Objective. Proton radiograph has been broadly applied in proton radiotherapy which is affected by scattered protons which result in the lower spatial resolution of proton radiographs than that of x-ray images. Traditional image denoising method may lead to the change of water equivalent path length (WEPL) resulting in the lower WEPL measurement accuracy. In this study, we proposed a new denoising method of proton radiographs based on energy resolved dose function curves. Approach. Firstly, the corresponding relationship between the distortion of WEPL characteristic curve, and energy and proportion of scattered protons was established. Then, to improve the accuracy of proton radiographs, deep learning technique was used to remove scattered protons and correct deviated WEPL values. Experiments on a calibration phantom to prove the effectiveness and feasibility of this method were performed. In addition, an anthropomorphic head phantom was selected to demonstrate the clinical relevance of this technology and the denoising effect was analyzed. Main results. The curves of WEPL profiles of proton radiographs became smoother and deviated WEPL values were corrected. For the calibration phantom proton radiograph, the average absolute error of WEPL values decreased from 2.23 to 1.72, the mean percentage difference of all materials of relative stopping power decreased from 1.24 to 0.39, and the average relative WEPL corrected due to the denoising process was 1.06%. In addition, WEPL values correcting were also observed on the proton radiograph for anthropomorphic head phantom due to this denoising process. Significance. The experiments showed that this new method was effective for proton radiograph denoising and had greater advantages than end-to-end image denoising methods, laying the foundation for the implementation of precise proton radiotherapy.