging systems has been limited by the challenges of accounting for their physical constraints. Here, we introduce a framework that addresses these limitations by modeling the probabilistic relationship between objects and their measurements. Using this framework, we develop a method to estimate information using only a dataset of noisy measurements, without making any assumptions about the image formation process. We demonstrate that these estimates comprehensively quantify measurement quality across a diverse range of imaging systems and applications. Furthermore, we introduce Information-Driven Encoder Analysis Learning (IDEAL), a technique to optimize the design of imaging hardware for maximum information capture. This work provides new insights into the fundamental performance limits of imaging systems and offers powerful new tools for their analysis and design.