Assume that we got a $n * m$ picture called $X$ and $X$ contains the noise picture $S$. $X - S = L$ where $L$ is the clean filtered ideal picture and $X = L + S$ is the real picture taken by camera.
I want to minimize $$||L||_* + \lambda ||S||_1$$ With the subject to: $$X = L + S$$
Where $||L||_*$ is the Nuclear norm (Sum of singular values) and $||S||_1$ is the L1-norm (Sum of absolute values) and $\lambda$ is just a tuning parameter e.g a number.
- What method should I use to solve this optimization problem?
- What algorithm should I use with that method?
- Can I solve this using least squares?
- Can I solve this with linear programming e.g simplex method?
- Can I solve this with dynamic programming?
I assume that this is a quadratic programming problem because we got two matrices to work with, $L$ and $S$.