Correction for compton scattering by analysis of spatially dependent energy spectra employing regularization

A method of producing an image having reduced effects of Compton scattered photons detected in a gamma ray detection arrangement, the method comprising the steps of:

• receiving data responsive to energy states of the detected photons and storing said data in memory locations corresponding to predetermined image grid points;
• calibrating the gamma ray detection arrangement by utilizing a spectral shape corresponding to a calibration function which is expected to correspond to a first data set corresponding to unscattered ones of the detected photons;
• processing said stored data for at least selected ones of said predetermined grid points employing a minimization of a function which includes a product of a spatial regularization term times a spatial regularization parameter, for separating said stored data into said first data set corresponding to unscattered ones of the detected photons and a second data set corresponding to scattered ones of the detected photons;
• summing said first data set for each of said selected ones of said predetermined grid points for determining a number of said unscattered ones of said detected photons;
• and
• forming the image utilizing said number of said unscattered ones of said detected photons.

A method of producing an image having reduced effects of Compton scattered photons detected in a gamma ray detection arrangement, the method comprising the steps of:

• receiving data responsive to energy states of the detected photons and storing said data in memory locations corresponding to predetermined image grid points;
• grouping said stored data, whereby a coarser grid having fewer image grid points is produced;
• calibrating the gamma ray detection arrangement by utilizing a spectral shape corresponding to a calibration function which is expected to correspond to a first data set corresponding to unscattered ones of the detected photons and by utilizing spectral shapes for mono-energetic gamma rays whose energies are higher than the energy of the gamma ray of primary interest and by utilizing spectral shapes for mono-energetic gamma rays whose energies are lower than the energy of the gamma ray of primary interest;
• processing said stored data for at least selected ones of said predetermined grid points using as a model of the unscattered spectrum a set of parameters, one for each energy channel, and employing minimization of a function which includes a product of an energy regularization term times an energy regularization parameter, for separating said stored data into said first data set corresponding to unscattered ones of the detected photons and a second data set corresponding to scattered ones of the detected photons;
• summing said second data set for each of said predetermined grid points on said coarser grid for determining a number of said scattered ones of said detected photons;
• interpolating from said second data set for each of said predetermined grid points on said coarser grid for producing a data set corresponding to said scattered ones of the detected photons for each of said predetermined number of grid points;
• subtracting said data set corresponding to said scattered ones of the detected photons for each of said predetermined number of grid points from a summation of said stored data corresponding to the detected photons for each of said predetermined number of grid points, to produce at each of said predetermined number of grid points a data set corresponding to unscattered ones of the detected photons;
• and
• forming the image utilizing said number of said unscattered ones of said detected photons.

A method of producing an image having reduced effects of Compton scattered photons detected in a gamma ray detection arrangement, the method comprising the steps of:

• receiving data responsive to energy states of the detected photons and storing said data in memory locations corresponding to predetermined image grid points;
• grouping said stored data, whereby a coarser grid having fewer image grid points is produced;
• calibrating the gamma ray detection arrangement by utilizing a spectral shape corresponding to a calibration function which is expected to correspond to a first data set corresponding to unscattered ones of the detected photons and by utilizing spectral shapes for mono-energetic gamma rays the energies of which are higher than the energy of the gamma ray of primary interest and by utilizing spectral shapes for mono-energetic gamma rays the energies of which are lower than the energy of the gamma ray of primary interest;
• processing said stored data for at least selected ones of said predetermined grid points using as a model of the unscattered spectrum a set of parameters, one for each energy channel, and employing minimization of a function which includes a product of an energy regularization term times an energy regularization parameter, for separating said stored data into said first data set corresponding to unscattered ones of the detected photons and a second data set corresponding to scattered ones of the detected photons;
• summing said first data set for each of said predetermined grid points on said coarser grid for determining a number of said unscattered ones of said detected photons;
• interpolating from said first data set for each of said predetermined grid points on said coarser grid for producing a data set corresponding to said unscattered ones of the detected photons for each of said predetermined number of grid points;
• and
• forming the image utilizing said number of said unscattered ones of said detected photons.

A method of producing an image having reduced effects of Compton scattered photons detected in a gamma ray detection arrangement, the method comprising the steps of:

• receiving data responsive to energy states of the detected photons and storing said data in memory locations corresponding to predetermined image grid points;
• grouping said stored data, whereby a coarser grid having fewer image grid points is produced;
• calibrating the gamma ray detection arrangement by utilizing a spectral shape corresponding to a calibration function which is expected to correspond to a first data set corresponding to unscattered ones of the detected photons and by utilizing spectral shapes for mono-energetic gamma rays whose energies are higher than the energy of the gamma ray of primary interest and by utilizing spectral shapes for mono-energetic gamma rays whose energies are lower than the energy of the gamma ray of primary interest;
• processing said stored data for at least selected ones of said predetermined grid points using as a model of the unscattered spectrum a set of parameters, one for each energy channel, and employing minimization of a function which includes a product of an energy regularization term times an energy regularization parameter, as well as a product of a spatial regularization term times a spatial regularization parameter for separating said stored data into said first data set corresponding to unscattered ones of the detected photons and a second data set corresponding to scattered ones of the detected photons;
• summing said first data set for each of said predetermined grid points on said coarser grid for determining a number of said unscattered ones of said detected photons;
• interpolating from said first data set for each of said predetermined grid points on said coarser grid for producing a data set corresponding to said unscattered ones of the detected photons for each of said predetermined number of grid points;
• and
• forming the image utilizing said number of said unscattered ones of said detected photons.

