  Computational imaging~(CI) has been attracting a lot of interest in recent
years for its superiority over traditional imaging in various applications. In
CI systems, information is generally acquired in an encoded form and
subsequently decoded via processing algorithms, which is quite in line with the
information transmission mode of modern communication, and leads to emerging
studies from the viewpoint of information optical imaging. Currently, one of
the most important issues to be theoretically studied for CI is to
quantitatively evaluate the fundamental ability of information acquisition,
which is essential for both objective performance assessment and efficient
design of imaging system. In this paper, by incorporating the Bayesian
filtering paradigm, we propose a framework for CI that enables quantitative
evaluation and design of the imaging system, and demonstate it based on ghost
imaging. In specific, this framework can provide a quantitative evaluation on
the acquired information through Fisher information and Cram\'er-Rao Lower
Bound (CRLB), and the intrinsic performance of the imaging system can be
accessed in real-time. With simulation and experiments, the framework is
validated and compared with existing linear unbiased algorithms. In particular,
the image retrieval can reach the CRLB. Furthermore, information-driven
adaptive design for optimizing the information acquisition procedure is also
achieved. By quantitative describing and efficient designing, the proposed
framework is expected to promote the practical applications of CI techniques.
