Matlab: need some help for a seemingly simple vectorization of an operation

Question

I would like to optimize this piece of Matlab code but so far I have failed. I have tried different combinations of repmat and sums and cumsums, but all my attempts seem to

Answer 1

Update: here are the results for the running times for the different proposals (10^5 trials):

So it looks like the transformation of the matrix is the most efficient intervention, and my original double-loop implementation is, amazingly, the best compared to the vectorized versions. However, in my hands (2017a) the improvement is only 16.6% compared to the original using the mean (18.2% using the median).

Maybe there is still room for improvement?