基于带约束TSVD方法的粒径分布反演

利用光全散射法，在独立模式下通过测量可见光不同波段下的光谱消光值反演几种常见粒径分布，其中正问题利用反常衍射近似（ADA）计算得到估计值，测量值通过Mie理论计算得到，反问题利用截断奇异值分解（TSVD）的正则化方法，并结合粒径分布非负和粒径分布积分和为1两个约束条件优化反演结果，通过数值模拟证明了带约束的TSVD方法在粒径分布的反演中具有更高的反演精度、稳定性和抗噪性。

Retrieval of particle size distribution based on TSVD method with constraints

Particle size distribution is one of the most important parameters and technical indicators. It not only directly affects the performance and quality of the products, but also helps to reduce energy consumption, improve the environment and safeguard human health. In this paper, several common particle size distributions were retrieved by measuring the extinction values of different visible spectrums using total light scattering methods under independent model. Wherein the estimation values were calculated by the Anomalous Diffraction Approximation (ADA), and the measurement values were obtained by applying Mie theory. A novel inversion algorithm was proposed by using Truncated Singular Value Decomposition (TSVD) regularization combined with two constraints, the particle size distribution is non-negative and the integral of the particle size distribution is equal to 1. To demonstrate the advantage performance of the proposed algorithm, several numerical test cases were investigated. The retrieval results show that the improved TSVD algorithm has higher retrieval accuracy than the traditional TSVD algorithm in the absence of measurement errors, and the improved TSVD algorithm has better anti-noise performance than the traditional TSVD algorithm under different measurement errors. Thus this improved TSVD algorithm can be used as an effective method for retrieval of particle size distribution.