sopt::objective_functions Namespace Reference

Functions
template<typename T >
std::function< t_real(T)> const	unconstrained_regularisation (const std::function< t_real(T)> &g, const t_real &sig, const T &y, const sopt::OperatorFunction< T > &measurement_operator)
	returns g(x) + ||y - Φ x||_2^2 as a function More...
template<typename T >
std::function< t_real(T)> const	unconstrained_L1_regularisation (const t_real &gamma, const t_real &sig, const T &y, const sopt::OperatorFunction< T > &measurement_operator, const sopt::LinearTransform< T > &wavelet_operator)
	returns ||ψ^t x||_1 + ||y - Φ x||_2^2 as a function More...
template<typename T >
std::function< t_real(T)> const	unconstrained_regularisation (const std::function< t_real(T)> &g, const t_real &sig, const T &y, const sopt::LinearTransform< T > &measurement_operator)
template<typename T >
std::function< t_real(T)> const	unconstrained_l1_regularisation (const t_real &gamma, const t_real &sig, const T &y, const sopt::LinearTransform< T > &measurement_operator, const sopt::LinearTransform< T > &wavelet_operator)
template<typename T >
std::function< t_real(T)> const	unconstrained_l1_regularisation (const t_real &gamma, const t_real &sig, const T &y, const sopt::OperatorFunction< T > &measurement_operator, const sopt::LinearTransform< T > &wavelet_operator)

Function Documentation

unconstrained_l1_regularisation() [1/2]

template<typename T >

std::function< t_real(T)> const sopt::objective_functions::unconstrained_l1_regularisation	(	const t_real &	gamma,
		const t_real &	sig,
		const T &	y,
		const sopt::LinearTransform< T > &	measurement_operator,
		const sopt::LinearTransform< T > &	wavelet_operator
	)

Definition at line 43 of file objective_functions.h.

                                                    {
  if (gamma <= 0) SOPT_THROW("regularsiation paramter is not greater than 0.");
  const std::function<t_real(T)> g = [=](const T &x) -> t_real {
    return sopt::l1_norm(wavelet_operator.adjoint() * x) * gamma;
  };
  return unconstrained_regularisation<T>(g, sig, y, measurement_operator);
}

References sopt::LinearTransform< VECTOR >::adjoint(), sopt::l1_norm(), and SOPT_THROW.

unconstrained_L1_regularisation()

template<typename T >

std::function<t_real(T)> const sopt::objective_functions::unconstrained_L1_regularisation	(	const t_real &	gamma,
		const t_real &	sig,
		const T &	y,
		const sopt::OperatorFunction< T > &	measurement_operator,
		const sopt::LinearTransform< T > &	wavelet_operator
	)

returns ||ψ^t x||_1 + ||y - Φ x||_2^2 as a function

unconstrained_l1_regularisation() [2/2]

template<typename T >

std::function<t_real(T)> const sopt::objective_functions::unconstrained_l1_regularisation	(	const t_real &	gamma,
		const t_real &	sig,
		const T &	y,
		const sopt::OperatorFunction< T > &	measurement_operator,
		const sopt::LinearTransform< T > &	wavelet_operator
	)

Definition at line 61 of file objective_functions.h.

                                                    {
  const LinearTransform<T> mop = {measurement_operator, measurement_operator};
  return unconstrained_l1_regularisation<T>(gamma, sig, mop * y, mop, wavelet_operator);
}

unconstrained_regularisation() [1/2]

template<typename T >

std::function< t_real(T)> const sopt::objective_functions::unconstrained_regularisation	(	const std::function< t_real(T)> &	g,
		const t_real &	sig,
		const T &	y,
		const sopt::LinearTransform< T > &	measurement_operator
	)

Definition at line 35 of file objective_functions.h.

                                                        {
  return [=](const T &x) -> t_real {
    return g(x) + 0.5 * std::pow(sopt::l2_norm(y - measurement_operator * x) / sig, 2);
  };
}

References sopt::l2_norm().

unconstrained_regularisation() [2/2]

template<typename T >

std::function< t_real(T)> const sopt::objective_functions::unconstrained_regularisation	(	const std::function< t_real(T)> &	g,
		const t_real &	sig,
		const T &	y,
		const sopt::OperatorFunction< T > &	measurement_operator
	)

returns g(x) + ||y - Φ x||_2^2 as a function

Definition at line 54 of file objective_functions.h.

                                                         {
  const LinearTransform<T> mop = {measurement_operator, measurement_operator};
  return unconstrained_regularisation<T>(g, sig, mop * y, mop);
}