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The study of the total variation problem is to solve the following problem: $$ \text{minimize} ~ \frac{1}{2}||x - b||_2^2 + \lambda * \sum_i^N |x_{i+1} - x_i| $$ where $x$ is the unknown, $b$ in $R^N$, and N is the length of vector x.

From the ADMM method in the Standford website, the solution is like this:

x =

    4.0546
    4.0546
    4.0546
    4.0546
    3.3319
    3.3319
    3.3319
    3.3319
    ...

If I define the number of degree freedom in the estimator $\hat{x}$, $df(\hat{x})= N - m$, where m is the number of equal coordinates in the vector $\hat{x}$.

Question: Is it possible for me to obtain the value m from the above ADMM solution? The difficult part is that I am not sure whether to treat two coordinates, say 1.3015 and 1.3016 equal or not?

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