Rotating and warping projector/backprojector for converging-beam geometries

A diagnostic imaging system for reconstructing a volume image in an image memory from emission data projections collected at a plurality of projection angles by a radiation detector head having a convergent ray collimator, the diagnostic imaging system comprising:

• a protector for projecting the volume image stored in the image memory along a selected projection direction to form a two-dimensional reprojection along the selected projection direction, the projector including a warping means for transforming the volume image such that rays which converge at a common angle with the convergent ray collimator become parallel;
• a projection combining means for combining each two-dimensional reprojection from the projector with a collected emission data projection in a common projection direction to generate a two-dimensional data array;
• a backprojector for backprojecting the two-dimensional data array to form a volume of correction factors, the backprojector including an unwarping means for transforming the backprojected data arrays such that parallel rays converge at the common angle with the convergent ray collimator;
• a volumetric image updating means for correcting the volume image in the image memory in accordance with the volume of correction factors;
• a memory for storing a series of functions for correcting for at least one of geometric point response and scatter functions which are scaled in accordance with a depth of each layer in the volume image;
• the backprojector and projector each including a convolver for convolving data with a corresponding function.

A diagnostic imaging system for reconstructing a volume image in an image memory from emission data projections collected at a plurality of projection angles by a radiation detector head having a convergent ray collimator, the diagnostic imaging system comprising:

• a rotation processor for rotating the volume image from the volume image memory to a preselected projection direction;
• a projector for projecting the volume image stored in the image memory along the preselected projection direction to form a two-dimensional reprojection along the preselected projection direction, the projector including a warping means for transforming the volume image such that rays which converge at a common angle with the convergent ray collimator become parallel;
• a convolver for convolving each layer of the volume image after transformation by the warping means by at least one of a point response function and a scatter correction function, the function being weighted in accordance with the depth of each layer into the volume image;
• an integrator for adding corresponding pixels in each layer to form the two-dimensional reprojection;
• a projection combining means for combining each two-dimensional reprojection from the projector with a collected emission data projection in a common projection direction to generate a two-dimensional data array;
• a backprojector for backprojecting the two-dimensional data array to form a volume of correction factors, the backprojector including an unwarping means for transforming the backprojected data arrays such that parallel rays converge at the common angle with the convergent ray collimator;
• and,
• a volumetric image updating means for correcting the volume image in the image memory in accordance with the volume of correction factors.

A diagnostic imaging system for reconstructing a volume image in an image memory from emission data projections collected at a plurality of projection angles by a radiation detector head having a convergent ray collimator, the diagnostic imaging system comprising:

• a projector for projecting the volume image stored in the image memory along a selected projection direction to form a two-dimensional reprojection along the selected projection direction, the projector including a warping means for transforming the volume image such that rays Which converge at a common angle With the convergent ray collimator become parallel;
• a projection combining means for combining each two-dimensional reprojection from the projector with a collected emission data projection in a common projection direction to generate a two-dimensional data array;
• a backprojector for backprojecting the two-dimensional data array to form a volume of correction factors, the backprojector including:
• a duplicator for making a plurality of copies of the two-dimensional array from the projection combining means;
• a convolver for convolving each of the copies with at least one of a point response function and a scatter correction function, the function being weighted in accordance with a depth with which each copy is to be backprojected;
• an unwarping means for weighting the transformed convolved two-dimensional arrays;
• and,
• a rotation processor for rotating the transformed, convolved two-dimensional arrays to a preselected direction, forming the volume of correction factors.

In a diagnostic imaging system which includes an image memory for storing a volumetric image representation, a backprojector for backprojecting two-dimensional projection data into three-dimensional data, and a projector for projecting three-dimensional data along a preselected projection direction to generate two-dimensional reprojection data, the improvement comprising:

• a projecting combining means for combining collected projection data with reprojection data from the backprojector along common projection directions to define a two-dimensional data array, the projection combining means being connected with the backprojector such that the backprojector backprojects the two-dimensional array into a three-dimensional array;
• a means for applying at least one of a point response function and a scatter correction function to the three-dimensional array;
• an unwarping means for transforming the convolved three-dimensional array such that rays which converge at a preselected angle become parallel;
• a first rotating means for rotating the transformed three-dimensional array from the unwarping means to a preselected direction;
• a means for updating the volumetric image representation in the image memory in accordance with a sum of the convolved, transformed, and rotates three-dimensional array from the first rotating means over a plurality of projection directions;
• a second rotating means for rotating the volumetric image representation from the image memory;
• a warping means for transforming the rotated volumetric image representation from the second rotating means such that rays which converge at the preselected angle are transformed to become parallel to each other, the warping means being connected with the projector such that the rotated and transformed volumetric image representation is projected to generate the reprojection data which is conveyed to the combining means.

