Interpolation to map from constant step size in X over to constant step size in Y with 2D arrays

Hi - I've been trying to think about the most elegant (fastest) way to execute the following procedure.

First is the process in general I am trying to achieve: I have an X,Y dataset where X is evenly spaced and Y represents the output of a particular function. I want to remap this to evenly spaced Y and function dependent X. I've been doing this using the interp1 function - seems pretty standard:

X = [1:5:100];
Y = 0.01 * Y.^2;
X2 = [min(Y):(max(Y)-min(Y))/20:max(Y)];
Y2 = interp1(Y,X,Y2,'linear','extrap');

The real problem I am facing is that X and Y in my application are actually both 2D arrays. The "x,y pairings" are such that Row 1 of X and Row 1 of Y represent an X,Y space that I want to remap from constant steps in X to constant steps in Y. So I need to do this interpolation procedure on each row individually. There is no common X to go with the multi-dimensional output Y, so the built-in multi-dimensional support for interp1 doesnt seem to apply.

Up to now, I have been using a FOR loop to step through each row and individually interpolate. It is unbearingly slow for large datasets. I think I could improve my code by minimizing the use of variable instantiation for handling each row, but I am thinking there might be a better way to do this in a true matrix operation anyway. I only need very simple linear interpolation, I might even be OK with a "nearest neighbor" approach because the dataset is quite dense unlike my example.

Any ideas?

Thanks a bunch, this community is great!