Distortion reduction in projection imaging by manipulation of fourier transform of projection sample

Claim 2

An imaging system of the kind in which an image of an object is reconstructed from projection samples by (a) transforming said samples to Fourier transform values, (b) deriving a grid of values from said Fourier transform values, and (c) inverse transforming said grid to obtain image values each having a distance from an origin of said image, the system comprising means for distributing said Fourier transform values to said grid of values in accordance with a predefined procedure which subjects said image values to distortion, and means for reducing said distortion by applying to said image values, a correction function that defines, for each of said image values, a weighting factor which is a function of a distance of said image value from an origin of said image.

Claim 3

The imaging system of claim 1 wherein said means for distributing comprises means for assigning each of said Fourier transform values to at least one of the nearest points on said grid.

Claim 4

The imaging system of claim 2 wherein said means for distributing comprises means for assigning each of said Fourier transform values to a single point which is nearest point on said grid to said Fourier transform value.

Claim 5

The imaging system of claim 3 wherein said correction function is of the type ##EQU10## where x, y, z represent the components of distance of the location of an image value that corresponds to said Fourier transform value from an origin of said image, G represents the total number of points of the grid in the x and y directions, and G z represents the total number of points of the grid in the z direction.

Claim 6

The imaging system of claim 2 wherein said means for distributing comprises means for assigning each of said Fourier transform values to Q points on said grid that are nearest to said Fourier transform value and define the space within which said Fourier transform value lies (Q=2 D where D is the number of dimensions of said image).

Claim 7

The imaging system of claim 2 or 5 wherein said correction function is of the type ##EQU11## where x, y, z represent the components of distance of the location of an image value that corresponds to said Fourier transform value from an origin of said image, G represents the total number of points of the grid in the x and y directions, and G z represents the total number of points of the grid in the z direction.

Claim 8

An imaging system of the kind in which an image of an object is reconstructed from projection samples by (a) transforming said samples to Fourier transform values, (b) deriving a grid of values from said Fourier transform values, and (c) inverse transforming said grid to obtain image values each having a distance from an origin of said image, the system comprising means for increasing the number and reducing the spacing of said Fourier transform values in the Fourier transform domain, means for distributing said Fourier transform values to said grid of values in accordance with a predefined procedure which subjects said image values to distortion, and means for reducing said distortion by applying to said projection samples, a correction function that defines, for each of said projection samples, a weighting factor which is a function of a distance of said projection samples from a sample that corresponds to an origin of said object.

Claim 9

An imaging system of the kind in which an image of an object is reconstructed from projection samples by (a) transforming said samples to Fourier transform values, (b) deriving a grid of values from said Fourier transform values, and (c) inverse transforming said grid to obtain image values each having a distance from an origin of said image, the system comprising means for increasing the number and reducing the spacing of said Fourier transform values in the Fourier transform domain, means for distributing said Fourier transform values to said grid of values in accordance with a predefined procedure which subjects said image values to distortion, and means for reducing said distortion by applying to said projection samples, a correction function that defines, for each of said projection samples, a weighting factor which is a function of a distance of said projection samples from a sample that corresponds to an origin of said object.

Claim 10

The system of claim 7 further comprising means for reducing said distortion by applying to said image values, correction function that defines, for each of said image values, a weighting factor which is a function of a distance of the location of said image value from an origin of said image.

Claim 11

The imaging system of claim 8 wherein said predefined procedure equates each interpolated value to a single Fourier transform value that is nearest to said interpolated value.

Claim 12

The imaging system of claim 9 wherein said means for reducing comprises means for dividing each said projection sample by said weighting factor.

Claim 13

The imaging system of claim 7 or 9 wherein said correction function is of the type ##EQU12## where x and z represent distances of a given projection sample from an origin of said object, M corresponds to a number of projection samples in the x direction, and M z corresponds to a number of projection samples in the z direction.

Claim 14

The imaging system of claim 7 wherein said predefined procedure equates each interpolated value based on a plurality, Q, of Fourier transform values that are nearest to said interpolated value and define the space within which said interpolated value lies (Q=2 D-1 where D is the number of dimensions of said image).

Claim 15

The imaging system of claim 7 or 12 wherein said correction function is of the type ##EQU13## where x and z represent distances of a given projection sample from an origin of said object, M corresponds to a number of projection samples in the x direction, and M z corresponds to a number of projection samples in the z direction.

