Viral load inference of high dynamic range signals using non-adaptive pooled testing

Abstract Medical diagnostic testing can be made significantly more efficient using pooled testing protocols. These typically require a sparse infection signal and use either binary or real-valued entries of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi class="MJX-tex-calligraphic" mathvariant="script">O</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:math> . However, existing methods do not allow for inferring viral loads which span many orders of magnitude. We develop a message passing algorithm coupled with a PCR (Polymerase Chain Reaction) specific noise function to allow accurate inference of realistic viral load signals. A version of the Combinatorial Orthogonal Matching Pursuit algorithm is employed to compare the obtained inference results with those of our probabilistic message passing. This work is in the non-adaptive setting and could open the possibility of efficient screening where viral load determination is clinically important.