Inverse Problems in Particle Size Distribution Retrieval
Summary
The retrieval of particle size distributions from measured scattering or attenuation data constitutes a classic inverse problem, whereby one seeks to infer an underlying size spectrum from indirect observations. Mathematically this task is often formulated as a Fredholm integral equation of the first kind, which is inherently ill-posed: small perturbations in measured data can lead to large variations in the recovered distribution. To counteract instability and non-uniqueness, regularisation techniques introduce auxiliary constraints or smoothness penalties, while iterative and optimisation-based algorithms guide the solution towards physically credible results. Advances in numerical methods have seen the adaptation of gradient-based solvers, Landweber iterations, and non-linear optimisers, as well as stochastic and population-based search strategies. Practical applications span environmental monitoring of aerosols and pollutants, quality control in food and pharmaceutical processing, combustion diagnostics and climate modelling, where accurate particle size information underpins assessments of radiative forcing, health impacts and material properties.
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Inverse Problems in Particle Size Distribution Retrieval publication trend
The graph below shows the total number of articles in inverse problems in particle size distribution retrieval across all publications each year (not limited to Nature Index journals).
Technical terms
Inverse problem: A reconstruction task in which model parameters are inferred from indirect or incomplete measurements.
Fredholm integral equation of the first kind: An integral equation where the solution function appears under the integral, commonly ill-posed in inverse problems.
Regularisation: A technique that imposes additional constraints or penalties to stabilise the solution of an ill-posed problem.
Particle size distribution (PSD): A quantitative description of the proportion of particles as a function of their size within a sample.
Genetic algorithm: A population-based, stochastic search method inspired by natural selection, used to optimise complex inverse problems.
Particle swarm optimisation: An evolutionary computation technique that simulates social behaviour to explore solution spaces and find global optima.
References
- A Modified Landweber Algorithm for Inversion of Particle Size Distribution Combined With Tikhonov Regularization Theory. IEEE Access (2018).
- Inversion method of particle size distribution of milk fat based on improved MPGA. Frontiers in Bioengineering and Biotechnology (2022).
- Inversion of Aerosol Particle Size Distribution Using an Improved Stochastic Particle Swarm Optimization Algorithm. Remote Sensing (2022).
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