Quantum limits of super-resolution of optical sparse objects via sparsity constraint

Area of Science:

• Quantum optics
• Signal processing
• Super-resolution imaging

Background:

• Sparsity constraint is a priori knowledge used in signal processing.
• Sparsity enables super-resolution imaging beyond the diffraction limit.
• Conventional methods often use Fourier basis for sensing sparse signals.

Purpose of the Study:

• Establish quantum limits of super-resolution for sparse objects.
• Introduce discrete prolate spheroidal sequences (DPSS) as a superior sensing basis.
• Investigate the impact of quantum fluctuations on reconstruction algorithms.

Main Methods:

• Development of a quantum theory for super-resolution.
• Utilizing discrete prolate spheroidal sequences (DPSS) as the sensing basis.
• Analytical and numerical demonstrations of super-resolution performance.

Main Results:

• DPSS basis demonstrates superior super-resolution performance compared to Fourier basis.
• DPSS are eigenfunctions of optical imaging systems, unlike Fourier basis.
• Criteria for stable reconstruction of sparse objects with super-resolution are formulated.

Conclusions:

• Sparsity alone does not solely determine achievable super-resolution.
• The choice of sensing basis (DPSS vs. Fourier) significantly impacts super-resolution.
• Quantum fluctuations play a crucial role in the stability and performance of reconstruction algorithms.