Many oceanographic applications necessitate data acquisition over a large support (spatial, temporal or frequency) where the information of interest is sparsely distributed. Sparsity refers to scenarios where the significant components of the data are few and occur over a much wider realm of possible values; for example, stars in a night sky represent a sparse distribution of light across the three-dimensional spatial support of the sky visible to the naked eye. Sparse distributions abound in oceanography—for example, the delay-Doppler spread in shallow-water acoustics, organisms of interest in the deep sea-and sparse spikes of interest in marine seismic signals, among many others.
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