A discrete linear method for transitions detection in noisy signals
Résumé
In this paper, we present a discrete linear method for the detection of transitions in noisy signals. By using an adequate discrete model, we formalize the objective of detection such that the obtained response is symmetrical and presents a local maximum at the transition position. This leads for noiseless transitions to a general solution having the form of an antisymmetric impulse response, similar to that of the existing linear edge detectors like the gradient-based and Canny-Deriche operators. For noisy signals, we propose an optimization method allowing to minimize the noise effect on the transition detection, based on the separability of the components due respectively to the transition and to the noise in the total response. The performance of the proposed method is successfully illustrated on some simulation examples.