Systems and methods for simultaneous single particle tracking, phase retrieval and PSF reconstruction

A system, comprising:

• a processor in communication with a memory, the memory including instructions executable by the processor to:
• access observation data including brightness data indicative of one or more light-emitting particles captured across a plurality of frames and across a plurality of planes by an imaging device, the plurality of frames having an aberration profile observable across each frame of the plurality of frames;
• sample a set of joint probability values associated with observing the observation data for values of each respective parameter of a plurality of parameters of a measurement model, the plurality of parameters including:
• a particle trajectory for each respective light-emitting particle of the one or more light-emitting particles across the plurality of frames;
• and
• a set of point spread function parameters of a point spread function of the imaging device;
• and
• jointly infer, based on the set of joint probability values and the observation data, a set of most probable values of the plurality of parameters;
• and
• sample probabilities associated with a background photon count per pixel for each frame of the plurality of frames using a Metropolis-Hasting procedure at each iteration of a Markov Chain Monte Carlo procedure.