Super-resolution with Binary Priors: Theory and Algorithms.

Area of Science:

• Signal Processing
• Computational Neuroscience
• Communications Engineering

Background:

• Super-resolution reconstructs localized events from filtered samples.
• Existing methods often rely on sparsity assumptions.
• Neural spike deconvolution and symbol detection are key applications.

Purpose of the Study:

• To explore the utility of binary priors in super-resolution.
• To develop algorithms for binary super-resolution with minimal measurements.
• To demonstrate advantages over sparsity-based approaches.

Main Methods:

• Utilized binary-valued priors for spike amplitudes.
• Developed algorithms enforcing exact binary constraints without relaxation.
• Formulated recovery as a one-dimensional binary search for autoregressive filters.

Main Results:

• Binary constraints provide stronger identifiability guarantees than sparsity.
• Achieved successful operation in extreme compression regimes (fewer measurements than sparsity).
• Validated theory and demonstrated benefits on real calcium imaging data.

Conclusions:

• Binary priors offer a powerful alternative for super-resolution, especially under severe data constraints.
• The proposed binary search approach effectively handles computational challenges.
• This method shows significant promise for neural signal processing and communication systems.