Monitoring sediment transport processes in rivers is of particular interest to engineers and scientists to assess the stability of rivers and hydraulic structures. Various methods for sediment transport processes description were proposed using conventional or surrogate measurement techniques. This paper addresses the topic of the passive acoustic monitoring of bedload transport in rivers and especially the estimation of the bedload grain size distribution from self-generated noise. It discusses the feasibility of linking the acoustic signal spectrum shape to bedload-grain sizes involved in elastic impacts with 15 the river bed treated as a massive slab. Bedload grain size distribution is estimated by a regularized algebraic inversion scheme fed with the power spectrum density of river noise estimated from one hydrophone. The inversion methodology relies upon a physical model that predicts the acoustic field generated by the collision between rigid bodies. Here we is proposed an analytic model of the acoustic energy spectrum generated by the impacts between a sphere and a slab. The proposed model computes the power spectral density of bedload noise using as a linear system of analytic energy spectra weighted by the grain size 20 distribution. The algebraic system of equations is then solved by least square optimization and solution regularization methods. The result of inversion leads directly to the estimation of the bedload grain size distribution. The inversion method was applied on real acoustic data from passive acoustics experiments realized on the Isère River, in France. The inversion of in situ measured spectra reveals good estimations of grain size distribution, fairly close to what was estimated by physical sampling instruments. These results illustrate the potential of the hydrophone technique to be used as a standalone method that could 25 ensure high spatial and temporal resolution measurements for sediment transport in rivers.