1. A magnetic resonance imaging (MRI) method comprising:

2. An MRI method in accordance with claim 1 wherein assuming comprises assuming that the sum of weighted sensitivity profiles of at least one of the detectors is the function of the angle between the vector k and the k

### x axis of the k-space, the function of the radius of the cylindrical surface formed by the array of detectors, and a function of an angle between two adjacent detectors in the array.

3. An MRI method in accordance with claim 1 wherein assuming comprises assuming that the sum is provided by
${e}^{j\text{\hspace{1em}}k\left(x\text{\hspace{1em}}\mathrm{cox}\text{\hspace{1em}}\varphi +y\text{\hspace{1em}}\mathrm{sin}\text{\hspace{1em}}\varphi \right)}=\sum _{m}C\left(m,k,\varphi \right)f\left(x-{r}_{0}\mathrm{cos}\text{\hspace{1em}}m\text{\hspace{1em}}{\theta}_{0},y-{r}_{0}\mathrm{sin}\text{\hspace{1em}}m\text{\hspace{1em}}{\theta}_{0}\right),$

being the angle between the vector k and the k

### x axis of the k-space, x and y being spatial co-ordinates of an image domain, r

### o being the radius of a cylindrical surface formed by the array of detectors, and

### o being an angle between two adjacent detectors in the array.

4. An MRI method in accordance with claim 3 wherein generating comprises calculating a weighted coefficient of any of the detectors, and wherein calculating the weighted coefficient includes calculating a weighted coefficient of an m

### th detector of the array by using
$C\text{\hspace{1em}}\left(m,k,\varphi \right)=\frac{{e}^{j\text{\hspace{1em}}{\mathrm{kr}}_{0}\text{\hspace{1em}}\mathrm{cos}\text{\hspace{1em}}\left(\varphi -m\text{\hspace{1em}}{\theta}_{0}\right)}}{F\text{\hspace{1em}}\left(k\text{\hspace{1em}}\mathrm{cos}\text{\hspace{1em}}\varphi ,k\text{\hspace{1em}}\mathrm{sin}\text{\hspace{1em}}\varphi \right)},$

C(m,k,) being the weighted coefficient of the m

### th detector, F(k

### x, k

### y) being a Fourier transform of f(x,y), k

### x being equal to k cos , and k

### y being equal to k sin .

5. An MRI method in accordance with claim 1 wherein generating comprises generating at least one of additional partial backprojection signals and additional complete backprojection signals.

6. An MRI method in accordance with claim 1 further comprising:

7. An MRI method in accordance with claim 1 wherein simultaneously acquiring comprises simultaneously acquiring the partial radial backprojection signals from a cylindrical array of equally spaced m detectors surrounding the object.

8. A system comprising:

9. A system in accordance with claim 8 wherein to retrieve from the memory the controller configured to obtain the sum of weighted sensitivity profiles of at least one of the detectors, the sum being the function of the angle between the vector k and the k

### x axis of the k-space, the function of the radius of the cylindrical surface formed by the array of detectors, and a function of an angle between two adjacent detectors in the array.

10. A system in accordance with claim 8 wherein to retrieve from the memory the controller configured to obtain the sum that is provided by
${e}^{j\text{\hspace{1em}}k\left(x\text{\hspace{1em}}\mathrm{cox}\text{\hspace{1em}}\varphi +y\text{\hspace{1em}}\mathrm{sin}\text{\hspace{1em}}\varphi \right)}=\sum _{m}C\left(m,k,\varphi \right)f\left(x-{r}_{0}\mathrm{cos}\text{\hspace{1em}}m\text{\hspace{1em}}{\theta}_{0},y-{r}_{0}\mathrm{sin}\text{\hspace{1em}}m\text{\hspace{1em}}{\theta}_{0}\right),$

being the angle between the vector k and the k

### x axis of the k-space, x and y being spatial co-ordinates of an image domain, r

### o being the radius of a cylindrical surface formed by the array of detectors, and

### o being an angle between two adjacent detectors in the array.

11. A system in accordance with claim 10 wherein to produce the spatial harmonics the controller configured to calculate a weighted coefficient of any of the detectors, and wherein to calculate the weighted coefficient the controller configured to calculate a weighted coefficient of an m

