Method for super-resolution reconstruction using focal underdetermined system solver algorithm

Abstract

Disclosed is a high-resolution image reconstruction method using a focal underdetermined system solver (FOCUSS) algorithm. The method comprises the steps of: outputting data for an image of an object; downsampling the outputted data; transforming the downsampled data into low-resolution image frequency data; and reconstructing a high-resolution image from the transformed low-resolution image frequency data by applying focal underdetermined system solver (FOCUSS) algorithm.

What is claimed is: 
     
       1. A method for forming a high-resolution image of an object, the method comprising the steps of:
 (a) using a medical device for:
 (a1) applying incident radiation to the object; 
 (a2) receiving response radiation from the object; and 
 (a3) outputting data for an image of an the object from the response radiation; 
 
 (b) downsampling the outputted data using the medical device; 
 (c) transforming the downsampled data into low-resolution image frequency data using the medical device; and 
 (d) reconstructing a, using the medical device, the high-resolution image from the transformed low-resolution image frequency data by applying a focal underdetermined system solver (FOCUSS) algorithm; and 
 (e) displaying the high-resolution image using a display for providing the high-resolution image for examining the object. 
 
     
     
       2. The method as claimed in  claim 1 , wherein, when the image is a still image, the outputted data corresponds to projection data obtained by a magnetic resonance imaging scheme, and the outputted data corresponds to radial data, the step (c) is performed by inverse Radon transformation. 
     
     
       3. The method as claimed in  claim 1 , wherein, when the image is a still image and the outputted data corresponds to spiral data, the step (c) is performed by inverse Fourier transformation. 
     
     
       4. The method as claimed in  claim 1 , wherein, when the image is a moving image, the method is performed in k-t space. 
     
     
       5. The method as claimed in  claim 4 , wherein the step (b) is performed by obtaining all data in a frequency encoding direction during a predetermined period in a time domain and random-pattern data in a phase encoding direction according to each period. 
     
     
       6. The method as claimed in  claim 4 , wherein the step (c) is performed by two-dimensional Fourier transformation. 
     
     
       7. The method as claimed in  claim 1 , wherein the step (d) further comprise the steps of:
 (1) calculating a weighting matrix from the low-resolution image frequency data; 
 (2) calculating image data from the weighting matrix and the low-resolution image frequency data satisfying a predetermined condition; and 
 (3) when the image data is converged the high-resolution image, performing inverse Fourier transformation along a time axis to reconstruct the high-resolution image; or when the image data is not converged, updating the weighting matrix by using a diagonal element of the image data and repeating the step (2) with the updated weighting matrix until the image data is converged to the high-resolution image. 
 
     
     
       8. The method as claimed in  claim 7 , wherein the low-resolution image frequency data satisfying a predetermined condition in the step (2) is calculated by Lagrangian transformation. 
     
     
       9. The method as claimed in  claim 8 , wherein when a Fourier transform transformed by the Lagrangian transformation is replaced by a Fourier transform applied along a time axis and Radon transformation, the FOCUSS algorithm is applied with respect to radial data in k or k-t space. 
     
     
       10. The method as claimed in  claim 9 , wherein the radial data corresponds to downsampled data obtained at a uniform angle. 
     
     
       11. The method as claimed in  claim 8 , wherein when a Fourier transform transformed by the Lagrangian transformation is replaced by a Fourier transform applied along a time axis and Radon transformation, the FOCUSS algorithm is applied with respect to spiral data in k or k-t space. 
     
     
       12. The method as claimed in  claim 11 , wherein the spiral data corresponds to downsampled data obtained at a uniform angle. 
     
     
       13. The method as claimed in  claim 7 , wherein the updating of weighting matrix in the step (3) is performed by applying a power factor to absolute value of the diagonal element. 
     
     
       14. The method as claimed in  claim 13 , wherein the power factor is in the range of 0.5 to 1. 
     
     
       15. A method for forming a high-resolution image of an object, the method comprising the steps of:
 (a) downsampling data representative of an image of the object at a rate lower than Nyquist sampling rate, the downsampled data being received from the object after applying incident radiation to the object using a medical device;   (b) transforming the downsampled data into low-resolution initial estimation data using the medical device applying a transformation to the downsampled data;   (c) reconstructing, using the medical device, the high-resolution image from the transformed low-resolution initial estimation data by applying a focal underdetermined system solver (FOCUSS) algorithm; and   (d) displaying the high-resolution image using a display for providing the high-resolution image for examining the object.   
     
     
       16. The method as claimed in claim 15, wherein, when the image is a still image, the data representative of the image corresponds to projection data obtained by a magnetic resonance imaging scheme, and the data representative of the image corresponds to radial data, the step (b) is performed by inverse Radon transformation. 
     
