Mobile, fast virus detection and classification is of increasing importance in times of epidemic diseases being spread by global traveling and transport. A possible solution is the PAMONO sensor, an optical biological sensor that is able to detect (nanometer-sized) viruses and virus-like particles, utilizing surface plasmon resonance. Captured sensor data is given as image sequences, which can be analyzed by methods from the field of image processing, which is the focus this work. We classify single particles based on their size, using state of the art machine learning techniques, namely convolutional neural networks. This classification allows the measurement of individual particle sizes and the compilation of particle size distributions for a given suspension, which contributes to the goal of classifying different virus types. The classification procedure and estimation of distributions is evaluated using real PAMONO sensor image sequences and particles that simulate viruses. The results show that informative features of the SPR signals can be automatically learned, extracted and used for classification, successfully.