# Image Restoration by Solving Constrained Least squares in Frequency Domain (Frequency Domain Filtering)

I am trying to implement the constrained least squares filtering as described in Rafael C. Gonzalez, Richard E. Woods - Digital Image Processing 3rd Edition Section 5.9. The equation (5.9-4) says that $$P \left( u, v \right)$$ is the Fourier transformation of the Laplacian filter ($$3 x 3$$). But the coordinates $$u$$, $$v$$ are the coordinates of the image which is much greater than 3x3.

How can I implement this 2D Filter in Frequency Domain?

• Could you link to the reference? – Royi Nov 7 '20 at 8:43
• So it's the book Rafael Gonzalez et.al 'Digital image processing 2007, chapter 5.9 p.380 in that edition of the book – Maciek Woźniak Nov 7 '20 at 18:28
• Could you post more context about the problem being solved and then I will be able to solve it for you? – Royi Nov 8 '20 at 6:01
• Do you want me to solve it? – Royi Nov 9 '20 at 5:06
• Hi i manage to solve it. Mainly the case is that the filter had to be shifted to the midle of the image and then padded to the size of image. In Matlab fft2(fftshift(o,d1,d2)) where d1 and d2 are dimensions of the img – Maciek Woźniak Nov 10 '20 at 6:12

As you wrote in the comments, one way to do it is simple zero padding and fftshift(). Yet this might cause some artifacts.