Returns a vector of double memory from the workspace. New memory is allocated on-demand @argument ws pointer to workspace */

Resets the memory assignments in the workspace @argument ws pointer to workspace to reset */

Computes the value of the Lp norm for a given vector. If the value of p is too similar to 1, the norm is approximated as an L1 norm. If the va

General function for 1 dimensional unweighted TV optimization. Invokes different algorithms depending on the TV norm p. @param y input signal

r"""Forces an scalar value into float format Parameters ---------- x: scalar value to check Returns ------- float Fl

r"""2D proximal oprator for :math:`\ell_1`. Specifically, this optimizes the following program: .. math:: \mathrm{min}_y \frac{1}{2

r"""Forces a numpy matrix into float format Parameters ---------- x: numpy array matrix to check Returns ------- num

Creates and initiallizes a workspace structure @argument n dimension of data vectors. @returns pointer to new workspace */

Generates a 2D array for the test

Allocs memory for an array of p workspaces */

Returns the sign of a number. @argument s input number @returns -1 if number is negative, +1 if positive, 0 if exactly 0 */

PN_LPp Given a reference signal y and a penalty parameter lambda, solves the proximity operator min_x 0.5 ||x-y||^2 + lambda ||x||_p ,

Returns a vector of int memory from the workspace. New memory is allocated on-demand @argument ws pointer to workspace */

Returns the maximum of two numbers @argument x @argument y @returns value of the maximum number */

LPp_project Given a point y, computes its euclidean projection onto the ||x||_p = lambda ball min_x ||x-y||^2 s.t. ||x||_p <= lambda

r"""1D proximal operator for :math:`\ell_1`. Specifically, this optimizes the following program: .. math:: \mathrm{min}_y \frac{1}{

r"""2D weighted proximal operator for :math:`\ell_1` using DR splitting. Specifically, this optimizes the following program: .. math::

r"""General TV proximal operator for multidimensional signals Specifically, this optimizes the following program: .. math:: \min_X \f

PN_LPpGap Computes the dual gap of the current PN-Lp prox solution. @argument x current PN-Lp prox solution @argument y reference point

Wrapper function for general implementaton of Chambolle-Pock + Condat

Returns the minimum of two numbers @argument x @argument y @returns value of the minimum number */

morePG_TV2 Given a reference signal y and a penalty parameter lambda, solves the proximity operator min_x 0.5 ||x-y||^2 + lambda ||x_i -

DR2_TV Applies a variant of the Douglas Rachford algorithm, a.k.a. Alternating Reflections method, to solve the 2D TV proximity problem.

Performs the columns proximity step in the DR algorithm. @param M number of rows in input signal @param N number of columns in input signal

Projection agains the base polyhedron of the columns in the DR algorithm. proj[B_{cols}](z) = z - prox_cols(z) @param M number of rows in in

Applies the weighted L1-TV proximity operator to the given 1D input and returns the difference between input and output of prox. @param n length of

Applies the TV proximity operator to the given 1D input and returns the difference between input and output of prox. This is equivalent to computing

Performs the rows proximity step in the DR algorithm. @param M number of rows in input signal @param N number of columns in input signal

Projection agains the base polyhedron of the (modified) rows in the DR algorithm. proj[B_{-rows*}](z) = z + prox_row(-z+y) @param M numb

GPFW_TVp Given a reference signal y and a penalty parameter lambda, solves the proximity operator min_x 0.5 ||x-y||^2 + lambda ||x_i - x

GP_TVp Given a reference signal y and a penalty parameter lambda, solves the proximity operator min_x 0.5 ||x-y||^2 + lambda ||x_i - x_(

LP1_project Given a point y, computes its euclidean projection onto the ||x||_1 = lambda ball min_x ||x-y||^2 s.t. ||x||_1 <= lambda

PD2_TV Optimized version of Proximal Dykstra for the case where only 1 or 2 penalty terms appear. Given a reference multidimensional signal

This function implements the 1D total variation denoising algorithm described in the paper referenced above. If output=input, the process is performed

Generates a blocky signal for the demo

For given input signal and weight, all TV1 methods must be similar

Frees all memory reserved by a Buffer */

Creates a new Buffer of the given size */

Solves the linear problem with Lp ball constraint argmin_s s · z s.t. ||s||_p <= lambda This is done in O(n) time. @argument z l

tautString_TV1_Weighted Given a reference signal y and a penalty parameter lambda, solves the proximity operator min_x 0.5 ||x-y||^2 + s

r"""Weighted 1D proximal operator for :math:`\ell_1`. Specifically, this optimizes the following program: .. math:: \mathrm{min}_y

CondatChambollePock2_TV Application of Condat's or Chambolle-Pock generic proximal algorithm for 2D TV-L1. min_X 0.5 ||X-Y||^2 + lambda

Kolmogorov2_TV Application of Kolmogorov et al's proximal algorithm for 2D TV-L1. min_X 0.5 ||X-Y||^2 + TV_cols(X) + TV_rows(X) Thi

