We present a method for reconstructing curved particle trajectories from particle streak velocimetry. The reflection properties of a particle are modeled as a point light source. The mapping of the particle on the image is spread by the point spread function of the camera lens. Therefore we can model the mapped particle trajectory as a convolution of the resting particle with its trajectory. Here we model the particle trajectory as a two-dimensional, symmetric Gaussian function convolved with a Bézier curve as an approximation of the trajectory with the pixel aperture of the camera. We assume that the velocity of the particle is constant over the measurement period. We will show that the particle trajectory can be reconstructed up to sub-pixel accuracy. This is verified with synthetic particle trajectories and qualitative comparisons with real world measurements.