Super-Resolution and Reconstruction of Sparse Sub-Wavelength Images

TL;DR

Optical diffraction removes spatial frequencies above 1/λ, making far-field recovery of sub-wavelength features virtually impossible. This paper uses compressed sensing with sparsity to recover low-frequency measurements into sub-wavelength amplitude and phase information, supported theoretically and experimentally.

• Problem

  Optical diffraction eliminates spatial frequencies higher than 1/λ, so sub-wavelength features are virtually impossible to resolve from the far field.

• Method

  Compressed sensing identifies the signal-bearing subspace from low spatial-frequency measurements, with iterative nonlocal thresholding enabling recovery of signals with non-uniform phase.

• Results

  The method theoretically reconstructs sub-wavelength amplitude and phase information and experimentally recovers image content beyond the available spatial-frequency cutoff.

• Takeaways & Limitations

  Far-field sub-wavelength reconstruction is supported when the image is sparse and the measured basis is sufficiently uncorrelated with the sparsity basis.

• Takeaways & Limitations

  The approach requires prior knowledge that the image is sparse.