Atomic decomposition has been a popular tool for extracting information about localised signal structures. This is a direct consequence of incorporating redundant time-frequency and time-scale dictionaries for signal decomposition. In this paper, we propose a measure of signal complexity related to a given decomposition dictionary and based on the number of atoms needed to represent the signal. This measure is directly extracted from the atomic decomposition and one of the potential applications is the detection of changes in signal structure. For example, automatic newborn EEG seizure detection can be achieved by detecting the change in signal structure as the EEG changes from the background state to the seizure state. This complexity measure is evaluated using two atomic decomposition methods; namely Basis Pursuit (BP) and Matching Pursuit (MP).