### th detector of the array using
$C\text{\hspace{1em}}\left(m,k,\varphi \right)=\frac{{e}^{j\text{\hspace{1em}}{\mathrm{kr}}_{0}\text{\hspace{1em}}\mathrm{cos}\text{\hspace{1em}}\left(\varphi -m\text{\hspace{1em}}{\theta}_{0}\right)}}{F\text{\hspace{1em}}\left(k\text{\hspace{1em}}\mathrm{cos}\text{\hspace{1em}}\varphi ,k\text{\hspace{1em}}\mathrm{sin}\text{\hspace{1em}}\varphi \right)},$

C(m,k,) being the weighted coefficient of the m

### th detector, F(k

### x, k

### y) being a Fourier transform of f(x,y), k

### x being equal to k cos , and k

### y being equal to k sin .

12. A system in accordance with claim 8 wherein to generate additional backprojection signals the controller configured to generate at least one of additional partial backprojection signals and additional complete backprojection signals.

13. A system in accordance with claim 8 wherein the controller is configured to:

14. A system in accordance with claim 8 wherein the detection device is configured to acquire at the same time partial radial backprojection signals from a cylindrical array of equally spaced m detectors surrounding the object.

15. A magnetic resonance imaging (MRI) system comprising:

16. An MRI system in accordance with claim 15 wherein to retrieve from the memory the controller configured to obtain the sum of weighted sensitivity profiles of at least one of the detectors, the sum being the function of the angle between the vector k and the k

### x axis of the k-space, the function of the radius of the cylindrical surface formed by the array of detectors, and a function of an angle between two adjacent detectors in the array.

17. An MRI system in accordance with claim 15 wherein to retrieve from the memory the controller configured to obtain the sum that is provided by
${e}^{j\text{\hspace{1em}}k\left(x\text{\hspace{1em}}\mathrm{cox}\text{\hspace{1em}}\varphi +y\text{\hspace{1em}}\mathrm{sin}\text{\hspace{1em}}\varphi \right)}=\sum _{m}C\left(m,k,\varphi \right)f\left(x-{r}_{0}\mathrm{cos}\text{\hspace{1em}}m\text{\hspace{1em}}{\theta}_{0},y-{r}_{0}\mathrm{sin}\text{\hspace{1em}}m\text{\hspace{1em}}{\theta}_{0}\right),$

being the angle between the vector k and the k

### x axis of the k-space, x and y being spatial co-ordinates of an image domain, r

### o being the radius of a cylindrical surface formed by the array of detectors, and

### o being an angle between two adjacent detectors in the array.

18. An MRI system in accordance with claim 17 wherein to produce the spatial harmonics the controller configured to calculate a weighted coefficient of any of the detectors, and wherein to calculate the weighted coefficient the controller configured to calculate a weighted coefficient of an m

### th detector of the array using
$C\text{\hspace{1em}}\left(m,k,\varphi \right)=\frac{{e}^{j\text{\hspace{1em}}{\mathrm{kr}}_{0}\text{\hspace{1em}}\mathrm{cos}\text{\hspace{1em}}\left(\varphi -m\text{\hspace{1em}}{\theta}_{0}\right)}}{F\text{\hspace{1em}}\left(k\text{\hspace{1em}}\mathrm{cos}\text{\hspace{1em}}\varphi ,k\text{\hspace{1em}}\mathrm{sin}\text{\hspace{1em}}\varphi \right)},$

C(m,k,) being the weighted coefficient of the m

### th detector, F(k

### x, k

### y) being a Fourier transform of f(x,y), k

### x being equal to k cos , and k

### y being equal to k sin .

19. An MRI system in accordance with claim 15 wherein to generate additional backprojection signals the controller configured to generate at least one of additional partial backprojection signals and additional complete backprojection signals.

20. An MRI system in accordance with claim 15 wherein each of the m detectors are equally spaced.