Retrieval of the aerosol particle size distribution function by incorporating a priori information

The determination of the aerosol particle size distribution function using the particle spectrum extinction equation is an ill-posed integral equation of the first kind. To overcome the ill-posedness, regularization techniques such as Phillips-Twomey's regularization, Tikhonov's smooth regularization as well as some iterative methods were developed. However, most of the literature focuses on improving the solvability of the problem without introducing some useful a priori information, which are essential to ill-posed inverse problems, since it is known that, we are often faced with limited/insufficient observations in remote sensing. Therefore, we restudy this problem. We first formulate the problem in 11 space and solve a nonnegative constrained problem to obtain a useful a priori solution, then we use this solution to reformulate the problem in 12 space and solve a regularized problem. Numerical results are based on the remotely sensed data by Sun-photometer CE 318 for Poyang lake region of Jiangxi Province and are performed to show the efficiency and feasibility of the proposed algorithms. (c) 2007 Elsevier Ltd. All rights reserved.