     
       17. The method as claimed in claim 15, wherein, when the image is a still image and the data representative of the image corresponds to spiral data, the step (b) is performed by inverse Fourier transformation. 
     
     
       18. The method as claimed in claim 15, wherein, when the image is a moving image, the method is performed in k-t space or k space. 
     
     
       19. The method as claimed in claim 18, wherein the step (a) is performed by obtaining all data in a frequency encoding direction during a predetermined period in a time domain and sparse data in a phase encoding direction according to each period. 
     
     
       20. The method as claimed in claim 18, wherein the step (b) is performed by a two-dimensional Fourier transformation. 
     
     
       21. The method as claimed in claim 15, wherein the step (c) further comprises the steps of: (1) calculating a weighting matrix from the low-resolution initial estimation data; (2) calculating image data from the weighting matrix and the low-resolution initial estimation data satisfying a predetermined condition; and (3) if the calculated image data of step (2) is convergent into the high-resolution image, performing an inverse Fourier transformation along a time axis to reconstruct the high-resolution image; and if the calculated image data is not convergent into the high-resolution image, updating the weighting matrix by using a diagonal element of the initial estimation data and repeating the step (2) with the updated weighting matrix until the calculated image data is convergent into the high-resolution image, and performing an inverse Fourier transformation along a time axis to reconstruct the high-resolution image. 
     
     
       22. The method as claimed in claim 21, wherein the low-resolution initial estimation data satisfying a predetermined condition in the step (2) is calculated by a Lagrangian transformation. 
     
     
       23. The method as claimed in claim 22, wherein the FOCUSS algorithm is applied with respect to radial or spiral data in k or k-t space. 
     
     
       24. The method as claimed in claim 23, wherein the radial or spiral data corresponds to the downsampled data obtained at a uniform angle. 
     
     
       25. The method as claimed in claim 21, wherein the updating of weighting matrix in the step (3) is performed by applying a power factor to an absolute value of the diagonal element of the initial estimation data. 
     
     
       26. The method as claimed in claim 25, wherein the power factor is in the range of 0.5 to 1. 
     
     
       27. The method as claimed in claim 15, wherein for a still image the step (c) further comprises the steps of: (1) calculating a weighting matrix from the low-resolution initial estimation data; (2) calculating image data from the weighting matrix and the low-resolution initial estimation data satisfying a predetermined condition; and (3) if the calculated image data of step (2) is convergent into the high-resolution image, providing the calculated image data as the high-resolution image; and if the calculated image data is not convergent into the high-resolution image, updating the weighting matrix by using a diagonal element of the initial estimation data and repeating the step (2) with the updated weighting matrix until the calculated image data is convergent into the high-resolution image. 
     
     
       28. The method as claimed in claim 15, wherein for a moving image the step (c) further comprises the steps of: (1) calculating a weighting matrix from the low-resolution initial estimation data; (2) calculating image data from the weighting matrix and the low-resolution initial estimation data satisfying a predetermined condition; and (3) if the calculated image data of step (2) is convergent into the high-resolution image, performing an inverse Fourier transformation of the calculated image data along a time axis to reconstruct the high-resolution image; and if the calculated image data is not convergent into the high-resolution image, updating the weighting matrix by using a diagonal element of the initial estimation data and repeating the step (2) with the updated weighting matrix until the calculated image data is convergent into the high-resolution image. 
     
     
       29. A magnetic resonance imaging apparatus comprising:
 a medical device for downsampling data representative of an image of the object at a rate lower than Nyquist sampling rate, the downsampled data being received from the object after applying incident radiation to the object using a medical device; transforming the downsampled data into low-resolution initial estimation data by applying a transformation to the downsampled data; and reconstructing a high-resolution image from the transformed low-resolution initial estimation data by applying a focal underdetermined system solver (FOCUSS) algorithm; and   a display for displaying the high-resolution image for providing the high-resolution image for examining the object.   
     
     
       30. A method for forming a high-resolution image of an object, the method comprising the steps of:
 (a) downsampling data representative of an image of the object at a rate lower than Nyquist sampling rate, the downsampled data being received from the object after applying incident radiation to the object using a medical device;   (b) transforming the downsampled data into low-resolution initial estimation data using the medical device applying a transformation to the downsampled data;   (c) reconstructing, using the medical device, the high-resolution image from the transformed low-resolution initial estimation data by applying a sparse recovery algorithm to the low-resolution initial estimation data, which algorithm multiplies the low-resolution initial estimation data by a weighting factor; and   (d) displaying the high-resolution image using a display for providing the high-resolution image for examining the object.   
     
