Compressed sensing reconstruction of sparse geophysical data: an example from regional magnetics

Reconstruction of discretely sampled geophysical data is generally done via gridding or interpolant algorithms. Such approaches typically consider local gradients which, while emphasising small-scale structure, can also introduce gridding artefacts, and modify the frequency characteristics of the original data. Here, we examine the potential of compressed sensing techniques for spatially-varying geophysical data, particularly line and gridded aeromagnetic data. We show that for sub-Nyquist sampling rates, the approach is still able to reconstruct a legible signal, and demonstrate the frequency representation of the reconstructed data varies with data sampling frequency, showing a reduced frequency range for sparser sampling. In contrast, we demonstrate that many widespread gridding approaches artificially introduce high-frequency signals into the gridded maps that are not present in the original nor in the compressed sensing reconstructions. This demonstrates the limitations of conventional gridding approaches in spectral fidelity and also suggests the conditions under which compressed sensing may be a more appropriate interpolant technique – namely when authentic spectral representation of the data is of higher precedent than small-scale target identification.