Classifications

• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
  • G01R33/00—Arrangements or instruments for measuring magnetic variables
  • G01R33/20—Arrangements or instruments for measuring magnetic variables involving magnetic resonance
  • G01R33/44—Arrangements or instruments for measuring magnetic variables involving magnetic resonance using nuclear magnetic resonance [NMR]
  • G01R33/48—NMR imaging systems
  • G01R33/54—Signal processing systems, e.g. using pulse sequences ; Generation or control of pulse sequences; Operator console
  • G01R33/56—Image enhancement or correction, e.g. subtraction or averaging techniques, e.g. improvement of signal-to-noise ratio and resolution
  • G01R33/561—Image enhancement or correction, e.g. subtraction or averaging techniques, e.g. improvement of signal-to-noise ratio and resolution by reduction of the scanning time, i.e. fast acquiring systems, e.g. using echo-planar pulse sequences
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
  • G01R33/00—Arrangements or instruments for measuring magnetic variables
  • G01R33/20—Arrangements or instruments for measuring magnetic variables involving magnetic resonance
  • G01R33/44—Arrangements or instruments for measuring magnetic variables involving magnetic resonance using nuclear magnetic resonance [NMR]
  • G01R33/48—NMR imaging systems
  • G01R33/54—Signal processing systems, e.g. using pulse sequences ; Generation or control of pulse sequences; Operator console
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
  • G01R33/00—Arrangements or instruments for measuring magnetic variables
  • G01R33/20—Arrangements or instruments for measuring magnetic variables involving magnetic resonance
  • G01R33/44—Arrangements or instruments for measuring magnetic variables involving magnetic resonance using nuclear magnetic resonance [NMR]
  • G01R33/48—NMR imaging systems
  • G01R33/54—Signal processing systems, e.g. using pulse sequences ; Generation or control of pulse sequences; Operator console
  • G01R33/56—Image enhancement or correction, e.g. subtraction or averaging techniques, e.g. improvement of signal-to-noise ratio and resolution
  • G01R33/5608—Data processing and visualization specially adapted for MR, e.g. for feature analysis and pattern recognition on the basis of measured MR data, segmentation of measured MR data, edge contour detection on the basis of measured MR data, for enhancing measured MR data in terms of signal-to-noise ratio by means of noise filtering or apodization, for enhancing measured MR data in terms of resolution by means for deblurring, windowing, zero filling, or generation of gray-scaled images, colour-coded images or images displaying vectors instead of pixels

