ℓ ₁-Norm-based reconstruction algorithm for particle sizing

An ℓ ₁-norm-based reconstruction algorithm for particle sizing by using ℓ ₁-regularization is introduced in this paper. Both simulation and experiment were conducted by using a photodiode array detector to evaluate the performance of the algorithm. Particle size distributions retrieved by using Chahine, truncated singular value decomposition (TSVD), and Tikhonov algorithms were also obtained to compare with that obtained by the ℓ ₁-norm-based algorithm. In computer simulation, Rosin-Rammler, normal, and lognormal distributions of spherical particles from 7.6 to 98 \mu{m} in diameter were created. The measurement data of the photodiode array detector were generated based on Fraunhofer diffraction theory. Simulation results show that the ℓ ₁-norm-based algorithm not only performs better than Chahine algorithm but also performs similar to the TSVD and Tikhonov algorithms for noise-free data and is less sensitive to the noise than the TSVD and Tikhonov algorithms for noise-contaminated data. In experiment, a standard particle plate covered by particles with known size distribution, i.e., Rosin-Rammler distribution, was used. The experimental results validated the effectiveness of the ℓ ₁ -norm-based algorithm.