Blind intensity estimation from shot-noise data

The estimation of the intensity function of an inhomogeneous Poisson process is considered when the observable data consists of sampled shot noise that results from passing the Poisson process through an unknown linear time-invariant system. The proposed method consists of first estimating a histogram of the underlying point process. The estimated histogram is used to construct a kernel estimate of the intensity function. An estimate of the unknown impulse response of the linear time-invariant system is constructed via a regularized backsubstitution of a discrete-time convolution with the estimated histogram