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

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 40 ms, in T2 decays from magnetic resonance imagining of the human brain. It was demonstrated that the test allowed the detection of a signal in a relaxation spectrum by 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 40 ms 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 40 ms time constant. The explicit implementation assessed the test's performance with and without prior information where the prior information was the non-negative 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. When the relaxation spectrum was assumed to be non-negative, the novel test required signal to noise ratios (SNRs) approaching 1000 in the T2 decays for detection of the myelin signal with high confidence. When the relaxation spectrum was not assumed to be non-negative, the SNR requirements for a detection with high confidence increased by a factor of 25. The application of the test to a T2 decay from human white matter, measured in vivo with a SNR of 650, demonstrated a solid detection of the signal below 40 ms believed to be due to the myelin water. This study demonstrated the robustness and reliability of extending the concept of rejecting the null hypothesis to relaxation spectrum space. The study also raised serious questions about the susceptibility to false positive detection of the myelin signal of the multiexponential reconstruction algorithms currently in use.