© 2018 IEEE. Many infants born prematurely develop brain injury within the first few days after birth. Near infrared spectroscopy (NIRS) is a safe technology that can continuously monitor the varying levels of oxygenation in the brain. Analysis of this signal has the potential to detect the onset of brain injury. We develop a method that extracts transient waveforms from the oxygenation signal. This method uses the cosine transform and singular-spectrum analysis to decompose the signal. We test different procedures to select a threshold for estimating the transient component. As part of the development of the method, we build a model of the cerebral oxygenation signals combining clusters of transient waveforms and nonstationary coloured noise. After development, we test on cerebral oxygenation recordings from 10 extremely preterm infants. We find that using the decomposition method to remove the transient components improves detection performance of brain injury, from an area-under the receiver operator characteristic of 0.91 to 1.00. These findings highlight the importance of specific signal processing methods for the cerebral oxygenation signal and the potential for NIRS as a neuromonitoring technology in neonatal intensive care.