Method, system and computer product for k-space correction of gradient non-linearities

A method for reconstructing a moving table MR image, the method comprising:

• receiving an input array that includes a plurality of uncorrected k-space data points;
• reconstructing the image of a sample in response to said plurality of uncorrected k-space data points, wherein said reconstructed image is:
• 9 FT - 1 ⁢ { ∑ t ∈ T ⁢ M ′ ⁡ ( j ⁡ ( t ) ) ⁢ ( ( exp ⁡ [ i2 ⁢ ⁢ π ⁡ ( q ′ ⁡ ( t ) · k ) ] ⁢ S ⁡ ( k ) ) * ( exp ⁡ [ i2 ⁢ ⁢ π ⁡ ( p ⁡ ( t ) · k ) ] ⁢ B j ⁡ ( t ) ⁡ ( k ) ) ) }
• where FT−1 is the inverse Fourier transform, M′(j(t)) is one of said plurality of uncorrected k-space data points written in j-space form, q′(t) is the position of the sample at time t minus the position of a coil at time t, k is the k-space data point, S(k) is a sensitivity factor, p(t) is the position of the sample at time t, and Bj(t)(k) is a kernel associated with the uncorrected k-space data point.

A system for reconstructing a MR image, the system comprising:

• a MRI system including at least one gradient coil, at least one RF coil, a moving table and an input array including a plurality of uncorrected k-space data points;
• and
• a computer system in communication with said MRI system including application software to implement the method comprising:
• receiving said input array from said MRI system;
• clearing a summation array;
• for an uncorrected k-space data point in said input array performing steps that include:
• obtaining a kernel associated with said uncorrected k-space data point;
• creating corrected data in response to said uncorrected k-space data point, said input array and said kernel, wherein said creating includes:
• correcting said uncorrected k-space data point for gradient non-linearities, wherein said correcting is performed in k-space;
• and
• correcting said uncorrected k-space data point for table movement;
• and
• adding said corrected data into said summation array;
• and
• reconstructing the image in response to said summation array.

A system for reconstructing a MR image, the system comprising:

• a computer system including application software to implement a method comprising:
• receiving an input array including a plurality of uncorrected k-space data points;
• clearing a summation array;
• for an uncorrected k-space data point in said input array performing steps that include:
• obtaining a kernel associated with said uncorrected k-space data point;
• creating corrected data in response to said uncorrected k-space data point, said input array and said kernel, wherein said creating includes:
• correcting said uncorrected k-space data point for gradient non-linearities, wherein said correcting is performed in k-space;
• and
• correcting said uncorrected k-space data point for table movement;
• and
• adding said corrected data into said summation array;
• and
• reconstructing the image in response to said summation array.

A computer program product for reconstructing a MR image, the product comprising:

• a storage medium readable by a processing circuit and storing instructions for execution by the processing circuit for:
• receiving an input array including a plurality of uncorrected k-space data points;
• clearing a summation array;
• for an uncorrected k-space data point in said input array performing steps that include:
• obtaining a kernel associated with said uncorrected k-space data point;
• creating corrected data in response to said uncorrected k-space data point, said input array and said kernel, wherein said creating includes:
• correcting said uncorrected k-space data point for gradient non-linearities, wherein said correcting is performed in k-space;
• and
• correcting said uncorrected k-space data point for table movement;
• and
• adding said corrected data into said summation array;
• and
• reconstructing the image in response to said summation array.