ℓ1 Norm based reconstruction algorithm for particle sizing

Reconstruction algorithm for particle sizing by using the ℓ₁-regularization was introduced in this paper. Compared with the Chahine algorithm, the results obtained by the ℓ₁ norm based algorithm were less sensitive to the additive noise. In the experiments, the data was acquired by a photodetector array that is composed of 31 separate circular rings. In order to validate the algorithm proposed in this paper, to kinds of size distribution was presented, i.e., single-peak and double-peak distributions. 0 to 1% additive noise was added into the data to test the sensitivity of the algorithms to the noise. Comparisons of the particle size distributions reconstructed by the proposed algorithm with those by the Chahine algorithm show that the ℓ₁ norm based algorithm performs better than the Chahine algorithm when the noise level is between 0 to 1%.