Multicoil NMR data acquisition and processing methods

Abstract

A multicoil NMR data acquisition apparatus and processing method for performing three-dimensional magnetic resonance imaging in a static magnetic field without the application of controlled static magnetic field gradients. A preferred application relates specifically to the detection and localization of groundwater using the Earth's magnetic field. Multicoil arrays are used in both transmit and receive modes. and coherent data processing algorithms applied to the data to generate three-dimensional NMR spin density estimates. Disclosed are methods for acquiring NMR data using an array of at least two transmit and receive coils, and for processing such multicoil data to estimate the three-dimensional NMR spin density distributions.

1. A method of obtaining a localized nuclear magnetic resonance Nuclear Magnetic Resonance (NMR) signal from a sample a subsurface three dimensional (3D) volume in a static magnetic field using an array of two or more magnetic field transmitting coils, and an array of two or more magnetic field receiving coils, the method comprising:
 a) generating a single an alternating current excitation pulse on one or more transmitting coils, each of said transmitting coils of the array, providing a spatially distinct an inhomogeneous magnetic field in the three dimensional (3D) volume; 
 b) acquiring NMR signals on two or more magnetic field receiving coils of the array of magnetic field coils; 
 c) applying a plurality of excitation pulses to each transmitting coil or combination of transmitting coils, wherein each excitation pulse has a unique pulse moment defined as the product of the pulse amplitude and pulse length, and wherein the nth pulse moment PM(n) is not equal to (2n−1)*PM(1); and repeating steps a and b using a plurality of excitation pulses, wherein the plurality of excitation pulses produce magnetic fields in the 3D volume, wherein at least one excitation pulse is produced by a transmitting coil of the array that is spatially distinct from another transmitting coil geometry or location, and wherein at least one excitation pulse comprises a pulse moment that is unique from a pulse moment of another excitation pulse, and wherein an nth pulse moment PM(n) is not equal to (2n−1)*PM(1); and  
 d) constructing a localized nuclear magnetic resonance NMR signal as a linear combination of NMR signals obtained using two or more transmitting coils or combinations of transmitting coils, two or more receiving coils, and two or more pulse moments for each transmitting coil excitation pulses corresponding to a plurality of different transmitting coil geometries or locations and a plurality of different pulse moments. 
 
     
     
       2. The method according to  claim 1 , wherein constructing the localized NMR signal is obtained comprises using a matched filtering data processing method comprising:
 a) computing the an expected tip angle and phase of a precessing unit-valued magnetic moment at the sample a location in the 3D volume, for each applied combination a plurality of combinations of magnetic field transmitting coils coil locations and pulse moments; 
 b) computing the expected amplitude and phase of each a forward-modeled NMR signal, each forward-modeled signal resulting from the modeled detection of the precessing unit-valued magnetic moment at the hypothetical sample corresponding to the location by each of magnetic field receiving coils in the 3D volume, and representing said expected amplitude and phase as a complex scalar; 
 c) arranging the set of said complex scalar values as a vector matched filter vector h, wherein each complex scalar represents the expected amplitude and phase of the signal response for a unit valued magnetic moment at the sample location for a given combination of transmit coil or coils, receive coil, and pulse moment; 
 d) computing a conjugate matched filter vector h* formed as a complex conjugate value of h of the vector matched filter vector; and 
 e) computing the localized NMR signal s as the a linear combination of the recorded acquired NMR signals wherein each recorded signal b j  is weighted by its respective NMR signals in the combination are weighted by conjugate matched filter vector coefficients h j *: s=Σ j h j *b j . 
 
     
     
       3. The method according to  claim 2 , wherein the localized NMR signal is obtained using an adaptive filtering data processing method comprising:
 a) computing a matched filter vector h according to  claim 2 ; 
 b) arranging the set of recorded nuclear magnetic resonance data as a matrix B with M×L×P rows, wherein each row is the sampled nuclear magnetic resonance signal recorded at one magnetic field receiving coil for one combination of transmitting coils and pulse moment; 
 c) computing a data correlation matrix
   R BB =BB H    
 
  where the superscript H denotes conjugate transpose; 
 d) computing the inverse R BB   −1  of the full-rank data correlation matrix R BB ; 
 e) computing the adaptive filter vector m=h R BB   −1 /(h R BB−1  h H ) 1/2 ; 
 f) computing a conjugate adaptive filter vector m* formed as a complex conjugate value of m; and 
 g) computing the localized NMR signal s as the linear combination of the recorded NMR signals wherein each recorded signal b j  is weighted by its respective conjugate adaptive filter vector coefficient m j *: s=Σ j m j *b j  wherein constructing the localized NMR signal further comprises applying an adaptive filtering data processing method to determine the location of an NMR signal source. 
 
