Efficient Field Reconstruction Using Compressive Sensing

Compressive sensing is used to reconstruct the time-harmonic electric field created by multipath fading from a limited number of measurement points over a planar region. The multipath fading signal is shown to be the superposition of multiple plane wave components and thus has a sparse representation in the spatial-frequency domain. The discrete Fourier basis used as the dictionary for orthogonal matching pursuit is oversampled to ensure sufficient resolution in the spatial-frequency domain. Experimental results at 10 GHz using an arbitrary plane wave expansion show that the signal-to-error ratio of the compressive sensing reconstruction is approximately 16 dB when randomly selecting only 7.5% of the total points.