Definitions

• the present invention relates to the acquisition and processing of signals by means of hypercomplex numbers and advantageously finds application in the field of nuclear magnetic resonance.
• Nuclear Magnetic Resonance is a technique that removes the degeneracy of a complex system that is to say to determine for it, what are the molecules present, in what quantities and what is their position in the space.
• the measured quantity is a magnetization, a sum of magnetic moments in rotation, the NMR signal written dS created by a small differential element is given by the following relation where p ⁇ ⁇ , y, z, v, t) represents the quantity that is sought, that is to say the spin density of the nucleus observed at the position ( ⁇ J * z ), ⁇ is introduced for take into account that the rotation frequency of the magnetic moments can be modified by a screen factor depending on the chemical environment (NMR spectroscopy), f ⁇ ⁇ , y, z, v>, t) is known and defined as an implicit or explicit function of time.
• the signal dS (x, y, z, X ) , t) is complex (element of the body of the complexes) because it represents the intensity and the phase of a magnetic moment in rotation. If we consider the sample as a whole, the total signal acquired is proportional to
• ⁇ x, ⁇ y, ⁇ z, ⁇ are the integration terminals of the signal along the x, y, z and frequency directions, respectively;
• the signal s (t) is a complex signal and is seen as being the sum of complex signals.
• each point of the acquired signal has two components: an intensity component and a phase component. These two components are measured throughout the acquisition, the measured phase is expressed in radians and is dimensionless.
• NMR allows from the acquired signal as a function of time to determine a (the) function P ⁇ ⁇ , y, z, v, t) which generated it.
• NMR makes it possible to reconstruct an image from the acquired signal, each point of the acquired signal corresponds to a point of the image object, for example the body of a patient.
• S (t) M ⁇ (x, y, z, 7) in which S is a known vector whose elements are complex numbers whose intensity and phase are known and given by the sampling of the signal over time, p is the vector to be determined and M is a matrix whose elements are also known as defined by the experimental conditions. Each element of each row of the matrix M is represented by the phase of each element of the volume to be reconstructed at a given acquisition time.
• the values k x (t), k y (t), k z (t), k ⁇ (t) are the conjugate variables of ⁇ , j, z, v and s (t) can be rewritten s (k x (t), k y (t), k z (t), k ⁇ ( ⁇ ), and S and p are connected by a Fourier transform.
• the purpose of an NMR acquisition is to make the acquired signal S (t) fit into the form s (k x , k y , k z , k ⁇ ).
• This condition is carried out for NMR imaging by "scanning" the space of the k (or also Fourier space) by means of magnetic field gradients which will make it possible to acquire enough points of coordinates k x , k y , k z , k ⁇ so that we can reconstruct a volume in the space ⁇ , y, z, v and thus remove the degeneracy of the acquired signal.
• the ability to acquire images quickly with high spatial resolution is conditioned by the ability to traverse the k space quickly and over a wide range of frequencies (intense field gradients and fast switching).
• Figures 1a and 1b illustrate the scanning of the space of k in the context of a sequence "Echo Planar Imaging" in the case of a 2D image.
• the transverse magnetization is created by the radio frequency, RF (see Figure 1a).
• the K points of the signal acquired over time between the marks 1 and N represent the signal S ⁇ t).
• each measured magnetization corresponds to a point of the object to be imaged, the patient for example.
• the spatial resolution in a space (x, y, z, v) is inversely proportional to the spatial resolution in the conjugate space (k x , k y , k z , k v ).
• This phenomenon generates a very strong acoustic noise, which can cause irreversible lesions of the eardrum in the patient placed in the field during the NMR experiment.
• this oscillation causes harmful direct nerve stimulation (tingling, tingling in the fingers).
• the time during which the signal can be acquired is generally limited to two or three hundred milliseconds, so the radio frequency pulses used to create the observable signal must be repeated to acquire images. Such a repetition induces localized tissue heating (SAR), which can be dangerous for the body.
• SAR tissue heating
• some tissues of the body are characterized by a short relaxation time. For these tissues, the signal can only be acquired over a very short period (of the order of ten micro-seconds for the bone). This specificity greatly limits the maximum spatial resolution that can be achieved, or even outright forbidden visualization of tissues (that is to say the bones).
• NMR makes it possible to remove the degeneracy of a signal acquired by a scanning of the space of the k, such a scanning implements complex numbers and space scanning paths generating the aforementioned drawbacks.
• the acquired signal is a series of complex numbers, each point of the signal represents an amplitude and a phase and can not represent anything more. Indeed, it can convey only two pieces of information, one in its real part, one in its imaginary part or even in the more specific case that interests us: one in its amplitude and only one other in its phase.
• the invention proposes an original approach for lifting the degeneracy of a signal.
• the invention is based on the fact that by using a form "superior" to that of a series of complex numbers it is possible to lift the degeneracy of an acquired signal.
• hypercomplex number is used to denote both quaternions and octonions as well as elements that are defined by Clifford's algebra as well as those algebras that are extended or that go beyond the number algebra. complex.
• the invention relates to a method for processing a complex signal comprising: acquisition of a signal in the form of complex numbers; a determination from the acquired complex signal of the associated hypercomplex components, said components corresponding to at least derivatives with respect to the time of the phase of the acquired complex signal; a processing of the hypercomplex signal thus determined so that the signal resulting from the processing comprises a number of component greater than the number of component of the acquired signal.
• each encoded spatial dimension is associated with a polynomial formed by linear combination of the different derivatives used to code the space, the polynomials associated with two orthogonal dimensions being orthogonal.
• the encoding consists of a creation of characterizing information for each point of the signal of the determined space in the form of time derivatives of each point of the signal of so that at each point of the coded space is associated a hypercomplex number whose components are the values of the different temporal derivatives characterizing this point spatially. at each point of the acquired signal is associated a hypercomplex number whose components are the different time derivatives of the signal used to code the space.
• a decoding step consisting in determining, from the signal, the spatial density of the points by the resolution in a hypercomplex space, of a linear system of equation formed by the hypercomplex vector formed by the acquired signal of on the one hand and the hypercomplex matrix of coding of the points of the space described on the other hand;
