You should use a reversible  procedure to be able to recover original data from transform space. Since the averaging is not reversible, you cant recover data correctly. Suppose the situation that the average value is 2.5, there is no way to find out that the original data is {1,4}, {4,1}, {2,3} or {3,2}.

I suggest you to use  the following procedure:

1- convert 2-D matrix to 1-D vector ( you can use different type of scanning like as zig-zag scan)

2- rearrange elements in a way that the similar symbols are put together. (e.g. burrows wheeler transform)

3- use run-length encoding (RLE)

and

4- finally, perform huffman coding

An interesting q . Please see attached pdf. It contains SVD application and a method to see periodicity. It will be necessary to obtain say sum or average of the yps matrix in pdf to see the pattern. 

Hope  it is useful.

Cheers

Check the following link

http://stackoverflow.com/questions/14154952/finding-pattern-in-a-matrix-in-r

It seems different interpretations of the q are possible:

1.One is given a pattern locate occurrences of the pattern in a matrix.

2. Other is given a large matrix, is there a repetitive  sequence segment.

Possibly self organizing maps could be used for 2.

Cheers.

@Aldo Dall'Osso.. Compliments. A nice elegant solution with many other possibilities and applications

Cheers.

@Aldo Dall'Osso.. Storing each of the numbers 1,2,3,4 requires 2 bits, so one row is stored in 8 bits. Storing an integer  0

@Ivan Slapnicar ·  A fine observation  for practical implementation but nevertheless from column vectors point of view replacing 4 column vectors with one is very appealing. I am trying to see how this fits with SVD .. just a conjecture..there seems some unique connection as we are able to retrieve the transformation matrix using affine and given resultant vector in column space.

Cheers