PD_TV Given a reference multidimensional signal y and a series of penalty terms P(x,lambda,d,p), solves the generalized Total Variation proxi

PG_TV2 Given a reference signal y and a penalty parameter lambda, solves the proximity operator min_x 0.5 ||x-y||^2 + lambda ||x_i - x_(

PN_LP1 Given a reference signal y and a penalty parameter lambda, solves the proximity operator min_x 0.5 ||x-y||^2 + lambda ||x||_1 ,

PN_LP2 Given a reference signal y and a penalty parameter lambda, solves the proximity operator min_x 0.5 ||x-y||^2 + lambda ||x||_2 ,

PN_LPinf Given a reference signal y and a penalty parameter lambda, solves the proximity operator min_x 0.5 ||x-y||^2 + lambda ||x||_inf

PN_TV1 Given a reference signal y and a penalty parameter lambda, solves the proximity operator min_x 0.5 ||x-y||^2 + lambda sum_i |x_i

PN_TV1_Weighted Given a reference signal y and a weight vector lambda, solves the proximity operator min_x 0.5 ||x-y||^2 + sum_i lambda_

non-weighted version

This function implements 1D total variation denoising by the taut string algorithm. It was adapted from the Matlab code written by Lutz Duembgen, whic

Yang2_TV Application of Yags's et al ADMM method for 2D TV-L1. min_X 0.5 ||X-Y||^2 + lambda * TV_cols(X) + lambda * TV_rows(X) The

Yang3_TV Application of Yags's et al ADMM method for 3D TV-L1. min_X 0.5 ||X-Y||^2 + lambda * TV_cols(X) + lambda * TV_rows(X) + lambda

Solves the Total-Variation l1 problem. To do so an efficient implementation of the classic taut-string method is used. Arguments: -

Solves the Total-Variation l1 problem To do so an efficient implementation of the classic taut-string method is used. Arguments: - s

Frees a workspace structure */

Solves the Total-Variation l1 problem through a hybrid method that selects the best approach for each case. The method starts by running Cond

linearizedTautString_TV1 Given a reference signal y and a penalty parameter lambda, solves the proximity operator min_x 0.5 ||x-y||^2 +

more_TV2 Given a reference signal y and a penalty parameter lambda, solves the proximity operator min_x 0.5 ||x-y||^2 + lambda ||x_i - x

Returns a new taut-string knot for given crossing majorant/minorant */

r"""1D proximal operator for :math:`\ell_2`. Specifically, this optimizes the following program: .. math:: \mathrm{min}_y \frac{1}{

r"""1D proximal operator for any :math:`\ell_p` norm. Specifically, this optimizes the following program: .. math:: \mathrm{min}_y

r"""2D proximal operator for any :math:`\ell_p` norm. Specifically, this optimizes the following program: .. math:: \mathrm{min}_y

FISTA_TVp Given a reference signal y and a penalty parameter lambda, solves the proximity operator min_x 0.5 ||x-y||^2 + lambda ||x_i -

FW_TVp Given a reference signal y and a penalty parameter lambda, solves the proximity operator min_x 0.5 ||x-y||^2 + lambda ||x_i - x_(

OGP_TVp Given a reference signal y and a penalty parameter lambda, solves the proximity operator min_x 0.5 ||x-y||^2 + lambda ||x_i - x_

TVval Given a reference multidimensional signal y and a series of penalty terms P(x,lambda,d,p), computes the value of the generalized Total

Chambolle and Pock's method for 2D TV proximity

Accelerated Chambolle and Pock's method for 2D TV proximity

Classic taut string method for TV1 proximity

Condat's method for TV1 proximity

Condat's method for 2D TV proximity

Condat's implementation of the taut string method for TV1 proximity

Johnson's dynamic programming method for TV1 proximity

Douglas Rachford parallel projections method for 2D TV proximity

Hybrid taut string method for TV1 proximity

Kolmogorov's method for TV1 proximity

Kolmogorov's method for 2D TV proximity

Linearized taut string method for TV1 proximity

More-Sorensen method for TV2 proximity

More-Sorensen + Projected Gradient hybrid method for TV2 proximity

Proximal dykstra method for 2D TV proximity

Projected Gradient method for TV2 proximity

Projected Newton method for TV1 proximity

Yang's method for 2D TV proximity

Comparison of floating point numbers, in reversed sense (to allow for descending sorting) */

Frees an array of p workspaces */

solveTV1_kolmogorov.cpp Solves the TV-L1 proximity problem by applying a message passing algorithm by Kolmogorov et al. Parameters: -

solveTV2d_DR.cpp Solves the 2 dimensional TV proximity problem by applying a Douglas-Rachford splitting algorithm. Parameters: - 0: bidim

solveTV2_morec.cpp Solves the TV-L2 proximity problem by applying a More-Sorensen algorithm. Parameters: - 0: reference signal y. -