Sparsity-based reconstruction of subwavelength images from their optical far-field

A study was conducted to demonstrate sparsity-based reconstruction of subwavelength images from their optical far-field. Subwavelength imaging was represented as a bandwidth extrapolation problem where propagation was equivalent to passing through a low-pass filter, with the diffraction limit as the cutoff frequency. The question was how to identify the correct extrapolation, out of the infinite possible extrapolations. The solutions in the presence of noise revealed that they were close to the original information when the noise was not exceedingly large.