Claim 16

An imaging system of the kind in which an image of an object is reconstructed from projection samples by (a) transforming said samples to Fourier transform values, (b) deriving a grid of values from said Fourier transform values, and (c) inverse transforming said grid to obtain image values, the system comprising means for distributing said Fourier transform values to said grid of values in accordance with a predefined procedure which subjects said image values to distortion, said predefined procedure distributing each of said Fourier transform values without regard to the distribution of any other said transform value, and means for reducing said distortion by applying to said image values, a correction function that corresponds to said predefined procedure.

Claim 17

An imaging system of the kind in which an image of an object is reconstructed from projection samples by (a) transforming said samples to Fourier transform values, (b) deriving a grid of values from said Fourier transform values, and (c) inverse transforming said grid to obtain image values, the system comprising means for distributing said Fourier transform values to said grid of values in accordance with a predefined procedure which subjects said image values to distortion, said predefined procedure distributing each of said Fourier transform values without regard to the distribution of any other said transform value, and means for reducing said distortion by applying to said image values, a correction function that corresponds to said predefined procedure.

Claim 18

An imaging system of the kind in which an image of an object is reconstructed from projection samples by (a) transforming said samples to Fourier transform values (b) deriving a grid of values from said Fourier transform values, and (c) inverse transforming said grid to obtain image values, the system comprising means for distributing said Fourier transform values to said grid of value sin accordance with a predefined procedure which subjects said image values to distortion, said predefined procedure distributing each of said Fourier transform values based on relative distances of said transform value to at least one of the nearest points of said grid, and means for reducing said distortion by applying to said image values, a correction function that corresponds to said predefined procedure.

Claim 19

An imaging system of the kind in which an image of an object is reconstructed from projection samples by (a) transforming said samples to Fourier transform values (b) deriving a grid of values from said Fourier transform values, and (c) inverse transforming said grid to obtain image values, the system comprising means for distributing said Fourier transform values to said grid of value sin accordance with a predefined procedure which subjects said image values to distortion, said predefined procedure distributing each of said Fourier transform values based on relative distances of said transform value to at least one of the nearest points of said grid, and means for reducing said distortion by applying to said image values, a correction function that corresponds to said predefined procedure.

Claim 20

The imaging system of claim 1, 7, 14, or 15 wherein said image is two-dimensional.

Claim 21

The imaging system of claim 1, 7, 14, or 15 wherein said image is three-dimensional.

Claim 22

An imaging method of the kind in which an image of an object is reconstructed from projection samples by (a) transforming said samples to Fourier transform values, (b) deriving a grid of values from said filtered Fourier transform values, and (c) inverse transforming said grid to obtain image values each having a distance from an origin of said image, the method comprising distributing said Fourier transform values to said grid of values in accordance with a predefined procedure which subjects said image values to distortion, and reducing said distortion by applying to said image values, a correction function that defines, for each of said image values, a weighting factor which is a function of a distance of said image value from an origin of said image.

Claim 23

An imaging method of the kind in which an image of an object is reconstructed from projection samples by (a) transforming said samples to Fourier transform values, (b) deriving a grid of values from said filtered Fourier transform values, and (c) inverse transforming said grid to obtain image values each having a distance from an origin of said image, the method comprising distributing said Fourier transform values to said grid of values in accordance with a predefined procedure which subjects said image values to distortion, and reducing said distortion by applying to said image values, a correction function that defines, for each of said image values, a weighting factor which is a function of a distance of said image value from an origin of said image.

Claim 24

The method of claim 18 wherein said distributing comprises assigning each of said Fourier transform values to at least one of the nearest points on said grid.

Claim 25

The method of claim 19 wherein said distributing comprises assigning each of said Fourier transform values to a single point which is the nearest point on said grid to said Fourier transform value.

Claim 26

The method of claim 20 wherein said correction function is one of the type ##EQU14## where x, y, z represent the components of distance of the location of an image value that corresponds to said Fourier transform value from an origin of said image, G represents the total number of points of the grid in the x and y directions, and G z represents the total number of points of the grid in the z direction.

Claim 27

The method of claim 19 wherein said distributing comprises assigning each of said Fourier transform values to Q points on said grid that are nearest to said Fourier transform value and define the space within which said Fourier transform value lies (Q=2 D where D is the number of dimensions of said image).

Claim 28

The method of claim 19 or 22 wherein said correction function is of the type ##EQU15## ##EQU16## where x, y, z represent the components of distance of the location of an image value that corresponds to said Fourier transform value from an origin of said image, G represents the total number of points of the grid in the x and y directions, and G z represents the total number of points of the grid in the z direction.

