2015/03/31 by L. Raczynski, L. Raczyński, P. Moskal +40 · 54 citations
Engineering · Mathematics · Medicine · Physics and Astronomy · #Algorithm #Artificial intelligence #Atomic and Subatomic Physics Research #Compressed sensing #Computer hardware #Computer science #Detector #Digital signal processing #Inverse problem #Mathematical analysis #Mathematics #Medical Imaging Techniques and Applications #SIGNAL (programming language) #Scanner #Scintillator #Signal processing #Sparse and Compressive Sensing Techniques #Telecommunications #Tikhonov regularization #physics.ins-det
paper · pdf · doi:10.1016/j.nima.2015.03.032
published in Nuclear Instruments and Methods in Physics Research Section A Accelerators Spectrometers Detectors and Associated Equipment 786, 105-112 (Elsevier BV)
arxiv created 2015/04/04 · openalex publication_date 2015/04/05 · arxiv updated 2015/06/24 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.