Disclosed is a compressed sensing-based FPM algorithm. The algorithm comprises the steps of 1) utilizing an FPM platform to collect a low-resolution image ri (x, y) under different illuminations; 2) based on images obtained under illumination of different angles, actually, obtained by translating images under normal illumination in a frequency domain, establishing a constraint for the collected image ri (x, y), and based on the constraint, solving the optimization problem of an optimal problem according to a compressed sensing structure; 3) solving the optimization problem through iteration to obtain a sparse coefficient a, and multiplying the a with an over-complete dictionary to obtain a final result. According to the compressed sensing-based FPM algorithm, by taking advantage of the compressed sensing technology, mathematical abstraction is performed on an original FPM algorithm, a frequency domain iteration method is abstracted into an optimal solution solving method, the image super-resolution reconstruction problem is solved from a new angle, and the algorithm reconstruction effects can be enhanced.