Let A, B, C and D be some matrix and x be a vector, I want to solve the following optimization problem:

$$ \min_x \| Ax -B\|^2_2 + \| Cx-D\|^2_2 $$ my solution:

$$ J = \| Ax -B\|^2_2 + \| Cx-D\|^2_2 $$

$$ \frac{\partial J}{\partial x} = 2A^T(Ax -B) + 2C^T(Cx-D) = 0 $$

so, $$ x = (A^TA+C^TC)^{-1}(A^TB+C^TD) $$

But in some literature, I see the authors use FFT to solve such problems.

My questions are:
1) How one can use FFT to solve the above problem?
2) What is the advantage to use FFT?



Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.