3. Assume that we have a CCD camera system that is cooled so that noise due to dark current is negligible. Then digitized pixel values will be given by D= (S+NA+Np)A+NQ (1) where S is the signal in electrons, NA is the zero-mean amplifier noise source with variance o Np is the zero-mean photon noise with variance S, A is the gain of the amplifier, and No is the zero-mean quantization noise with variance oa. Assume that the noise sources are independent. a) Show that for a constant signal level S the expected value of D is u= SA (2) and the variance of D is given by oh = Au + og = (3) where og = Ao+ - (4) b) Write a program that reads a digital image II, y) of size N N where N = 100 and estimates u by 1 Na I [ () (, 24) (5) N2 1