Computational Spectral Imaging: Theory Algorithms and Fundamental Performance Limits

Spectral imaging, the simultaneous imaging and spectroscopy of a radiating scene, is a fundamental diagnostic technique in the physical sciences with widespread application. The limits of the attainable temporal, spatial, and spectral resolutions of conventional spectral imaging techniques are imposed by their reliance on purely physical measurement systems such as two-dimensional detectors which are intrinsically limited in capturing inherently three-dimensional data. On the other hand, recent developments in computational spectral imaging techniques offer the prospect of transcending these physical limitations by combining information from different multiplexed measurements and/or by incorporating additional prior (statistical) knowledge (in the form of spatial and spectral distributions) about the objects of interest into the image formation process.

The overarching goal of the proposed research is to develop a class of novel spectral imaging techniques to overcome the temporal, spectral, and spatial resolution limitations of conventional spectral imaging systems. Each development is based on the computational imaging paradigm, which involves distributing the spectral imaging task between a physical and a computational system and then digitally forming images of interest from multiplexed measurements by means of solving an inverse problem. The development of each computational imaging technique requires the following three steps. First, a novel optical system is designed with the goal of overcoming the resolution limitations of conventional systems. Second, the associated inverse problem for image reconstruction is formulated by combining multiplexed measurements with an image formation model based on an estimation-theoretic framework. Third, computationally efficient algorithms are designed to solve the resulting nonlinear optimization problems.

Since an inversion is required for the reconstruction of the spectral imaging information from incomplete and imperfect measurements, a rigorous theory is essential for quantitative evaluation of the performance of the techniques. Therefore, in addition to the development of each technique, Professor Kamalabadi aims to attain fundamental performance bounds in order to characterize the estimation uncertainties and quantify performance limits, as well as to attain insights that would guide optimal system design. Finally, he plans to investigate and illustrate the effectiveness of the proposed computational spectral imaging techniques in applications involving remote sensing of space plasmas in general, and the solar atmosphere in particular. With the emerging trend toward distributed sensing from diverse platforms, it is anticipated that such novel approaches to spectral imaging will have a profound and timely impact on many sensing applications.