     
     
       4. The method according to claim  3  2, wherein the elements of the vector matched filter vector h are equal to a fixed constant scalar value for NMR data recorded on one a first receive coil only, and wherein the elements of the vector matched filter vector h are zero for NMR data recorded on all other receive coils. 
     
     
       5. The method according to  claim 1 , wherein the localized NMR signal is obtained using a linear inverse/least-squares data processing method comprising:
 a) selecting a set of discrete volume elements (voxels) that encompass the 2-D or 3-D a two-dimensional (2D) or 3D volume or object of interest in the 3D volume; and 
 b) developing a set of linear equations Ax=b relating a modeled response for the voxels to the NMR data; and the sampled signal arising from the unknown spin density within each individual voxel to each sample in the experimentally recorded data set comprising:
 1) arranging the entire set of recorded nuclear magnetic resonance data samples as a vector b; 
 2) arranging the set of unknown voxel spin density values as a vector x; 
 3) computing each coefficient of the matrix A as a complex value describing the amplitude and phase of the recorded NMR signal that would result from the detection of a collection of precessing nuclear magnetic resonance spins, of unit spin density, contained within the hypothetical voxel corresponding to an unknown sample of x, using one particular combination of transmit coil or coils, receive coil, and pulse moment; 
 4) c) calculating the a set of localized NMR signals x as the a least squares solution to the system set of linear equations Ax=b, or as a regularized least squares solution to Ax=b the set of linear equations, using any mathematical algorithm that computes an estimate of the least squares solution or regularized least squares solution to the set of linear equations Ax=b. 
 
 
     
     
       6. The method according to  claim 5 , wherein the inverse or pseudo-inverse of the matrix A is computed once, and is applied sequentially to discrete time samples to obtain linear inverse/least-squares data processing method further comprises obtaining localized NMR signals on a time-sample-by-sample basis. 
     
     
       7. The method according to  claim 5 , wherein the least squares solution is calculated by one of the direct pseudo-inverse x=(A H A) −1 A H b, or by the regularized direct pseudo-inverse, where small scalar values are added to the diagonal elements of A or A H A, prior to computing the inverse of(A H A) using one or more matrices describing amplitude and phase of a hypothetical NMR signal that would result from detection of a collection of precessing NMR spins, of unit spin density, contained within a hypothetical voxel. 
     
     
       8. The method according to  claim 5 , wherein the least squares solution or regularized least squares solution is calculated by a singular value decomposition method comprising:
 a) calculating the singular value decomposition of the matrix A=USV H ; and 
 b) one of calculating the least squares solution as x=V[diag (l/σ j )]U H b, or calculating a weighted last squares solution, where the diagonal terms diag(l/σ j ) are each multiplied by a weighting factor prior to performing the matrix multiplication. 
 
     
     
       9. The method according to  claim 5 , wherein the least squares solution or regularized least squares solution is calculated using by a computer equipped with computer software, the software configured to use a linear iterative least squares solution algorithm comprising:
 a) the gradient descent algorithm; 
 b) the steepest descent algorithm; or 
 c) the conjugate-gradient algorithm in order to process stored NMR data. 
 
     
     
       10. The method according to  claim 1  wherein at least some of the nuclear magnetic resonance NMR signals result from the presence of groundwater in the 3D volume. 
     
     
       11. The method according to  claim 1  wherein the static magnetic field is the Earth's magnetic field. 
     
     
       12. The method according to  claim 1 , wherein each recorded nuclear magnetic resonance signal is initially reduced further comprising reducing an acquired NMR signal to a single complex number by multiplying each data sample corresponding to an acquired NMR signal by the sampled an exponential function e (−j2πfnT)  or the sampled exponential function e (−j2πfnT)  and coherently summing the a resulting series of samples. 
     
     
       13. The method according to  claim 1  wherein at least one of the transmitting magnetic field coils coil of the array and receiving magnetic field coils is the coil of the array are provided by a same coil, and this coil is used for the purposes of both transmitting and receiving. 
     
     
       14. The method according to  claim 1  wherein a reduced number of transmittigg magnetic field coils and/or receiving magnetic field coils are further comprising physically displaced and additional nuclear magnetic resonance signals are recorded via the displaced coils, so as displacing a transmitting coil of the array between excitation pulses to generate a set of data equivalent to that obtained using a full set of multiple transmitting and receiving magnetic field coils. 
     
     
       15. The method according to  claim 1 , wherein each recorded nuclear magnetic resonance sample is a single sample of the discrete Fourier transform (DFT) of the sampled nuclear magnetic resonance signal further comprising applying a Discrete Fourier transform (DFT) on acquired NMR signals, and recording samples from the DFT output on a computer memory. 
     
     
       16. The method according to  claim 1 , wherein an image is computed over a 3-dimensional field of view further comprising computing a 3D image of the 3D volume. 
     
