Abstract:
A method for combining UNFOLD with a parallel magnetic resonance imaging (MRI) technique, such as SMASH, SENSE, or SPACE-RIP is provided. When acquiring only one n th  of the usual amount of k-space data, data is acquired n times faster, but n signals will overlap in the resulting images. By spreading the n signals over all of the available temporal frequency bandwidth, UNFOLD reduces the amount of overlap to n/2. A parallel imaging method with an acceleration n/2 can finish the reconstruction by separating the n/2 overlapped signals. The result is a time series of non-corrupted images that are acquired n times faster than normal.

Description:
This application claims that benefit of provisional application Ser. No. 60/285,399 filed on Apr. 20, 2001. 
    
    
     FIELD OF THE INVENTION 
     The present application relates generally to reconstruction methods for magnetic resonance (MR) image data. 
     BACKGROUND OF THE INVENTION 
     UNFOLD is a method disclosed in U.S. Pat. No. 6,144,873 to Madore et al., which is herein incorporated by reference, for data encoding to improve temporal resolution in magnetic resonance imaging. UNFOLD can provide an acceleration rate of nearly 2. Parallel imaging forms a family of methods that also aim at improving temporal resolution in MRI. SMASH and SENSE are examples of parallel imaging methods. 
     It has previously been proposed to combine the methods of UNFOLD with SENSE or SMASH in the publication entitled  Method for Combining UNFOLD with SENSE or SMASH,  8 PROC. INTL. SOC. MAG. RESON. MED. 1507 (2000) by Peter Kellman &amp; Elliot R. McVeigh. When the UNFOLD method is combined with SENSE or SMASH, acceleration is nearly doubled compared to using SMASH or SENSE alone. With the disclosed method, however, the dynamic portion of the field of view (FOV) is typically constrained to one quarter of the FOV. Thus, the remaining three-quarters of the FOV typically cannot display fully dynamic features of the image sought to be viewed. In contrast, the present method provides high temporal resolution to a region twice bigger; i.e., half the FOV. 
     SUMMARY OF THE INVENTION 
     One embodiment of the invention is a method for combining an UNFOLD technique with a parallel MR imaging technique to obtain of an object an MR image having a one-half dynamic portion. The method includes (a) obtaining k-space information about the object at a first time point and a first set of k-space locations; (b) obtaining k-space information about the object at a second time point and a second set of k-space locations, wherein at least one of the k-space locations in said second set is not contained in said first set, (c) obtaining information for images at the first and the second time points using the first and the second sets of k-space data, respectively, said images containing spatially aliased and non-aliased components, the image having image pixels; (d) decomposing time variations of one of the image pixels into its frequency content; (e) for a predetermined frequency of the frequency content, using a parallel imaging technique to separate the aliased and the non-aliased components that are overlapped; (f) repeating step (e) for a plurality of frequencies; and (g) repeating steps (d) through (f) for a plurality of image pixels. 
     An advantage of one or more embodiments of the invention include combining the MRI techniques of UNFOLD with parallel imaging while retaining one-half of a dynamic field of view and obtaining an acceleration nearly twice higher than would be obtained with parallel imaging alone. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a diagram of an image pixel after combining UNFOLD with a parallel magnetic imaging technique without using the invention; 
     FIG. 1B is a diagram of time frames showing the UNFOLD acquisition technique; 
     FIG. 2 is a diagram of four image pixels after using an embodiment of the invention on the data of the image pixel of FIG. 1; 
     FIG. 3 is a graph of amplitude vs. frequency for an image pixel that has four spectra after acquiring data using UNFOLD with parallel magnetic imaging technique; 
     FIG. 4 is a flowchart for combining UNFOLD with a parallel magnetic imaging technique; 
     FIG. 5 is another flowchart for combining UNFOLD with a parallel magnetic imaging technique; 
     FIG. 6 is a reconstructed MR image in which the acquired data was reconstructed using a simple root-sum-of-squares algorithm instead of the present UNFOLD-SENSE hybrid method; and 
     FIG. 7 is the reconstructed MR image of FIG. 6 after using an embodiment of the invention. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     FIG. 1 shows a representation of an image pixel  10  where an acceleration factor of 4 was achieved, but the acquired data is reconstructed normally instead of using the present method. The data is obtained by acquiring only one line of every 4, and shifting the sampling function by 2 lines from time frame to time frame, as required by UNFOLD (See FIG.  1 B). Due to four-fold spatial aliasing, the image pixel  10  has the data for four spatial points P A , P B , P C  and P D  located therein. The spatial aliasing occurred because not enough k-space data was acquired for the area of the MRI image sought to be produced. In this example, only a quarter of all the k-space lines were actually measured, and without correction the acquired field of view (FOV) is 4 times smaller than the full FOV to be reconstructed. If the data of FIG. 1 is reconstructed without correction, an image such as that shown in FIG. 7 would be shown in which at each pixel, the data for four spatial points would be displayed. 
