Method and Apparatus for the Reconstruction of MR Images

A method for producing an image of an object located in the field of view of a Magnetic Resonance (MR) imaging system, the image being reconstructed from a subset of data elements less than a raw matrix of data elements having N number of rows of data elements and M number of columns of data elements, the method comprising:

• determining a center of an echo corresponding to a column of the raw matrix and a row of the raw matrix with a data element having the largest magnitude;
• shifting the data elements of the raw matrix by whole positions to align the center of the echo with the center of the raw matrix;
• multiplying the shifted raw matrix by a low pass filter to provide a filtered matrix;
• Fourier transforming the filtered matrix to provide a low resolution complex image and divided each nonzero pixel of the low resolution complex image by its magnitude to provide a phase map;
• Fourier transforming the shifted raw matrix to provide a complex image;
• applying a phase correction to the complex image by multiplying each pixel by the complex conjugate of the corresponding pixel of the phase map;
• Fourier transforming the columns of the image to obtain a half-transformed matrix;
• calculating a blending function having blending function coefficient values for the data elements, said blending function cutting off rows of data damaged by the phase correction;
• multiplying the rows of data elements of the half-transformed matrix by corresponding blending function coefficient values;
• inverse Fourier transforming in a column direction and extracting real parts of the complex numbers to provide the image of the object.

An article of manufacture for operating a Magnetic Resonance (MR) image reconstructing system, the article of manufacture comprising a non-transitory, tangible computer-readable medium holding computer-executable instructions for performing a method for producing an image of an object located in the field of view of a Magnetic Resonance (MR) imaging system, the image being reconstructed from a subset of data elements less than a raw matrix of data elements having N number of rows of data elements and M number of columns of data elements, the method comprising:

• determining a center of an echo expressed as a whole column number, a fractional column number, a whole row number and a fractional row number of the raw matrix;
• shifting the data elements of the raw matrix by whole positions to align the center of the echo, expressed as the whole column number and the whole row number, with the center of the raw matrix;
• multiplying the shifted raw matrix by a low pass filter to provide a filtered matrix;
• Fourier transforming the filtered matrix to provide a low resolution complex image and dividing each nonzero pixel of the low resolution complex image by its magnitude to provide a phase map;
• calculating a blending function that compensates for the image artifacts created by fractional misalignment of the echo center with elements of the raw matrix, said blending function being shifted by the determined fractional echo position, and having blending coefficient values corresponding to each line of raw matrix data elements;
• multiplying each data element of each row of the raw matrix by corresponding blending function coefficient values;
• performing a two-dimensional Fourier transform in row directions and column directions to provide a complex image;
• multiplying the complex image by a complex conjugate of the phase map to provide a phase corrected image;
• and
• extracting the real part of the complex numbers in the phase corrected image to provide the image of the object.