Claim 29

An imaging method of the kind in which an image of an object is reconstructed from projection samples by (a) transforming said samples to Fourier transform values, (b) deriving a grid of values from said Fourier transform values, and (c) inverse transforming said grid to obtain image values each having a distance from an origin of said image, the method comprising increasing the number and reducing the spacing of said Fourier transform values in the Fourier transform domain, distributing said Fourier transform values to said grid of values in accordance with a predefined procedure which subjects said image values to distortion, and reducing said distortion by applying to said projection samples, a correction function that defines, for each of said projection samples, a weighting factor which is a function of a distance of said projection sample from a sample that correspond to an origin of said object.

Claim 30

An imaging method of the kind in which an image of an object is reconstructed from projection samples by (a) transforming said samples to Fourier transform values, (b) deriving a grid of values from said Fourier transform values, and (c) inverse transforming said grid to obtain image values each having a distance from an origin of said image, the method comprising increasing the number and reducing the spacing of said Fourier transform values in the Fourier transform domain, distributing said Fourier transform values to said grid of values in accordance with a predefined procedure which subjects said image values to distortion, and reducing said distortion by applying to said projection samples, a correction function that defines, for each of said projection samples, a weighting factor which is a function of a distance of said projection sample from a sample that correspond to an origin of said object.

Claim 31

The method of claim 24 wherein said predefined procedure equates each interpolated value to a single Fourier transform value that is nearest to said interpolated value.

Claim 32

The method of claim 24 or 25 wherein said correction function is of the type ##EQU17## where x and z represent distances of a give projection sample from an origin of said object, M corresponds to a number of projection samples in the x direction, and M z corresponds to a number of projection samples in the z direction.

Claim 33

The method of claim 24 wherein said predefined procedure equates each interpolated value based on a plurality, Q, of Fourier transform values that are nearest to said interpolated value and define the space within which said interpolated value lies (Q=2 D-1 where D is the number of dimensions of said image).

Claim 34

The method of claim 24 or 27 wherein said correction function is of the type ##EQU18## ##EQU19## where x and z represent distances of a given projection sample from an origin of said object, M corresponds to a number of projection samples in the x direction, and M z corresponds to a number of projection samples in the z direction.

Claim 35

The method of claim 24 wherein said reducing comprises dividing each said projection sample by said weighting factor.

Claim 36

An imaging method of the kind in which an image of an object is reconstructed from projection samples by (a) transforming said samples to Fourier transform values, (b) deriving a grid of values from said filtered Fourier transform values, and (c) inverse transforming said grid to obtain image values each having a distance from an origin of said image, the method comprising distributing said Fourier transform values to said grid of values in accordance with a predefined procedure which subjects said image values to distortion, said predefined procedure distributing each of said Fourier transform values based on relative distances of said transform value to points of said grid, reducing said distortion by applying to said image values, a correction function that corresponds to said predefined procedure.

Claim 37

An imaging method of the kind in which an image of an object is reconstructed from projection samples by (a) transforming said samples to Fourier transform values, (b) deriving a grid of values from said filtered Fourier transform values, and (c) inverse transforming said grid to obtain image values each having a distance from an origin of said image, the method comprising distributing said Fourier transform values to said grid of values in accordance with a predefined procedure which subjects said image values to distortion, said predefined procedure distributing each of said Fourier transform values based on relative distances of said transform value to points of said grid, reducing said distortion by applying to said image values, a correction function that corresponds to said predefined procedure.

Claim 38

An imaging method of the kind in which an image of an object is reconstructed from projection samples by (a) transforming said samples to Fourier transform values, (b) deriving a grid of values from said filtered Fourier transform values, and (c) inverse transforming said grid to obtain image values each having a distance from an origin of said image, the method comprising distributing said Fourier transform values to said grid of values in accordance with a predefined procedure which subjects said image values to distortion, said predefined procedure distributing each of said Fourier transform values to at least one of the nearest points of said grid without regard to the distribution of any other transform point, reducing said distortion by applying to said image values, a correction function that corresponds to said predefined procedure.

Claim 39

An imaging method of the kind in which an image of an object is reconstructed from projection samples by (a) transforming said samples to Fourier transform values, (b) deriving a grid of values from said filtered Fourier transform values, and (c) inverse transforming said grid to obtain image values each having a distance from an origin of said image, the method comprising distributing said Fourier transform values to said grid of values in accordance with a predefined procedure which subjects said image values to distortion, said predefined procedure distributing each of said Fourier transform values to at least one of the nearest points of said grid without regard to the distribution of any other transform point, reducing said distortion by applying to said image values, a correction function that corresponds to said predefined procedure.

Claim 40

The imaging method of claim 18, 24, 30, or 31 wherein said image is two-dimensional.

Claim 41

The imaging method of claim 17, 23, 30, or 31 wherein said image is three-dimensional.