An efficient gradient method for maximum entropy regularizing retrieval of atmospheric aerosol particle size distribution function

The aerosol particle size distribution function can be retrieved by solving the moment problem. This is an ill-posed problem, since it is known that, we are often faced with limited/insufficient observations in remote sensing and the observations are contaminated. To overcome the ill-posed nature, regularization techniques such as Phillips–Twomey's regularization, Tikhonov's smooth regularization as well as some iterative methods were developed. Since the particle size distribution function is always nonnegative, and we are often faced with incomplete data, the concept of maximum entropy from information theory and statistic mechanics can be used for this purpose. Therefore, in this paper, we study the maximum entropy-based regularization method and develop a nonmonotone gradient method for solving the corresponding optimization problem. Our numerical tests for both synthetic problem and practical problem are given to show the efficiency and feasibility of the proposed algorithm.