On gradient methods for maximum entropy regularizing retrieval of atmospheric aerosol particle size distribution function

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, since as is known, we are often faced with limited or insufficient observations in remote sensing and the observations are contaminated. Physically, the particle size distribution is always nonnegative, and we are often faced with incomplete data. Therefore, the concept of maximum entropy from information theory and statistic mechanics can be used to counteract this problem of missing or erroneous data. Therefore, in this paper, we study the maximum entropy based regularization model and gradient methods for solving the corresponding optimization problem. Numerical tests are made for synthetic aerosol data to show the efficiency and feasibility of the proposed algorithms. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)