Abstract:
An MRI system acquires NMR signals and digitizes them at a fixed sample rate. A lower, prescribed sample rate is obtained by fractionally decimating the sampled NMR signals. Fractional decimation is achieved by a combination of zeropadding the sampled NMR signal in the frequency domain and decimating the sampled NMR signal in the time domain.

Description:
BACKGROUND OF THE INVENTION 
     The field of the invention is nuclear magnetic resonance imaging methods and systems. More particularly, the invention relates to the sampling of acquired NMR signals at prescribed sample rates. 
     When a substance such as human tissue is subjected to a uniform magnetic field (polarizing field B 0 ), the individual magnetic moments of the spins in the tissue attempt to align with this polarizing field, but precess about it in random order at their characteristic Larmor frequency. If the substance, or tissue, is subjected to a magnetic field (excitation field B 1 ) which is in the x-y plane and which is near the Larmor frequency, the net aligned moment, M z , may be rotated, or “tipped”, into the x-y plane to produce a net transverse magnetic moment M t . A signal is emitted by the excited spins after the excitation signal B 1  is terminated, this signal may be received and processed to form an image. 
     When utilizing these signals to produce images, magnetic field gradients (G x  G y  and G z ) are employed. Typically, the region to be imaged is scanned by a sequence of measurement cycles in which these gradients vary according to the particular localization method being used. The resulting set of received NMR signals are digitized and processed to reconstruct the image using one of many well known reconstruction techniques. 
     The rate at which the received NMR signals are digitized is an important scan parameter. The signal-to-noise ratio of an NMR image can be improved if the effective bandwidth (which is the inverse of the sampling period per point) is reduced. This is usually accomplished by widening the read-out gradient pulse and reducing the amplitude of the read-out gradient to encode the positions into a narrower bandwidth and to retain the same spatial resolution. The anti-aliasing filters are modified to match the reduced bandwidth and the analog-to-digital conversion (A/D) sample rate is reduced to acquire the same number of samples over the longer read-out gradient pulse. The SNR improvement is proportional to the square root of the bandwidth reduction. 
     A higher SNR and corresponding lower A/D sample rate is not always desired, since the increase in SNR is accompanied by two disadvantages. First, the minimum echo delay (TE 1min ) for the first NMR echo signal is increased due to the widening of the read-out gradient pulse. For some rf spin echo acquisitions the delay is twice what might be expected, since the time between the 90° RF excitation pulse and the 180° RF pulse must also be increased to orient the NMR echo signal at the center of the widened read-out gradient pulse. The lengthening of TE 1  is a disadvantage when T 2  weighting of the NMR image is not desired. A second disadvantage which accompanies this increase in SNR is an increase in chemical shift artifacts. Since the bandwidth per image pixel is reduced, the frequency difference between lipid and water resonances becomes more significant. For example, at 1.5 Tesla main field strength, the approximately 220 Hertz difference in resonant frequency will appear approximately three times further apart in an image where each image pixel represents a difference in frequency of 42 Hertz rather than 125 Hertz. The result is an increased relative displacement between the lipid structures and the water structures. This displacement can be especially disturbing with images reconstructed from the first NMR echo signal since the second echo signal often has lower lipid signal components due to the shorter T 2  decay time of lipids. 
     To allow maximum flexibility of the SNR, spatial resolution and field of view of an image for each particular application, a completely adjustable A/D sampling rate is desirable. 
     A number of methods have been used in prior MRI systems to enable the A/D sample rate to be precisely prescribed to enable the best image acquisition possible. One approach is to employ an analog-to-digital converter circuit (“ADC”) in which the sample rate is adjustable and can be precisely controlled. Such ADCs are expensive. 
     Another approach is to employ an ADC which has a fixed sample rate far higher than that required to achieve the desired sample rates. The sample rate is reduced to the prescribed A/D sample rate by using decimation. The decimation ratio (r) is an integer value. Decimation effectively reduces the A/D sample rate to one-half (r=2) by selecting alternate digitized samples, to one-third (r=3) by selecting every third digitized sample, to one-fourth (r=4) by selecting every fourth digitized sample, etc. The difficulty with this method is that the effective A/D sample rate can only be changed in discrete steps. If the ADC sample rate is very high and the decimation ratio (r) necessary to achieve operable A/D sample rates is very high (e.g. r=10, 11, 12), these discrete steps are relatively small and a desired A/D sample rate can be achieved with reasonable accuracy. However, ADC devices that operate at such high sample rates are expensive. 
