# Image recovery from partial Fourier Measurement via TV minimization

Hello !

I would like to solve $$f^{#}=\underset{g \in \mathbb{C}^{NxN}}{\operatorname{argmin}} |g|{\textrm{TV}}\ \ \ \textrm{such that}\ \ \ |\rho\circ(\mathcal{F}\Omega g-y)|_2 \leq \xi$$ where f would be our initial Image, y = \mathcal{F}_\Omega f + \xi is our partial Fourier Measurement and \rho denotes a weight vector (but if I implement it without that \rho I would already be happy).

I played around with cvx and got it working for smaller images(~64x64), but it didn’t work for bigger problems so I looked for other solvers, namely TFOCS.

Can anyone help me with the implementation, or point me in the right direction (or even towards another solver)?

Thanks!

Did you try MOSEK?

We are the maker and of MOSEK and if did not work then it would interest us.