Fingerprint Residual Orientation Field

I am trying to build a residual orientation field of fingerprint. This field has cosine and sine part.

For this purpose i have to find the coefficients of set of polynomials. They are obtained using least squares estimation by minimizing the second equations (see the picture).

The set of polynomial coefficients are {ai,j} and {bi,j} And they are of course unknown. I have no idea how to represent the sum of squares and then minimize it.

Can someone point me into to the right direction?

The residual orientation field concept is from: Yoon, S., Feng, J., and Jain, A. K. Latent fingerprint enhancement via robust orientation field estimation . In 2011 IEEE International Joint Conference on Biometrics (IJCB), 1–8.