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

Abstract

The concept of rejecting the null hypothesis for definitively detecting a signal was extended to relaxation spectrum space for multiexponential reconstruction. The novel test was applied to the problem of detecting the myelin signal, which is believed to have a time constant below 40ms, in T2 decays from MRI's of the human brain. It was demonstrated that the test allowed the detection of a signal in a relaxation spectrum using only the information in the data, thus avoiding any potentially unreliable prior information. The test was implemented both explicitly and implicitly for simulated T2 measurements. For the explicit implementation, the null hypothesis was that a relaxation spectrum existed that had no signal below 40ms and that was consistent with the T2 decay. The confidence level by which the null hypothesis could be rejected gave the confidence level that there was signal below the 40ms time constant. The explicit implementation assessed the test's performance with and without prior information where the prior information was the nonnegative relaxation spectrum assumption. The test was also implemented implicitly with a data conserving multiexponential reconstruction algorithm that used left invertible matrices and that has been published previously. The implicit and explicit implementations demonstrated similar characteristics in detecting 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]