A method of producing an image having reduced effects of Compton scattered photos detected in a gamma ray detection arrangement, the method comprising the steps of:

• receiving data responsive to energy states of the detected photons and storing said data in memory locations corresponding to predetermined image grid points;
• grouping said stored data, whereby a coarser grid having fewer image grid points is produced;
• calibrating the gamma ray detection arrangement by utilizing a spectral shape corresponding to a calibration function which is expected to correspond to a first data set corresponding to unscattered ones of the detected photons;
• processing said stored data for at least selected ones of said predetermined grid points employing minimization of a function which includes a product of a spatial regularization term times a spatial regularization parameter, for separating said stored data into said first data set corresponding to unscattered ones of the detected photons and a second data set corresponding to scattered ones of the detected photons;
• summing said first data set for each of said predetermined grid points on said coarser grid for determining a number of said unscattered ones of said detected photons;
• interpolating from said first data set for each of said predetermined grid points on said coarser grid for producing a data set corresponding to said unscattered ones of the detected photons for each of said predetermined number of grid points;
• and
• forming the image utilizing said number of said unscattered ones of said detected photons.

A method of producing an image having reduced effects of Compton scattered photons detected in a gamma ray detection arrangement, the method comprising the steps of:

• receiving data responsive to energy states of the detected photons and storing said data in memory locations corresponding to predetermined image grid points;
• calibrating the gamma ray detection arrangement by acquiring a spectral shape corresponding to a calibration function which is expected to correspond to a first data set corresponding to unscattered ones of the detected photons and by acquiring spectral shapes for mono-energetic gamma rays whose energies are higher than the energy of the gamma ray of primary interest and by acquiring spectral shapes for mono-energetic gamma rays whose energies are lower than the energy of the gamma ray of primary interest;
• processing said stored data for at least selected ones of said predetermined grids point using as a model of the unscattered spectrum a set of parameters, one for each energy channel, and employing minimization of a function which includes a product of an of a spatial regularization term times a spatial regularization parameter for separating said stored data into said first data set corresponding to unscattered ones of the detected photons and a second data set corresponding to scattered ones of the detected photons;
• summing said first data set for each of said selected ones of said predetermined grid points for determining a number of said unscattered ones of said detected photons;
• and
• forming the image utilizing said number of said unscattered one of said detected photons.

A method of producing an image having reduced effects of Compton scattered photons detected in a gamma ray detection arrangement, the method comprising the steps of:

• receiving data responsive to energy states of the detected photons and storing said data in memory locations corresponding to predetermined image grid points;
• calibrating the gamma ray detection arrangement by utilizing a spectral shape corresponding to a calibration function which is expected to correspond to a first data set corresponding to unscattered ones of the detected photons and by utilizing spectral shapes for mono-energetic gamma rays the energies of which are higher than the energy of the gamma ray of primary interest and by utilizing spectral shapes for mono-energetic gamma rays, the energies of which are lower than the energy of the gamma ray of primary interest;
• processing said stored data for at least selected ones of said predetermined grid points using as a model of the unscattered spectrum a set of parameters, one for each energy channel, and employing minimization of a function which includes a product of an energy regularization term times an energy regularization parameter, stepping through various values of energy shift, performing a minimization for each, and choosing the correct shift by a specified criterion, for separating said stored data into said first data set corresponding to unscattered ones of the detected photons and a second data set corresponding to scattered ones of the detected photons;
• summing said first data set for each of said selected ones of said predetermined grid points for determining a number of said unscattered ones of said detected photons;
• and
• forming the image utilizing said number of said unscattered ones of said detected photons.

A method of producing an image having reduced effects of Compton scattered photons detected in a gamma ray detection arrangement, the method comprising the steps of:

• receiving data responsive to energy states of the detected photons and storing said data in memory locations corresponding to predetermined image grid points;
• calibrating the gamma ray detection arrangement by utilizing a spectral shape corresponding to a calibration function which is expected to correspond to a first data set corresponding to unscattered ones of the detected photons and by utilizing spectral shapes for mono-energetic gamma rays the energies of which are higher than the energy of the gamma ray of primary interest and by utilizing spectral shapes for mono-energetic gamma rays, the energies of which are lower than the energy of the gamma ray of primary interest;
• processing said stored data for at least selected ones of said predetermined grid points using as a model of the unscattered spectrum a set of parameters, one for each energy channel, and employing minimization of a function which includes a product of an energy regularization term times an energy regularization parameter, as well as a product of a spatial regularization term times a spatial regularization parameter, stepping through various values of energy shift, performing a minimization for each, and choosing the correct shift by a specified criterion, for separating said stored data into said first data set corresponding to unscattered ones of the detected photons and a second data set corresponding to scattered ones of the detected photons;
• summing said first data set for each of said selected ones of said predetermined grid points for determining a number of said unscattered ones of said detected photons;
• and
• forming the image utilizing said number of said unscattered ones of said detected photons.