     
       31. The method as claimed in claim 30, wherein the step (c) further comprises the steps of: (1) calculating the weighting matrix from the low-resolution initial estimation data; (2) calculating image data from the weighting matrix and the low-resolution initial estimation data satisfying a predetermined condition; and (3) if the calculated image data of step (2) is convergent into the high-resolution image, performing an inverse Fourier transformation along a time axis to reconstruct the high-resolution image; and if the calculated image data is not convergent into the high-resolution image, updating the weighting matrix by using a diagonal element of the initial estimation data and repeating the step (2) with the updated weighting matrix until the calculated image data is convergent into the high-resolution image, and performing an inverse Fourier transformation along a time axis to reconstruct the high-resolution image. 
     
     
       32. A magnetic resonance imaging apparatus comprising:
 a medical device for downsampling data representative of the image of the object at a rate lower than Nyquist sampling rate, the downsampled data being received from the object after applying incident radiation to the object using a medical device; transforming the downsampled data into low-resolution initial estimation data by applying a transformation to the downsampled data; and reconstructing a high-resolution image from the transformed low-resolution initial estimation data by applying a sparse recovery algorithm to the low-resolution initial estimation data, which algorithm multiplies the low-resolution initial estimation data by a weighting factor; and   a display for displaying the high-resolution image for providing the high-resolution image for examining the object.   
     
     
       33. A method for processing dynamic image data obtained from a magnetic resonance imaging (MRI) apparatus, for forming a high resolution moving image of at least a portion of a living subject, the method comprising the following steps:
 (a) downsampling a set of data representative of an moving image of the moving object from the response radiation at a rate lower than Nyquist sampling rate, the downsampled data being received from the object after applying incident radiation to the object using a medical device;   (b) transforming the downsampled data into low-resolution initial estimation data using the medical device applying a transformation to the downsampled data;   (c) reconstructing, using the medical device, the high-resolution moving image from the transformed low-resolution initial estimation data by applying a sparse recovery algorithm to the low-resolution initial estimation data, which algorithm multiplies the low-resolution initial estimation data by a weighting factor; and   (d) displaying the high-resolution moving image using a display for providing the high-resolution moving image for examining the moving object.   
     
     
       34. The method as claimed in claim 33, wherein the dynamic image data is representative of blood flow as the moving object in the portion of a living subject imaged by the MRI apparatus. 
     
     
       35. The method as claimed in claim 33, wherein the dynamic image data is representative of a beating heart as the moving object in the living subject imaged by the MRI apparatus. 
     
     
       36. The method as claimed in claim 33, wherein the sparse recovery algorithm comprises a focal underdetermined system solver (FOCUSS) algorithm. 
     
     
       37. A magnetic resonance imaging apparatus for performing a high resolution image reconstruction on data representative of an image of an object, the magnetic resonance imaging apparatus comprising:
 a medical device for downsampling a set of the data representative of the image of the object at a rate lower than Nyquist sampling rate, the downsampled data being received from the object after applying incident radiation to the object using a medical device; transforming the downsampled data into low-resolution initial estimation data by applying a transformation to the downsampled data; and reconstructing a high-resolution image from the transformed low-resolution initial estimation data by applying a sparse recovery algorithm to the low-resolution initial estimation data, which algorithm multiplies the low-resolution initial estimation data by a weighting factor; and   a display for displaying the high-resolution image for providing the high-resolution image for examining the object.   
     
     
       38. The magnetic resonance imaging apparatus of claim 37, wherein the sparse recovery algorithm comprises a focal underdetermined system solver (FOCUSS) algorithm. 
     
     
       39. A parallel imaging method for processing magnetic resonance imaging (MRI) data obtained by the use of multiple coils of an MRI apparatus, for forming a high resolution image of an object, the method comprising:
 (a) down sampling a set of MRI data from each of a respective one of the multiple coils at a rate lower than Nyquist sampling rate, the downsampled data being received from the object after applying incident radiation to the object using a medical device, where each set of MRI data is representative of the object;   (b) transforming each of the down sampled data sets into low-resolution initial estimation data sets using the medical device applying a transformation to the obtained data sets; and   (c) reconstructing, using the medical device, the high-resolution image from the transformed low-resolution initial estimation data sets by applying a sparse recovery algorithm to the low-resolution initial estimation data, which algorithm multiplies the low-resolution initial estimation data by a weighting factor; and   (d) displaying the high-resolution image using a display for providing the high-resolution image for examining the object.   
     
     
       40. The method as claimed in claim 39, wherein the sparse recovery algorithm comprises a focal underdetermined system solver (FOCUSS) algorithm. 
     
     
       41. The method as claimed in claim 39, wherein the multiple coils are parallel coils. 
     
     
       42. The method as claimed in claim 15, wherein the transformation is selected from a Fourier transformation, an inverse Fourier transformation, a Radon transformation, and an inverse Radon transformation.