Noisy Pooled PCR for Virus Testing

Junan Zhu; Kristina Rivera; Dror Baron

In this expression, (5), we have mean and variance values for w m , and can interpret g out (k m , y m , Θ m ) as a correction term that reflects residual information, which is provided by the noisy measurements vector, y, but is not yet reflected in our estimates, k for Ax, and x. The correction term is used in later iterations to compute q and g in (·). GAMP uses these two scalar functions, g in (·) (4) and g out (·) (5), to estimate x and w = Ax (1) from q (3) and y (2), respectively. That is, GAMP iteratively cleans the input and output channels. A numerical illustration is provided in Fig. 2 ; Sec. IV discusses this figure in detail. GAMP also uses derivatives of these scalar functions to estimate the variance. In words, knowing not only the mean but also the variance around the mean allows GAMP to judiciously use information from x when estimating w and vice versa.