Numerous physiological processes are cyclical, but sampling these processes densely enough to perform frequency decomposition and subsequent analyses can be challenging. Mathematical approaches for decomposition and reconstruction of sparsely and irregularly sampled signals are well established but have been under-utilized in physiological applications. We developed a basis pursuit denoising with polynomial detrending (BPWP) model that recovers oscillations and trends from sparse and irregularly sampled timeseries. We validated this model on a unique dataset of long-term inter-ictal epileptiform discharge (IED) rates from human hippocampus recorded with a novel investigational device with continuous local field potential sensing. IED rates have well established circadian and multiday cycles related to sleep, wakefulness, and seizure clusters. Given sparse and irregular samples of IED rates from multi-month intracranial EEG recordings from ambulatory humans, we used BPWP to compute narrowband spectral power and polynomial trend coefficients and identify IED rate cycles in three subjects. In select cases, we propose that random and irregular sampling may be leveraged for frequency decomposition of physiological signals. Trial Registration: NCT03946618.

Bioelectronics Neurophysiology and Engineering Laboratory Department of Neurology Mayo Clinic Rochester Minnesota United States of America

Biomedical Engineering and Physiology Graduate Program Mayo Clinic Graduate School of Biomedical Sciences Rochester Minnesota United States of America

Czech Institute of Informatics Robotics and Cybernetics Czech Technical University Prague Prague Czechia

Department of Neurosurgery Mayo Clinic Rochester Minnesota United States of America

Department of Psychiatry and Psychology Mayo Clinic Rochester Minnesota United States of America

Department of Radiology Mayo Clinic Rochester Minnesota United States of America

Faculty of Biomedical Engineering Czech Technical University Prague Czechia

Faculty of Electrical Engineering and Communication Department of Biomedical Engineering Brno University of Technology Brno Czechia

International Clinic Research Center St Anne's University Research Hospital Brno Czech Republic

Mayo Clinic Alix School of Medicine Rochester Minnesota United States of America

Mayo Clinic Medical Scientist Training Program Rochester Minnesota United States of America

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NCT03946618