Imagine a SAR image of a smooth land surface where the NRCS does not change much within large areas. The image has been processed to full spatial resolution, i.e. the detected pixel intensities have an exponential distribution due to speckle noise. Calibration has been performed such that the pixel intensities can be assumed to represent realizations of NRCS measurements.

a) To get a first impression of the NRCS in one area of the image, you compute the mean value of 400-pixel values. What is the theoretical remaining uncertainty of this NRCS estimate relative to the correct value of the NRCS?

b) A large homogeneous region in the image has a true NRCS of 0.24 on one end and 0.21 on the other end, but it is difficult to see this trend at full resolution because of the speckle noise. You see it much better after rebinning the image to 1/25 of the original array size in each direction (i.e. each new pixel represents the mean intensity of 2525 original pixels). Show how this can be explained quantitatively, based on theoretical standard deviations before and after the rebinning process.

c) One of your colleagues has analyzed another part of the image and tells you the NRCS in that test area is some dB value with an error bar of 0.1 dB. You try to understand how this result was obtained. Can you figure out how many pixels the colleague must have averaged to obtain an error bar of 0.1 dB?