     
       17. The method according  claim 1 , wherein an image is computed over a 2-dimensional field of view further comprising computing a 2D image of the 3D volume. 
     
     
       18. The method according to  claim 1 , wherein an image is computed over a 1-dimensional field of view further comprising computing a one dimensional (1D) image of the 3D volume. 
     
     
       19. The method according to claim 1, further comprising:
 a) deploying one of more auxiliary devices to measure noise in the vicinity of the two or more magnetic field receiving coils of the array; and   b) subtracting noise from obtained NMR signals.    
     
     
       20. The method according to claim 1, further comprising:
 a) deploying one or more auxiliary devices to measure noise in the vicinity of the two or more magnetic field receiving coils of the array;   b) constructing a set of noise reference data samples {n(1)), . . . ,n(N)} from noise measurements;   c) constructing a linearly transformed surface NMR data sample X from data acquired from the two or more magnetic field receiving coils;   d) computing an estimate of a noise process on the linearly transformed surface NMR data sample X; and   e) subtracting an estimated noise sample from the linearly transformed surface NMR data sample X.    
     
     
       21. A multi-channel Nuclear Magnetic Resonance (NMR) data acquisition apparatus that uses an array of magnetic field coils to obtain a localized NMR signal from a three dimensional (3D) volume in a static magnetic field, comprising:
 a computer;   one or more signal generators and power amplifiers configured to produce alternating current excitation pulses on one or more coils;   an array of coils, wherein:
 one or more of the coils of the array are configured to produce magnetic fields in a three-dimensional (3D) volume in response to excitation pulses produced by the one or more signal generators and power amplifiers, wherein at least one excitation pulse is produced by a coil that is spatially distinct from another coil geometry or location, and wherein at least one excitation pulse comprises a pulse moment that is unique from a pulse moment of another excitation pulse, and wherein an nth pulse moment PM(n) is not equal to (2n−1)*PM(1); and 
 two or more of the coils of the array of coils are configured to receive NMR signals produced in the 3D volume in response to the produced magnetic fields; 
   a multi-channel Analog to Digital (AD) data acquisition device configured to receive NMR signals via the coils configured to receive NMR signals, convert received NMR signals to digital signals, and output the digital signals to the computer;   wherein the computer is configured to record the digital signals produced by the AD data acquisition device; and   wherein the computer is configured to construct a localized NMR signal as a linear combination of NMR signals obtained using excitation pulses corresponding to a plurality of different transmitting coil geometries or locations and a plurality of different pulse moments.    
     
     
       22. An apparatus according to claim 21, wherein the plurality of coils comprises one or more combined transmit and receive coils.  
     
     
       23. An apparatus according to claim 21, further comprising one or more switches configured to electronically isolate the AD data acquisition device during transmit pulses produced by the one or more signal generators and power amplifiers.  
     
     
       24. An apparatus according to claim 21, further comprising one or more tuning circuits coupled to one or more of the coils in the array of coils.  
     
     
       25. An apparatus according to claim 21, further comprising one or more pre-amplifiers configured to receive NMR signals via the coils configured to receive NMR signals, amplify the NMR signals, and output the amplified NMR signals to the AD data acquisition device.  
     
     
       26. An apparatus according to claim 21, wherein the computer is configured to process recorded digital signals using a matched filtering data processing method.  
     
     
       27. An apparatus according to claim 21, wherein the computer is configured to process recorded digital signals using an adaptive filtering data processing method.  
     
     
       28. An apparatus according to claim 21, wherein the computer is configured to process recorded digital signals using a linear inverse/least-squares data processing method.  
     
     
       29. An apparatus according to claim 21, wherein the computer is configured to process recorded digital signals using synthetic aperture processing.  
     
     
       30. An apparatus according to claim 21, wherein the computer is configured to generate a one dimensional (1D), two dimensional (2D), or 3D image of at least a portion of the 3D volume.  
     
     
       31. An apparatus according to claim 21, further comprising one or more auxiliary devices configured to measure noise in the vicinity of the coils of the array configured to receive NMR signals.  
     
     
       32. An apparatus according to claim 31, wherein the one or more auxiliary devices comprise an auxiliary surface coil.  
     
     
       33. An apparatus according to claim 31, wherein the apparatus is configured to subtract noise from obtained NMR signals.  
     
     
       34. An apparatus according to claim 31, wherein the apparatus is configured to:
 construct a set of noise reference data samples {n(1)), . . . ,n(N)} from noise measurements;   construct a linearly transformed surface NMR data sample X from data acquired from the coils of the array configured to receive NMR signals;   compute an estimate of a noise process on the linearly transformed surface NMR data sample X; and   subtract an estimated noise sample from the linearly transformed surface NMR data sample X.    
     
     
       35. The method according to claim 1 further comprising physically displacing a receiving coil of the array of coils between measurements to synthesize a larger receive array.