Performance of an optimal multiplicative jump detector based on the continuous wavelet transform

Additive and multiplicative abrupt changes in random signals have been studied in many applications. In segmentation theory, the detection of these additive abrupt changes allows the determination of stationary parts of signals. In radar images, multiplicative abrupt jumps have been used to model "speckled" signal: these multiplicative jumps correspond to object edges on piecewise constant backgrounds. The Continuous Wavelet Transform (CWT) has shown nice properties for the detection of abrupt additive jumps. The paper studies the problem of abrupt multiplicative jump detection using the CWT. The time-scale plane Neyman-Pearson test is studied and its performance is evaluated.