• the method is implemented in a nuclear magnetic resonance system, the signal to be processed being a nuclear magnetic resonance signal
• encoding is performed by means of magnetic field gradients.
• the invention relates to a nuclear magnetic resonance imaging system.
• the device of the invention is characterized in that it comprises means for implementing the method according to the first aspect of the invention.
• each point of the acquired trajectory is defined by a complex number thus having two dimensions, a real dimension and an imaginary dimension (we speak of the complex plane).
• Each point of this trajectory characterizes the phase and the amplitude of the signal at a given instant.
• the trajectory of the signal acquired over time must describe a volume in a space of the same dimensionality N as the object to be encoded.
• the total number of independent dimensions used to code an object with N dimension is 2N which represents the dimensionality of complex numbers positioned in an N-dimensional space.
• each acquired point is a hypercomplex dimensionality number (2N) whose component pair no longer represents just amplitudes and phases of magnetization but also angular amplitudes and velocities, angular amplitudes and acceleration, etc.
• the invention makes it possible to increase enormously flexibility in how to inject information during encoding into a signal (which will be processed in hypercomplex form); reduce, or even eliminate, acoustic noise; during the acquisition of NMR images to in some cases go over 12OdB to values below 20dB; to reduce or even eliminate direct nerve stimulation in the patient; to decrease warming of the patient's tissues; to improve the temporal resolution of the NMR images; to improve the spatial resolution of NMR images. It is possible in this context, to fully encode an image or volume without having to use intense gradients and without having to switch them very quickly.
• the present invention allows the acquisition and reconstruction, including images or volumes using hypercomplex numbers, this in a framework that is no longer limited by the Heisenberg equations.
• the ratio between acquisition time and spatial resolution is advantageous compared to known techniques.
• the method of the invention is particularly well suited to NMR devices of known type.
• FIGS. 3a and 3b illustrate what would be in the space of k, a trajectory (parabolic in k space) used in the method of the invention
• FIG. 4a illustrates the image to be encoded (the system) and
• FIG. 4b shows in the space of k the trajectory used during the method of the invention
• FIGS. 5a and 5b illustrate the reconstructed image after decoding by using respectively the Fourier transform as known and that obtained by the process of the invention.
• FIG. 2 illustrates a flowchart of the method of acquiring an NMR signal using four-dimensional hypercomplex numbers, that is to say quaternions.
• an object to be encoded is placed in a magnetic field.
• E1 is applied to a Radio Frequency (RF) signal which will serve to create the observable magnetization and to scan the two-dimensional space
• RF Radio Frequency
• Figure 3b illustrates a scan of the space of k by applying the gradients of Figure 3a.
• a constant magnetic field gradient is applied: according to this dimension, the rotation frequency of the magnetizations becomes a linear function of their position.
• a ramp-shaped magnetic field gradient is applied: according to this dimension, the acceleration of the rotation speed of the magnetizations becomes a linear function of their position. Consequently, in the classical representation using the notion of space of k, the trajectory to traverse the space to be encoded is parabolic (see Figure 3b).
• the constant magnetic field gradient makes it possible to inject into the signal information on the rotational speed of the magnetizations as a function of their position in a first direction and the ramp-shaped magnetic gradient of the field of view. injecting into the signal information on the acceleration of the rotational speeds of the magnetizations as a function of their position along the second direction.
• the acquisition of this unique parabolic trajectory is sufficient to allow the reconstruction of the image.
• the trajectory used to traverse the space to be coded is much simpler.
• the magnetic field gradients used have very low intensity variations which results in a very large decrease in the noise generated by the signal acquisition process as well as the energy required to generate them.
• the acquisition time may be lower than with conventional techniques which can help avoid tissue heating and nerve stimulation harmful to the body.
• the acquired signal E4 is used in hypercomplex form.
• a four-component hypercomplex signal is used, in this case a quaternion.
• a quaternion has four components.
• a real component denoted r
• an imaginary component denoted i
• two other components denoted j and k.
• the function f (t) represents the trajectory used to traverse the space to be coded.
• n ⁇ for which the index n represents the dimensions to be coded.
• Other trajectories can be used, the only constraint is that the trajectory used can "sufficiently" well lift the signal degeneracy that is to say that the trajectory traveled brings enough information in the equation system to solve. for the resolution of this one to obtain information useful to the desired locations (that the information is completely degenerate outside the object which interests us is obviously of no importance).
• the trajectories may themselves be polynomial, provided that the polynomials corresponding to orthogonal directions are themselves orthogonal. More precisely, in the example we describe, the acquired signal is expressed as a function of the applied magnetic field gradients:
• Figure 4b illustrates (in the space of k) the real part of the acquired signal by applying a constant gradient in the direction x and a ramp in the direction y (parabolic trajectory).
• the only points containing information are those placed on the parabolic trajectory.
• FIG. 5a illustrates the image obtained by using Fourier Transforms: in this example, the conditions of use of the Fourier transform require that the information be distributed on a plane. The fact that the acquired information can not be put in this form prevents its correct use, the reconstructed image has nothing to compare with the original image. In this case, more than degenerate, the reconstructed image is totally different from the coded image.
• FIG. 5b illustrates the decoded image by having previously stored the acquired signal in quaternionic form as previously described and by solving the hypercomplex linear equation system. This approach allows to lift the degeneracy and reconstruct an image identical to the original without the disadvantages of the previous techniques.

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• Physics & Mathematics (AREA)
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• High Energy & Nuclear Physics (AREA)
• Condensed Matter Physics & Semiconductors (AREA)
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• Health & Medical Sciences (AREA)
• General Health & Medical Sciences (AREA)
• Nuclear Medicine, Radiotherapy & Molecular Imaging (AREA)
• Radiology & Medical Imaging (AREA)
• Magnetic Resonance Imaging Apparatus (AREA)

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• 2007
  • 2007-09-18 FR FR0757654A patent/FR2921160B1/fr not_active Expired - Fee Related
• 2008
  • 2008-09-18 WO PCT/EP2008/062480 patent/WO2009037326A1/fr active Application Filing
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