     FIG. 2 shows a representation of four image pixels  14 ,  16 ,  18  and  20  labeled P A , P B , P C  and P D , correctly separated and mapped after applying one of the embodiments of the invention. Each spatial point P A , P B , P C  and P D  corresponds to only one pixel. The spatial points  16  and  18  are fully dynamic and thus can display a dynamic object. The spatial points  14  and  20  are less dynamic and cannot fully show the dynamic properties of an object. 
     FIG. 3 shows a spectrum  22  for the pixel  10  of FIG. 1 in the temporal frequency domain before using the present invention. The spectrum  22  can be obtained by taking the fast Fourier transform of the pixel  10  of FIG.  1 . The spectrum has spectral information for four spectra  24  (and  32 ),  26 ,  28  (and  34 ) and  30  that correspond to spatial points P A , P B , P C  and P D . The spectra  26  and  28  (and  34 ) for P B  and P C  are wider than the spectra  24  (and  32 ) and  30  for P A  and P D  because they correspond to fully dynamic material in the imaged object rather than less dynamic material. In this example, no more than two of the four spectra overlap at any given temporal frequency. For example, spectra  26  and  30  for P B  and P D  overlap in the shaded area  36  around direct current (DC). Spectra  24  and  28  for P A  and P C  overlap in the shaded areas  38   a  around Nyquist. Spectra P B , and P C  overlap at  40  and  40   b  in the spectrum. Spectra like the one in FIG. 3 are cyclic, meaning that the right-most frequency point in the spectrum is actually the same as the left-most one, both of which are the Nyquist Frequency. Thus, region  38   a  and  38   b  form really only one continuous region. 
     Embodiments of the invention take advantage that only two spectra overlap at any given temporal frequency. (At any given temporal frequency, 2 of the 4 spectra in FIG. 3 are assumed to have a negligible contribution.) The other two overlapped signals of this given frequency would be separated using an MR imaging technique, such as parallel imaging. 
     With the invention, UNFOLD is combined with a parallel imaging technique, such as SENSE or SMASH. SENSE is typically applied to a time series of images one time frame at a time. However, because of the linearity characteristic of the Fourier transform, SENSE can also be applied one temporal frequency at a time. SENSE is able to separate two overlapped signals at any one frequency. The SENSE technique can be provided with information that certain spectra did not contribute to a specific frequency being considered by SENSE. For example, SENSE can be provided with information that spectra  24  and  28  for P A  and P C  are known to have not contributed to the measured DC signal, for example. This is done by zeroing the regions  14  and  18  of the FOV in FIG. 2 in all the sensitivity maps that are input into SENSE for the treatment of DC, which will “inform” SENSE that only 2 spatial points, P B  and P D , are overlapped when considering DC signal. Thus, SENSE will be able to separate the P B , and P D  signals at DC and the two overlapped signals at any given frequency in FIG.  3 . 
