Optimal multiplexed sensing: bounds, conditions and a graph theory link.

Area of Science:

• Measurement science
• Signal processing
• Applied mathematics

Background:

• Multiplexing variables enhances signal-to-noise ratio and dynamic range in systems like imagers and spectrometers.
• Existing multiplexing codes face limitations due to sensor saturation and scene-dependent photon noise.

Purpose of the Study:

• To find optimal multiplexing codes that maximize signal-to-noise ratio while mitigating sensor saturation and noise.
• To derive lower bounds on the mean square error for demultiplexed variables.

Main Methods:

• Derivation of lower bounds on the mean square error for demultiplexed variables.
• Application of graph theory, specifically strongly regular graphs, to identify optimal multiplexing codes.

Main Results:

• Established lower bounds for assessing the optimality of multiplexing codes.
• Identified strongly regular graphs as a method for discovering ideal multiplexing codes.
• Provided necessary conditions for codes to attain derived lower bounds.

Conclusions:

• Optimal multiplexing codes can be found using graph theory, specifically strongly regular graphs.
• The derived lower bounds facilitate the search for superior multiplexing strategies.
• This approach addresses limitations of existing methods, improving measurement accuracy and dynamic range.