Faint and clustered components in exponential analysis

An important hurdle in multi-exponential analysis is the correct detection of the number of components in a multi-exponential signal and their subsequent identification. This is especially difficult if one or more of these terms are faint and/or covered by noise. We present an approach to tackle this problem and illustrate its usefulness in motor current signature analysis (MCSA), relaxometry (in FLIM and MRI) and magnetic resonance spectroscopy (MRS). The approach is based on viewing the exponential analysis as a Padé approximation problem and makes use of some well-known theorems from Padé approximation theory. We show how to achieve a clear separation of signal and noise by computing sufficiently high order Padé approximants, thus modeling both the signal and the noise, rather than filtering out the noise at an earlier stage and return a low order approximant. We illustrate the usefulness of the approach in different practical situations, where some exponential components are difficult to detect and retrieve because they are either faint compared to the other signal elements or contained in a cluster of similar exponential components.