How to solve L1-TV formulation

[Mark_L_Stone]

Please show explicitly what the L1 TV formulation is.

You might find these links to be of value:

How to Formulate in CVX - 1D Total Variation Extension

Given the problem \min_{ x \in {\mathbb{R}}^{n} } \frac{1}{2} {\left\| x - y \right\|}_{2}^{2} + \sum_{i = 1}^{n - 2} \sqrt{{\left( {x}_{i} - {x}_{i + 1} \right)}^{2} + {\left( {x}_{i + 1} - {x}_{i + 2} \right)}^{2}} How could one formulate it in CVX? I could handle it without the sqrt yet couldn’t do it in this form. Thank You.

Total Variation (TV) Norm Function Input: Vector or Matrix?

I am trying to use the CVX toolbox with my own TV norm Matlab function. I know that the TV norm is also known as the “discrete TV seminorm” and that it meets the first three properties of a vector norm; therefore it is convex because all norms are convex. My Matlab function’s input is a matrix (namely, an image); however, from reading CVX the manual it appears that the CVX toolbox works better with vectors; so, can I modify my TV norm function’s inputs to be a vector, number or rows (m) and co…