Take a look at the literature that does similar things for facial recognition -- search for the term "eigenface", for example.
The point to make in this context is that the information you are looking for does not actually require you to consider high-resolution images. You may have $10,000\times 10,000$ pixels, for which any non-trivial ...
We construct an operator based on the assumption that the system is a linear space invariant system. The blurred image is denoted $b$ and the input is denoted $x$.
Since the convolution is commutative, we can write
b &= h*x\\
So we can have two equal representations using the matrices $H$ and $X$ corresponding to ...
Let us proceed systematically:
numerical precision of data (you said from medical imaging)
number of operations required for standard methods (as from libraries)
possible out-of-core computation (i.e. not the whole matrix at all times in memory).
In all cases, I am afraid, you would have to be prepared to suffer. Incidentally, out-of-core methods are very ...