There is not any support for image with log-scale in GRABIT yet. However, as a workaround you could do the following.
For this particular image, in GRABIT, set the origin of the x-axis as 1 ( for 10^1) and the max of x-axis as 5 (for 10^5). Similarly for y-axis, set the origin as -2 ( for 10^-2) and the max of y-axis as 1 (for 10^1). After getting the points, you could do the following to get the same plot on a log-scale:
load('Data001.mat','Data001');
x = Data001(:,1);
y = Data001(:,2);
x = 10.^x;
y = 10.^y;
loglog(x,y);
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