pp

Question 1

experimental image space

Answer 1

Experimental image space should be illustrated as a stack of images. Each image corresponds to a different observation in experimental space. In the simple case, experimental space may refer to repeated acquisitions of the same scene. However, it may refer to the same anatomical structure in different patients (for example), or – more generally – different visual representations of states of the world

Question 2

steps required to use the concept of experimental image space to estimate an average anatomical structure

Answer 2

First, we need to ensure that it makes sense to average
the images, i.e. those pixels that are being averaged together in the direction of image space actually represent the same physical structure, in some sense.
For the case of images of the same anatomical structure across different patients, this may result in something like the “average brain” or the “average face”. However, the objects in the images need to be aligned in a sensible
way between observations in image space, and the way in which this is done depends very much on the nature of “what” is being averaged, and the sorts of spatial transformations that might be relevant in describing variations across experimental space. Examples would include aligning objects:
according to some well-defined boundary;
aligning objects according to their centroids;
aligning them according to well defined semantic landmarks (e.g. tips of noses is a common landmark used to align faces!).
Once images are satisfactorily aligned, one then averages pixels across experimental space,
resulting in a representation of average anatomical structure.
For 2D images in experimental space, the result of this average will be an average image,
and for 3D, it will be an average volume.

Question 3

Estimate the signal-to-noise ratio due to random noise effects, and to determine if the noise level is spatially varying

Answer 3

1) take repeated scan to obtain experimental space
2) Find the average image by averaging each pixel across each observation, creating an average image of phantom
3) Under the assumption of symmetrically distributed noise, averaging over large numbers of measurements should lead to estimates of the true (random-noise free)
image appearance
4) SNR can then be calculated as a function of spatial location, to see if it differs
5) To calculate signal and noise energies, one can use the standard formulae, based around the 2-norm, treating the images as one-dimensional vectors.
6) A gaussian or normal distribution is assumed for the deviations away from the mean image at each pixel, with each pixel also being treated as an independent variable.