Method and apparatus for signal restoration without knowledge of the

Abstract

A noisy signal obtained from an acquisition system, such as a conventional or confocal microscope, is reconstructed in a manner which simultaneously estimates the true or ideal signal as well as the response function of the acquisition system. The restored signal can be a function of one or more variables, e.g., time or space. Prior knowledge of the response function of the acquisition system is not required, there is no the need to calibrate the acquisition system before acquiring a signal. The true signal and the response function of the acquisition system are estimated in iterative manner. The actual signal data and the frequency content of the actual signal data may be used to determine constraints to be applied to the estimates of the true signal and the impulse response of the acquisition system. These constraints include constraints on the signal (in the spatial domain) and constraints in the frequency domain. In each iteration, an updated estimate of the ideal signal is used to update an estimate in the frequency domain of the response function, and then the updated response function is used to provide an updated estimate of the signal in the frequency domain. The spatial and frequency domain constraints are applied at each iteration. Iterations continue until a selected criterion is reached, such as a selected number of iterations.