The paper is devoted to a computational super-resolution microscopy. A complex-valued wavefront of a transparent biological cellular specimen is restored from multiple intensity diffraction patterns registered with noise. For this problem, the recently developed lensless super-resolution phase retrieval algorithm [Optica, 4(7), 786 (2017)] is modified and tuned. This algorithm is based on a random phase coding of the wavefront and on a sparse complex-domain approximation of the specimen. It is demonstrated in experiments, that the reliable phase and amplitude imaging of the specimen is achieved for the low signal-to-noise ratio provided a low dynamic range of observations. The filterings in the observation domain and specimen variables are specific features of the applied algorithm. If these filterings are omitted the algorithm becomes a super-resolution version of the standard iterative phase retrieval algorithms. In comparison with this simplified algorithm with no filterings, our algorithm shows a valuable improvement in imaging with much smaller number of observations and shorter exposure time. In this way, presented algorithm demonstrates ability to work in a low radiation photon-limited mode.