Functionals::CompressiveSensing Class Reference

Compressive sensing example using convex optimization as discussed in [1]: [1] G. Kutyniok. Compressed Sensing: Theory and Applications. Computing Research Repository, abs/1203.3815, 2012. More...

#include <functionals.h>

Static Public Member Functions
static float	f (const Eigen::MatrixXf &x, const Eigen::MatrixXf &A, const Eigen::MatrixXf &y, float lambda)
	Differentiable but non-convex part: |Ax - y|_2^2. More...
static void	df (const Eigen::MatrixXf &x, const Eigen::MatrixXf &A, const Eigen::MatrixXf &y, Eigen::MatrixXf &df_x, float lambda)
	Derivative of f. More...
static float	g (const Eigen::MatrixXf &x)
	Non-differentiable but convex part: |x|_1. More...
static void	prox_g (const Eigen::MatrixXf &x, Eigen::MatrixXf &prox_g_x, float alpha)
	Proximal map of g. More...

Detailed Description

Compressive sensing example using convex optimization as discussed in [1]: [1] G. Kutyniok. Compressed Sensing: Theory and Applications. Computing Research Repository, abs/1203.3815, 2012.

Member Function Documentation

void Functionals::CompressiveSensing::df ( const Eigen::MatrixXf &  x, const Eigen::MatrixXf &  A, const Eigen::MatrixXf &  y, Eigen::MatrixXf &  df_x, float  lambda  )

static

Derivative of f.

Parameters

[in]	x
[out]	df_x
[in]	epsilon

float Functionals::CompressiveSensing::f ( const Eigen::MatrixXf &  x, const Eigen::MatrixXf &  A, const Eigen::MatrixXf &  y, float  lambda  )

static

Differentiable but non-convex part: |Ax - y|_2^2.

Parameters

[in]	x
[in]	epsilon

float Functionals::CompressiveSensing::g ( const Eigen::MatrixXf &  x )

static

Non-differentiable but convex part: |x|_1.

Parameters

[in]	x
[in]	x_0
[in]	Cp
[in]	Cm
[in]	epsilon
[in]	lambda

void Functionals::CompressiveSensing::prox_g ( const Eigen::MatrixXf &  x, Eigen::MatrixXf &  prox_g_x, float  alpha  )

static

Proximal map of g.

Parameters

[in]	x
[in]	x_0
[out]	prox_g_x
[in]	Cp
[in]	Cm
[in]	epsilon
[in]	lambda
[in]	alpha

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The documentation for this class was generated from the following file:

• lib_ipiano/functionals.h