Extreme Compressed Sensing of Poisson Rates from Multiple Measurements.

Area of Science:

• Signal Processing
• Statistical Modeling
• Biosensing

Background:

• Compressed sensing (CS) recovers sparse signals from fewer measurements than traditional methods.
• The multiple measurement vector (MMV) framework addresses recovering multiple related sparse signals.
• Existing CS methods struggle with signals derived from Poisson distributions, common in biosensing.

Purpose of the Study:

• To develop a novel compressed sensing algorithm for signals modeled by a sparse, multivariate Poisson distribution.
• To address the challenge of recovering sparse signals in biosensing applications using microfluidics.
• To introduce the Sparse Poisson Recovery (SPoRe) algorithm for enhanced signal recovery under resource-limited conditions.

Main Methods:

• Developed the Sparse Poisson Recovery (SPoRe) algorithm using maximum likelihood estimation.
• Employed batch stochastic gradient ascent with Monte Carlo approximations for gradient computation.
• Leveraged the unique properties of the Poisson distribution for signal recovery.

Main Results:

• SPoRe significantly outperforms existing CS algorithms, including custom baselines.
• The algorithm demonstrates high performance even with one-dimensional measurements and high noise.
• Identifiability of the Poisson model is proven under relaxed conditions.

Conclusions:

• SPoRe offers unprecedented resource efficiency for compressed sensing, ideal for microfluidic biosensing.
• The algorithm's performance validates the Poisson model for sparse signal recovery in specific applications.
• Findings pave the way for new biosensing approaches and generalize to other Poisson signal applications.