Line data    Source code

       1             : #pragma once
       2             : 
       3             : #include "WLSProblem.h"
       4             : 
       5             : namespace elsa
       6             : {
       7             :     /**
       8             :      * @brief Class representing a Tikhonov regularized weighted least squares problem
       9             :      *
      10             :      * @author Nikola Dinev
      11             :      *
      12             :      * @tparam data_t data type for the domain and range of the problem, defaulting to real_t
      13             :      *
      14             :      * This class represents a Tikhonov regularized weighted least squares problem.
      15             :      * Some common examples are:
      16             :      * - \f$ \argmin_x \frac{1}{2} \| Ax - b \|_2^2 + \lambda \| x \|_2^2 \f$
      17             :      * - \f$ \argmin_x \frac{1}{2} \| Ax - b \|_2^2 + \lambda \| x - x^* \|_2^2 \f$
      18             :      * - \f$ \argmin_x \frac{1}{2} \| Ax - b \|_2^2 + \lambda \| Lx \|_2^2 \f$
      19             :      * - \f$ \argmin_x \frac{1}{2} \| Ax - b \|_2^2 + \lambda \| L(x - x^*) \|_2^2 \f$,
      20             :      * where \f$ A \f$ is a linear operator and \f$ b \f$ and \f$ x^* \f$ are data vectors,
      21             :      * \f$ \lambda \f$ is the regularization weight, and \f$ L \f$ is a discretized differential
      22             :      * operator.
      23             :      *
      24             :      * This class supports a wider range of problems - any problem of the form
      25             :      * \f$ \argmin_x \frac{1}{2} \| Ax - b \|_{W,2}^2 + \sum_{i=1}^n \lambda_i \| B_ix - x^*_i
      26             :      * \|_{V_i,2}^2 \f$ is considered a Tikhonov problem. Here \f$ A \f$ and \f$ B_i \f$ are linear
      27             :      * operators, \f$ b \f$ and \f$ x^*_i \f$ are data vectors, \f$ \lambda_i \f$ are the
      28             :      * regularization weights, and \f$ W \f$ and \f$ V_i \f$ are scaling operators.
      29             :      */
      30             :     template <typename data_t = real_t>
      31             :     class TikhonovProblem : public Problem<data_t>
      32             :     {
      33             :     public:
      34             :         /**
      35             :          * @brief Construct a Tikhonov problem of the form
      36             :          * \f$ \argmin_x \frac{1}{2} \| Ax - b \|_2^2 + \lambda \| x \|_2^2 \f$
      37             :          *
      38             :          * @param[in] A a linear operator
      39             :          * @param[in] b a data vector
      40             :          * @param[in] lambda regularization weight
      41             :          */
      42             :         TikhonovProblem(const LinearOperator<data_t>& A, const DataContainer<data_t> b,
      43             :                         real_t lambda = 0.5f);
      44             : 
      45             :         /**
      46             :          * @brief Constructor for a Tikhonov problem
      47             :          *
      48             :          * @param[in] wlsProblem a wls problem specifying the data term and the initial solution
      49             :          * @param[in] regTerms the regularization terms, all should be of type L2NormPow2 or
      50             :          * WeightedL2NormPow2
      51             :          */
      52             :         TikhonovProblem(const WLSProblem<data_t>& wlsProblem,
      53             :                         const std::vector<RegularizationTerm<data_t>>& regTerms);
      54             : 
      55             :         /**
      56             :          * @brief Constructor for a Tikhonov problem
      57             :          *
      58             :          * @param[in] wlsProblem a wls problem specifying the data term and the initial solution
      59             :          * @param[in] regTerm the regularization term, should be of type L2NormPow2 or
      60             :          * WeightedL2NormPow2
      61             :          */
      62             :         TikhonovProblem(const WLSProblem<data_t>& wlsProblem,
      63             :                         const RegularizationTerm<data_t>& regTerm);
      64             : 
      65             :         /// default destructor
      66          34 :         ~TikhonovProblem() override = default;
      67             : 
      68             :     protected:
      69             :         /// default copy constructor, hidden from non-derived classes to prevent potential slicing
      70           8 :         TikhonovProblem(const TikhonovProblem<data_t>&) = default;
      71             : 
      72             :         /// implement the polymorphic clone operation
      73             :         TikhonovProblem<data_t>* cloneImpl() const override;
      74             : 
      75             :     private:
      76             :         /// lift from base class
      77             :         using Problem<data_t>::_regTerms;
      78             :     };
      79             : } // namespace elsa