interpolating data from surrounding cells

I have a large array of ocean climate data that contains many NaN values. I want to interpolate the neighbouring cells of the missing NaN cells, and replace that NaN cell with the mean of it's neighbouring cells that contain actual data.

I think it's best to do this an expanding circular fashion eg. if the nearest surrounding cells of the NaN cell only contain more NaN values, I want to take the second nearest circle of cells and so on, until numeric values are found.

So far, I have been following an answer from here:

https://uk.mathworks.com/matlabcentral/answers/86900-how-to-find-all-neighbours-of-an-element-in-n-dimensional-matrix

A = [1 2 NaN; 3 NaN 5; 6 7 NaN]

A =

     1     2   NaN
     3   NaN     5
     6     7   NaN

A = padarray(A,[1 1],NaN) % pad the edges with NaNs

A =

   NaN   NaN   NaN   NaN   NaN   NaN   NaN
   NaN   NaN   NaN   NaN   NaN   NaN   NaN
   NaN   NaN     1     2   NaN   NaN   NaN
   NaN   NaN     3   NaN     5   NaN   NaN
   NaN   NaN     6     7   NaN   NaN   NaN
   NaN   NaN   NaN   NaN   NaN   NaN   NaN
   NaN   NaN   NaN   NaN   NaN   NaN   NaN

s=size(A);
N=length(s);
[c1{1:N}]=ndgrid(1:3);
c2(1:N)={2};
offsets=sub2ind(s,c1{:}) - sub2ind(s,c2{:})

offsets =

    -8    -1     6
    -7     0     7
    -6     1     8

L = find(isnan(A))   % find linear indices of NaNs

% find neighbours of one index, 19
neighbors = A(19+offsets)

neighbors =

   NaN     3   NaN
   NaN     6     7
   NaN   NaN   NaN

Advice on the following would be much appreciated:

1. How do I get the mean of the surrounding cells? EDIT (answer) below.

2. How can I do this to run over the whole matrix?

[Roisin Loughnane]

EDIT:

For Question 1,

The following code uses linear indexing to get the mean of the surrounding cells omitting the NaNs using nanmean(), and replaces the NaN cell in question (here index 13) with this value.

neighbors = A(13+offsets) % find neighbours of one index NaN cell, 13
repnan = nanmean(neighbors([1 2 3 4 6 7 8 9])) % get the mean of the surrounding cells
A([13]) = repnan % insert mean into that NaN cell