     SUMMARY OF THE INVENTION 
     The present invention is a method for using a fixed sample rate ADC to acquire NMR image data and providing a fractional decimation to produce the prescribed sample rate. The decimation ratio is expressed as r=n/2 m , where n and m are integers that may be selected to obtain the prescribed sample rate. The selected decimation ratio is achieved by Fourier transforming the NMR signal to the frequency domain, zeropadding the transformed signal by a factor 2 m , Fourier transforming the zeropadded signal back to the time domain, and decimating the zeropadded time domain signal by a factor n. 
     A general object of the invention is to provide finer control over the decimation ratio so that desired rates can be more accurately achieved with a fixed rate analog to digital converter. By combining decimation in the time domain with zeropadding in the frequency domain, the decimation ratio (r) can be set to many more discrete values. This enables a decimation ratio (r) to be selected which more closely produces the desired sample rate. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a block diagram of an MRI system which employs the present invention; 
     FIG. 2 is an electrical block diagram of the transceiver which forms part of the MRI system of FIG. 1; and 
     FIG. 3 is a flow chart of the method used by the MRI system of FIG. 1 to practice the present invention. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENT 
     Referring first to FIG. 1, there is shown the major components of a preferred MRI system which incorporates the present invention. The operation of the system is controlled from an operator console  100  which includes a keyboard and control panel  102  and a display  104 . The console  100  communicates through a link  116  with a separate computer system  107  that enables an operator to control the production and display of images on the screen  104 . The computer system  107  includes a number of modules which communicate with each other through a backplane. These include an image processor module  106 , a CPU module  108  and a memory module  113 , known in the art as a frame buffer for storing image data arrays. The computer system  107  is linked to a disk storage  111  and a tape drive  112  for storage of image data and programs, and it communicates with a separate system control  122  through a high speed serial link  115 . 
     The system control  122  includes a set of modules connected together by a backplane. These include a CPU module  119  and a pulse generator module  121  which connects to the operator console  100  through a serial link  125 . It is through this link  125  that the system control  122  receives commands from the operator which indicate the scan sequence that is to be performed. The pulse generator module  121  operates the system components to carry out the desired scan sequence. It produces data which indicates the timing, strength and shape of the RF pulses which are to be produced, and the timing of and length of the data acquisition window. The pulse generator module  121  connects to a set of gradient amplifiers  127 , to indicate the timing and shape of the gradient pulses to be produced during the scan. The pulse generator module  121  also receives patient data from a physiological acquisition controller  129  that receives signals from a number of different sensors connected to the patient, such as ECG signals from electrodes or respiratory signals from a bellows. And finally, the pulse generator module  121  connects to a scan room interface circuit  133  which receives signals from various sensors associated with the condition of the patient and the magnet system. It is also through the scan room interface circuit  133  that a patient positioning system  134  receives commands to move the patient to the desired position for the scan. 
     The gradient waveforms produced by the pulse generator module  121  are applied to a gradient amplifier system  127  comprised of G x , G y  and G z  amplifiers. Each gradient amplifier excites a corresponding gradient coil in an assembly generally designated  139  to produce the magnetic field gradients used for position encoding acquired signals. The gradient coil assembly  139  forms part of a magnet assembly  141  which includes a polarizing magnet  140  and a whole-body RF coil  152 . A transceiver module  150  in the system control  122  produces pulses which are amplified by an RF amplifier  151  and coupled to the RF coil  152  by a transmit/receive switch  154 . The resulting signals radiated by the excited nuclei in the patient may be sensed by the same RF coil  152  and coupled through the transmit/receive switch  154  to a preamplifier  153 . The amplified NMR signals are demodulated, filtered, and digitized in the receiver section of the transceiver  150 . The transmit/receive switch  154  is controlled by a signal from the pulse generator module  121  to electrically connect the RF amplifier  151  to the coil  152  during the transmit mode and to connect the preamplifier  153  during the receive mode. The transmit/receive switch  154  also enables a separate RF coil (for example, a head coil or surface coil) to be used in either the transmit or receive mode. 