     Flowcharts 
     FIG. 4 shows a flowchart  50  for an embodiment of a method of combining UNFOLD with a parallel magnetic resonance imaging (MRI) technique. The method begins at  52 , with obtaining an MRI data set that was acquired in the way required by the UNFOLD technique combined with the parallel MRI technique, such as SENSE or SMASH (See FIG.  1 B). At least some of the points in the data set will have at least four spectra in a temporal frequency domain. At  54 , image pixels are Fourier transformed in time. At  56 , for a given frequency, SENSE is informed that some of the overlapped object locations are not expected to contribute at this frequency. At  58 , the remaining, overlapped signals are separated using parallel imaging. At  60  and  62 , the method is continued for all temporal frequencies and all image pixels, respectively. 
     FIG. 5 presents another embodiment of how UNFOLD can be combined with a parallel MR imaging technique. The method begins at  66 , at which k-space information is obtained about the object at a first time point and a first set of k-space locations. At  68 , k-space information is obtained about the object at a second time point and a second set of k-space locations, wherein at least one of the k-space locations in said second set is not contained in said first set. At  70 , information is obtained for images at the first and the second time points using the first and the second sets of k-space data, respectively. The images will have image pixels and will contain spatially aliased and non-aliased components. At  72 , time variations of one of the image pixels are decomposed into its frequency content. For example, the Fourier transform of the image pixel can be taken through time. At  74 , for a predetermined frequency of the frequency content, a parallel imaging technique is used to separate the aliased and the non-aliased components that are overlapped. At  76 , step  74  is repeated for a plurality of frequencies. At  78 , steps  74  and  76  are repeated for a plurality of image pixels. 
     Experimental Results 
     The experimental data of FIGS. 6 and 7 were obtained by taking 18 time frames of a static phantom with a four-coil cardiac array. Only 70% of the k-space matrix contained data, and only one k-space line every 4 was used in this truncated k-space matrix (partial Fourier was applied along with SENSE and UNFOLD). The FOV and spatial resolution of a full 256 line k-space matrix was obtained with only 0.7×0.5×0.5×256=45 lines. 
     FIG. 6 shows an image reconstructed from the experimental data in which fourfold aliasing is present after combining UNFOLD with SENSE and without using the invention. In FIG. 7, the four-fold aliasing of FIG. 6 is completely corrected by using the invention. The reconstructed image of FIG. 7 includes a dynamic portion  42  and less dynamic portions  44  and  46 . 
     A noisy data set for FIG. 7 was intentionally chosen, as noise is an easily observable indicator of temporal resolution. The UNFOLD part of the process does not reduce the signal-to-noise (SNR) efficiency; any SNR decrease/increases comes from a corresponding temporal resolution increase/decrease. The dynamic half of the reconstructed FOV was given a temporal resolution five times higher than the outer half, and this extra resolution comes hand-in-hand with an increase in noise in the dynamic half by a factor of square-root of five. The SENSE part of the algorithm, on the other hand, may amplify noise in some locations (a well-known weakness of SENSE). The invention can be very effective in certain applications, such as cardiac imaging, in which the heart can occupy the fully dynamic half of the full FOV. 
     The methods of the invention can be accomplished through computer software. The software can be stored on computer usable medium for storing data, such as, for example, but not limited to, floppy disks, magnetic tape, zip disks, hard drives, CD-ROM, optical disks, or a combination of these. 
     Thus, the MRI techniques of UNFOLD and parallel imaging can be combined while retaining greater than one-quarter of a dynamic field of view. By itself, UNFOLD can typically achieve an acceleration factor of nearly 2. When combined with either SENSE or SMASH, however, UNFOLD can provide half of a fully dynamic FOV and can provide an acceleration nearly twice higher than that of parallel imaging alone (the method can be easily extended to higher acceleration factors). It should be understood that the order of the proposed steps may easily be changed; for example, one could perform the filtering operations on k-space data and then generate images, rather than generating images before performing the filtering operations. 
     Having thus described at least one illustrative embodiment of the invention, various alterations, modifications and improvements will readily occur to those skilled in the art. Such alterations, modifications and improvements are intended to be within the scope and spirit of the invention. Accordingly, the foregoing description is by way of example only and is not intended as limiting. The invention&#39;s limit is defined only in the following claims and the equivalents thereto.