Compressive Sensing of Signals Generated in Plastic Scintillators in a Novel J-PET Instrument

TL;DR

This paper demonstrates that signals from plastic scintillators in the J-PET scanner can be accurately reconstructed from few samples using a compressive sensing approach combined with PCA and Tikhonov regularization, enabling efficient signal recovery.

Contribution

It introduces a novel compressive sensing method for reconstructing signals in the J-PET scanner using PCA and Tikhonov regularization, providing a closed-form solution and error analysis.

Findings

Signal recovery error is inversely proportional to the number of samples.

The method achieves accurate reconstruction with fewer samples.

Analytical formulas for error estimation are derived.

Abstract

The J-PET scanner, which allows for single bed imaging of the whole human body, is currently under development at the Jagiellonian University. The dis- cussed detector offers improvement of the Time of Flight (TOF) resolution due to the use of fast plastic scintillators and dedicated electronics allowing for sam- pling in the voltage domain of signals with durations of few nanoseconds. In this paper we show that recovery of the whole signal, based on only a few samples, is possible. In order to do that, we incorporate the training signals into the Tikhonov regularization framework and we perform the Principal Component Analysis decomposition, which is well known for its compaction properties. The method yields a simple closed form analytical solution that does not require iter- ative processing. Moreover, from the Bayes theory the properties of regularized solution, especially its covariance matrix, may be easily derived. This is the key to introduce and prove the formula for calculations of the signal recovery error. In this paper we show that an average recovery error is approximately inversely proportional to the number of acquired samples.