     The NMR signals picked up by the RF coil  152  are digitized by the transceiver module  150  and transferred to a memory module  160  in the system control  122 . When the scan is completed and an entire array of data has been acquired in the memory module  160 , an array processor  161  operates to Fourier transform the data into an array of image data. This image data is conveyed through the serial link  115  to the computer system  107  where it is stored in the disk memory  111 . In response to commands received from the operator console  100 , this image data may be archived on the tape drive  112 , or it may be further processed by the image processor  106  and conveyed to the operator console  100  and presented on the display  104 . 
     Referring particularly to FIGS. 1 and 2, the transceiver  150  produces the RF excitation field B 1  through power amplifier  151  at a coil  152 A and receives the resulting signal induced in a coil  152 B. As indicated above, the coils  152 A and B may be separate as shown in FIG. 2, or they may be a single wholebody coil as shown in FIG.  1 . The base, or carrier, frequency of the RF excitation field is produced under control of a frequency synthesizer  200  which receives a set of digital signals (CF) from the CPU module  119  and pulse generator module  121 . These digital signals indicate the frequency and phase of the RF carrier signal produced at an output  201 . The commanded RF carrier is applied to a modulator and up converter  202  where its amplitude is modulated in response to a signal R(t) also received from the pulse generator module  121 . The signal R(t) defines the envelope of the RF excitation pulse to be produced and is produced in the module  121  by sequentially reading out a series of stored digital values. These stored digital values may, in turn, be changed from the operator console  100  to enable any desired RF pulse envelope to be produced. 
     The magnitude of the RF excitation pulse produced at output  205  is attenuated by an exciter attenuator circuit  206  which receives a digital command, TA, from the backplane  118 . The attenuated RF excitation pulses are applied to the power amplifier  151  that drives the RF coil  152 A. For a more detailed description of this portion of the transceiver  122 , reference is made to U.S. Pat. No. 4,952,877 which is incorporated herein by reference. 
     Referring still to FIG. 1 and 2 the signal produced by the subject is picked up by the receiver coil  152 B and applied through the preamplifier  153  to the input of a receiver attenuator  207 . The receiver attenuator  207  further amplifies the signal by an amount determined by a digital attenuation signal (RA) received from the backplane  118 . 
     The received signal is at or around the Larmor frequency, and this high frequency signal is down converted in a two step process by a down converter  208  which first mixes the NMR signal with the carrier signal on line  201  and then mixes the resulting difference signal with the 205 MHz reference signal on line  204 . The down converted NMR signal is applied to the input of an analog-to-digital converter (ADC)  209  which samples and digitizes the analog signal and applies it to a digital detector and signal processor  210  which produces 16-bit in-phase (I) values and 16-bit quadrature (Q) values corresponding to the received signal. The resulting stream of digitized I and Q values of the received signal are output through backplane  118  to the memory module  160  where they are employed to reconstruct an image. In the preferred embodiment the ADC  209  operates at a fixed sample rate of 500 kHz so that complex pairs I and Q are sampled at a 250 kHz rate, yielding a maximum bandwidth of ±125 kHz. 
     The 2.5 MHz reference signal as well as the 250 kHz sampling signal and the 5, 10 and 60 MHz reference signals are produced by a reference frequency generator  203  from a common 20 MHz master clock signal. For a more detailed description of the receiver, reference is made to U.S. Pat. No. 4,992,736 which is incorporated herein by reference. 
     The present invention is implemented on the digitized I and Q samples of each acquired NMR signal. A prescribed receive bandwidth is established prior to the scan, and from this value a desired decimation ratio is calculated to reduce the 250 kHz=±125 kHz fixed sample rate of the ADC  109 . For example, if the prescribed bandwidth is ±100 kHz, a decimation ratio of 5/4 is needed (i.e. 125/100=5/4). 
     The decimation ratio (r) produced by the present invention is a function of a decimation factor (n) and a zeropadding factor (2 m ) in accordance with the following formula: 
     
