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The concept of rejecting the null hypothesis for definitively detecting asignal was extended to relaxation spectrum space for multiexponentialreconstruction. The novel test was applied to the problem of detecting themyelin signal, which is believed to have a time constant below 40ms, in T2decays from MRI's of the human brain. It was demonstrated that the test allowedthe detection of a signal in a relaxation spectrum using only the informationin the data, thus avoiding any potentially unreliable prior information. Thetest was implemented both explicitly and implicitly for simulated T2measurements. For the explicit implementation, the null hypothesis was that arelaxation spectrum existed that had no signal below 40ms and that wasconsistent with the T2 decay. The confidence level by which the null hypothesiscould be rejected gave the confidence level that there was signal below the40ms time constant. The explicit implementation assessed the test's performancewith and without prior information where the prior information was thenonnegative relaxation spectrum assumption. The test was also implementedimplicitly with a data conserving multiexponential reconstruction algorithmthat used left invertible matrices and that has been published previously. Theimplicit and explicit implementations demonstrated similar characteristics indetecting the myelin signal in both the simulated and experimental T2 decays,providing additional evidence to support the close link between the two tests.[Full abstract in paper]

A robust and reliable method for detecting signals of interest in multiexponential decays