The retrieval of an unknown desired function from a set of physical measurements taken from an instrument constitutes an important inverse problem in indirect sensing measurement theory. In general, given a set of discrete fractional measurements and a set of instrument kernel functions, the mathematical formulation reduces to solving a system of discrete Fredholm integral equations of the first kind which is generating an ill-posed problem. In order to deal with the ill-posedness of the inverse problem, a modified first-order regularization procedure, subject to certain physical constraints and bounds on the variables, which does not use any a priori information regarding the parameterised form of the solution, is employed and compared with other available methods. As a practical application the numerical method is illustrated for the determination of the particle size distribution from diffusion battery data. For exact data, it is shown how the degree of non-uniqueness of the inverse problem analysed may be reduced by decreasing the flow rate at which the diffusion battery operates or better by recording additional deposition data corresponding to several flow rates. For noisy data, a detailed numerical investigation with respect to the bounds on which the unknown variables are to be constrained is analysed.