Most existing bounds for signal reconstruction from compressive measurements make the assumption of additive signal-independent noise. However in many compressive imaging systems, the noise statistics are more accurately represented by Poisson or Poisson-Gaussian noise models. In this paper, we derive upper bounds for signal reconstruction error from compressive measurements which are corrupted...

Let X be a Poisson point process and K ⊂ R d a measurable set. Construct the Voronoi cells of all points x ∈ X with respect to X, and denote by vX (K) the union of all Voronoi cells with nucleus in K. For K a compact convex set the expectation of the volume difference V (vX (K)) − V (K) and the symmetric difference V (vX (K)△K) is computed. Precise estimates for the variance of both quantities ...

We consider a point process obtained summing to each point i of the set of the integer Z an i.i.d random variable ξi having a variance that can be also much larger than 1. We compare the process obtained with this construction with the standard Poisson process, and we show that in some sense our process tends to converge for large variance of ξ to the Poisson process in total variation. We then...

We show that, for a stationary version of Hammersley's process, with Poisson sources on the positive x-axis and Poisson sinks on the positive y-axis, the variance of the length of a longest weakly NorthEast path L(t, t) from (0, 0) to (t, t) is equal to 2E(t − X(t)) + , where X(t) is the location of a second class particle at time t. This implies that both E(t − X(t)) + and the variance of L(t,...

Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 General Probability Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Conditional Probability . . . . . . . . . . . . . . . . . . . . . . . ...

Abstract. In this research we try to consider the problem of applying the Nonhomogeneous Poisson process to trends of economic development. More specifically, a modified Nonhomogeneous Poisson process is derived when the intensity rate is considered as a solution of stochastic differential equation which satisfies the geometric Brownian motion. The mean and the variance of the modified process ...

The performance of the Lasso is well understood under the assumptions of the standard sparse linear model with homoscedastic noise. However, in several applications, the standard model does not describe the important features of the data. This paper examines how the Lasso performs on a non-standard model that is motivated by medical imaging applications. In these applications, the variance of t...

This paper proposes a mathematical model and formalism to study coded exposure (flutter shutter) cameras. The model includes the Poisson photon (shot) noise as well as any additive (readout) noise of finite variance. This is an improvement compared to our previous work that only considered the Poisson noise. In addition, closed formulae for the Mean Square Error and Signal to Noise Ratio of the...

Concentration inequalities are obtained on Poisson space, for random functionals with finite or infinite variance. In particular, dimension free tail estimates and exponential integrability results are given for the Euclidean norm of vectors of independent functionals. In the finite variance case these results are applied to infinitely divisible random variables such as quadratic Wiener functio...