copt.prox.prox_tv1d

copt.prox.prox_tv1d(step_size, w)[source]

Computes the proximal operator of the 1-dimensional total variation operator.

This solves a problem of the form

argmin_x TV(x) + (1/(2 stepsize)) ||x - w||^2

where TV(x) is the one-dimensional total variation

Parameters:
  • w (array) – vector of coefficients
  • step_size (float) – step size (sometimes denoted gamma) in proximal objective function

References

Condat, Laurent. “A direct algorithm for 1D total variation denoising.” IEEE Signal Processing Letters (2013)

Return type:ndarray