Digital filter based on the Fisher linear discriminant to reduce dead-time paralysis in photon counting

Shane Z. Sullivan; Paul D. Schmitt; Emma L. DeWalt; Ryan D. Muir; Garth J. Simpson

doi:10.1117/12.2048875

7 March 2014 Digital filter based on the Fisher linear discriminant to reduce dead-time paralysis in photon counting

Shane Z. Sullivan, Paul D. Schmitt, Emma L. DeWalt, Ryan D. Muir, Garth J. Simpson

Proceedings Volume 9020, Computational Imaging XII; 902009 (2014) https://doi.org/10.1117/12.2048875
Event: IS&T/SPIE Electronic Imaging, 2014, San Francisco, California, United States

Abstract

Photon counting represents the Poisson limit in signal to noise, but can often be complicated in imaging applications by detector paralysis, arising from the finite rise / fall time of the detector upon photon absorption. We present here an approach for reducing dead-time by generating a deconvolution digital filter based on optimizing the Fisher linear discriminant. In brief, two classes are defined, one in which a photon event is initiated at the origin of the digital filter, and one in the photon event is non-coincident with the filter origin. Linear discriminant analysis (LDA) is then performed to optimize the digital filter that best resolves the coincident and non-coincident training set data.1 Once trained, implementation of the filter can be performed quickly, significantly reducing dead-time issues and measurement bias in photon counting applications. Experimental demonstration of the LDA-filter approach was performed in fluorescence microscopy measurements using a highly convolved impulse response with considerable ringing. Analysis of the counts supports the capabilities of the filter in recovering deconvolved impulse responses under the conditions considered in the study. Potential additional applications and possible limitations are also considered.

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Shane Z. Sullivan, Paul D. Schmitt, Emma L. DeWalt, Ryan D. Muir, and Garth J. Simpson "Digital filter based on the Fisher linear discriminant to reduce dead-time paralysis in photon counting", Proc. SPIE 9020, Computational Imaging XII, 902009 (7 March 2014); https://doi.org/10.1117/12.2048875

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KEYWORDS

Digital filtering

Photon counting

Linear filtering

Sensors

Deconvolution

Time correlated photon counting

Luminescence

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