       
         r=n/2 m . 
       
     
     The values of the integers n and m which produce the closest value to the desired decimation ratio (r) are calculated. In the example above, the 5/4 decimation ratio can be produced exactly by setting n=5 and m=2. In practice, a table of sample rates and the factors n and m which produce each rate are stored in the system control  122 . The sample rate closest to that which is prescribed is looked up in this table and the values of the factors n and m are read out and used in the following process. 
     Referring particularly to FIG. 3, the first step in the fractional decimation method is to post-fill after the digitized signal with zeroes as indicated at process block  252 . This is done to ensure that the length of the signal is a power of 2 (e.g. 512, 1024, 2048) so that an inverse fast Fourier transform (FFT −1 ) can be performed in the next step indicated at process block  254 . The inverse FFT transforms the time domain NMR signal samples into a corresponding number of signal components which represent the frequency domain version of the NMR signal. Signal components in this frequency domain representation of the NMR signal which are outside the prescribed bandwidth are suppressed by a multiplicative low-pass filter  256 . 
     The next step in the fractional decimation process is to zeropad the frequency domain NMR signal as indicated at process block  258 . The number of zeros added to the frequency domain NMR signal is determined by the zeropadding factor m. The total number of components in the NMR signal plus those added by the zeropadding must be a power of two for the FFT which follows. The number of zeros added is thus given by the following expression: 
      (2 m −1) (number of NMR signal components). 
     For example, if m=1, then zeros equal in number to the NMR signal component size are added to double the component size of the frequency domain NMR signal. If m=2, then zeros equal in number to three times the NMR signal size are added as zeropadding. Half the total number of zeroes are added symmetrically to both sides of the NMR signal. 
     After the zeropadding is completed the NMR signal is transformed back to the time domain by performing a fast Fourier transform (FFT) as indicated at process block  260 . A decimation process is then performed as indicated at process block  264 . This decimation process  264  selects one sample out of each n successive samples in the transformed time domain NMR signal. The result of this fast Fourier transformation may be scaled by a multiplicative factor that depends on the value m. As a result, a digitized time domain representation of the NMR signal is produced which is reduced to the prescribed sample rate. This decimated signal is ready for use in the image reconstruction process described above. 
     The fractional decimation process of the present invention enables one to obtain a decimation ratio (r) which can be changed in finer steps compared to integer decimation, even when the fixed sample rate of the ADC is slightly higher than the desired sample rate. This is because the decimation ratio (r) is controlled by two factors, (n) and (m) in accordance with the relationship 
     
       
         r=n/2 m . 
       
     
     In the preferred embodiment n is odd, and a table of fractional decimation ratios is stored along with the factors (n) and (m) required to produce them. An example of such a table is as follows. 
     
       
         
               
               
               
             
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                   
                   
               
               
                   
                 n → 
                   
               
             
          
           
               
                   
                 3 
                 5 
                 7 
                 9 
               
               
                   
                   
               
             
          
           
               
                   
                 m 
                 1 
                 1.5 
                 2.5 
                 3.5 
                 4.5 
               
               
                   
                 ↓ 
                 2 
                   
                 1.25 
                 1.75 
                 2.25 
               
               
                   
                   
                 3 
                   
                   
                   
                 1.125 
               
               
                   
                   
               
             
          
         
       
     
     The full effective bandwidth can be determined from the fractional decimation ratio (r=n/2 m ) and the fixed sample rate of the ADC  209  by the relationship: 
     
       
         effective bandwidth=sample rate/r. 
       
     
     Since the effective bandwidth is prescribed by the operator, and the sample rate of the ADC  209  is fixed, the fractional decimation ratio (r) can be computed from this equation. To minimize computation, constraints may be imposed on the fractional decimation rates used. A limit on the maximum value of m serves this purpose. If such a constraint is imposed, the best match to the desired decimation ratio is looked-up in the stored table and the factors n and m are read therefrom, and used in the fractional decimation process described above.