A method of diagnostic imaging in which a volume image is reconstructed from emission data projections collected at a plurality of projection angles by a detector head having a convergent ray collimator having a preselected convergence angle, the diagnostic imaging method comprising:

• rotating the volume image into alignment with a selected projection direction;
• transforming the volume image such that rays which converge at the preselected convergence angle become parallel;
• projecting the transformed volume image along the selected projection direction to form a two-dimensional reprojection;
• combining the two-dimensional reprojection with a collected emission data projection along the selected projection direction to generate a two-dimensional data array including determining ratios of corresponding pixels of the reprojection and the collected emission data projection to create an array of ratios;
• backprojecting the arrays of ratios to form a three-dimensional data array;
• transforming the three-dimensional data array such that parallel rays are transformed to converge at the preselected convergence angle to generate a three-dimensional array of correction factors;
• rotating the three-dimensional array of correction factors to a preselected direction;
• summing the three-dimensional arrays of correction factors corresponding to a plurality of projection directions;
• updating the volume image with the sum of the three-dimensional arrays of correction factors.

A method of diagnostic imaging in which volumetric data are reconstructed from emission data projections collected at a plurality of projection angles by a detector head having a convergent ray collimator having a preselected convergence angle, the diagnostic imaging method comprising:

• rotating the volumetric data into alignment with a selected projection direction;
• transforming the volumetric data such that rays which converge at the preselected convergence angle become parallel;
• projecting the transformed volume image along the selected projection direction to form a two-dimensional reprojections for each of a plurality of layers in the volumetric data, including convolving the volumetric data with a function that is scaled in accordance with a depth of each layer of the volumetric data;
• combining the two-dimensional reprojection with a collected emission data projection along the selected projection direction to generate a two-dimensional data array;
• backprojecting the two-dimensional data array to form a three-dimensional data array including convolving the three-dimensional data array with a function that is scaled in accordance with a depth of each layer;
• transforming the three-dimensional data array such that parallel rays are transformed to converge at the preselected convergence angle to generate a three-dimensional array of correction factors;
• rotating the three-dimensional array of correction factors to a preselected direction;
• summing the three-dimensional arrays of correction factors corresponding to a plurality of projection directions;
• updating the volumetric data with the sum of the three-dimensional arrays Of correction factors.

A method of diagnostic imaging in which a volume image is reconstructed from emission data projections collected at a plurality of projection angles by a detector head having a convergent ray collimator having a preselected convergence angle, the diagnostic imaging method comprising:

• rotating the volume image into alignment with a selected projection direction;
• transforming the volume image such that rays which converge at the preselected convergence angle become parallel;
• projecting the transformed volume image along the selected projection direction to form two-dimensional reprojections;
• combining each two-dimensional reprojection with collected emission data projection along the selected projection direction to generate a two-dimensional data array;
• making a plurality of copies of the two-dimensional array;
• convolving each copy of the two-dimensional array with a function which is weighted in accordance with a depth into a three-dimensional array to which each copy is to be backprojected;
• backprojecting each convolved two-dimensional array to form the three-dimensional array;
• transforming the three-dimensional data array such that parallel rays are transformed to converge at the preselected convergence angle to generate a three-dimensional array of correction factors;
• rotating the three-dimensional array of correction factors to a preselected direction;
• summing the three-dimensional arrays of correction factors corresponding to a plurality of projection directions;
• updating the volume image with the sum of the three-dimensional arrays of correction factors.

A method of diagnostic imaging in which a volume image is reconstructed from emission data projections collected at a plurality of projection angles by a detector head having a convergent ray collimator having a preselected convergence angle, the diagnostic imaging method comprising:

• rotating the volume image into alignment with a selected projection direction;
• transforming the volume image such that rays which converge at the preselected convergence angle become parallel;
• convolving each layer of the volume image after transformation with a function that is weighted in accordance with a depth of each layer into the volume image;
• adding corresponding pixels in each convolved layer to form a two-dimensional reprojection;
• combining the two-dimensional reprojection with a collected emission data projection along the selected projection direction to generate a two-dimensional data array;
• backprojecting the two-dimensional data array to form a three-dimensional data array;
• transforming the three-dimensional data array such that parallel rays are transformed to converge at the preselected convergence angle to generate a three-dimensional array of correction factors;
• rotating the three-dimensional array of correction factors to a preselected direction;
• summing the three-dimensional arrays of correction factors corresponding to a plurality of projection directions;
• updating the volume image with the sum of the three-dimensional arrays of correction factors.