This is derived from the paper Multi-view stereoviadepthmapfusion:Acoordinatedecent
optimizationmethod. In the given paper the formulation is solved by coordinate decent . However, I want to solve it using the ADMM algorithm. The first part of the equation is is L1 minimization with respect to the neighboring voxel values. Whereas the second part is fitting the function fi in the voxel itself.

This can be entered in a straightforward manner into CVX.

All the solvers callable by CVX, except for GLPK, can be used to solve this as an SOCP problem as transformed internally by CVX. But none of these solvers use ADMM.