WO2008010221A1

WO2008010221A1 - Method and system for signal processing

Info

Publication number: WO2008010221A1
Application number: PCT/IL2007/000901
Authority: WO
Inventors: Doron Kwiat
Original assignee: Mri Microsystems Ltd.
Priority date: 2006-07-17
Filing date: 2007-07-17
Publication date: 2008-01-24
Also published as: IL176906A0; WO2008010221B1

Abstract

The invention provides a method and system for processing an n-dimensional vector of analog signals n analog signals (S1(t),…Sk(t),…Sn(t)). A non-singular linear transformation A is applied to the vector (S1(t),…Sk(t),…Sn(t)) to generate an n-dimensional vector of analog signals ( 1(t),… k(t),… n(t)). The analog signals 1(t) to n(t) are amplified to produce an n-dimensional vector of analog signals ( 1(t),… k(t),… n(t)).

Description

METHOD AND SYSTEM FOR SIGNAL PROCESSING

FIELD OF THE INVENTION

This invention relates to methods and systems for noise reduction in signals.

BACKGROUND OF THE INVENTION The present invention pertains to devices and systems generating a plurality of electronic signals. Such systems and devices typically include multiple detector arrays, such as are found in magnetic resonance imaging (MRI) devices, ultrasound imaging devices, and multiple antenna radar devices. These systems include one or more detectors that detect a time dependent level of a form of energy and generate an electronic signal correlative with the amount energy detected. The generated electronic signals contain noise arising from two sources. One source is random noise that was already present in the energy signal before being transduced into an electronic signal by a detector. Additional noise is subsequently introduced into the electronic signal by the electronics of the system. Methods are known for improving the signal to noise ratio in devices generating a plurality of electronic signals. One class of methods used to reduce noise attempts to decrease the noise in the energy signal by improving the conditions in which the energy signal is detected. For example, US Patent No. 7,187,169 discloses detecting nuclear magnetic resonance (NMR) signals in microtesla fields. Prepolarization in millitesla fields is followed by detection with an untuned dc superconducting quantum interference device (SQUID) magnetometer. Because the sensitivity of the SQUID is frequency independent, the signal-to-noise ratio (SNR) is enhanced by detecting the NMR signals in extremely low magnetic fields, where the NMR lines become very narrow even for grossly inhomogeneous measurement fields. This patent further discloses that an additional improvement of the signal to noise is obtained by use of a low noise polarization coil. US Patent 7,230,424 to Morrone discloses that phase shifting of the RF (radiofrequency) pulse used in MRI with each phase-encoding gradient level, improves the signal-to-noise ratio of the recorded signals by correcting for main magnetic field inhomogeneities. Other methods for noise reduction attempt to remove noise from the electronic signals by mathematically processing the signals. US Patent No. 6,992,484 to Frank, for example discloses a method for analyzing MRI diffusion data in which methods of mathematical group theory are used to reduce noise in the signals. US Patent No. 6,486,671 discloses improvement of MRI image quality using matrix regularization. A correction matrix is defined that is used to alter the sensitivities matrix and the altered sensitivities matrix and the intensity matrix are used to generate an estimated spin density matrix which is used to generate the final image.

SUMMARY OF THE INVENTION

The present invention provides a method for processing a plurality of analog signals. The analog signals may be, for example, analog signals produced by a multi- detector device, such as an MRI system ultrasound imaging devices, and multiple antenna radar devices. As further examples, the analog signals may be seismographic signals, RGB encoding and decoding signals, sound signals and astronomical signals.

The system and method of the invention receives as an input n analog signals S₁Ct) to S_n(t) having about the same signal to noise ratio that are input to an analog signal adder. The analog signal adder outputs n analog signals σ^t) to σ_π(t), where each of the analog signals σ^t) to σ_n(t) is a linear combination of the n input signals Si(t) to S_n(t). The ή-dimensional vector of signals (σi(t),...σ_j(t),...σ_n(t)) is thus obtained by applying a linear transformation A to the n-dimensional input vector of signals (S₁(t)...S_j(t)...S_n(t)).

The analog signals σι (t) to σ_n(t) are amplified using one or more analog signal amplifiers. If the input signals S₁(I) to S_n(t) are uncorrelated and have about the same signal-to-noise ratio, the signals σ^t) to σ_n(t), being a linear combination of the signals Si(t) to S_n(t), will have a lower signal-to-noise ratio than that of the signals Si(t) to S_n(t). The signal-to-noise ratio of a signal θj(t) will be reduced from that of the input signals by a factor of 1/ Λ[N , where N is the number of input signals of which σ_j(t) is a linear combination. Thus, the larger N, the lower the signal-to-noise ratio of the σ_j(t). Since the signals σ₁(t),...σi_c(t),...σ_n(t) have a higher signal to noise ratio than the signals S₁(I) to S_n(t), the amplification may be accomplished using amplifier or amplifiers having a lower sensitivity than would be required to amplify the signals Si(t) to S_n(t). The amplified signals are digitized. A^'1 (the inverse of the linear transformation

A) is applied to the vector of the digitized signals to generate digital signals S'^t_j) to S'_n(tj), which is the output of the method and system of the invention.

It will also be understood that the system according to the invention may be a suitably programmed computer. Likewise, the invention contemplates a computer program being readable by a computer for executing the method of the invention. The invention further contemplates a machine-readable memory tangibly embodying a program of instructions executable by the machine for executing the method of the invention.

Thus, in its first aspect, the invention provides a method for processing an n- dimensional vector of analog signals n analog signals (S₁(I),...S_k(t),...S_n(t)) comprising:

(a) applying a non-singular linear transformation A to the vector (Si(t),...S_k(t),...S_n(t)) to generate an n-dimensional vector of analog signals (σj(t),...σ_k(t),...σ_n(t)); and

(b) amplifying each of the analog signals σ^t) to σ_n(t) to produce an n-dimensional vector of analog signals (∑!(t), ... Σ _k(t), ... ∑_n(t))-

In its second aspect, the invention provides a system for processing an n- dimensional vector of analog signals n analog signals (Si(t),...S_k(t),...S_n(t)) comprising:

(a) an analog signal adder applying a non-singular linear transformation A to the vector (S₁(I)₅...S_k(t),...S_n(t)) to generate an n-dimensional vector of analog signals

(σ₁(t),...σ_k(t),...σ_n(t)); and

(b) one or more analog signal amplifiers amplifying the analog signals σ^t) to σ_n(t) to produce an n-dimensional vector of analog signals (∑i(t),...Σ _k(t),...∑_n(t)). BRIEF DESCRIPTION OF THE DRAWING

In order to understand the invention and to see how it may be carried out in practice, embodiments will now be described, by way of non-limiting example only, with reference to the accompanying drawings, in which: Fig. 1 shows a system for processing signals generated by a multi-detector device, in accordance with one embodiment of the invention; and

Fig. 2 shows a magnet.

DETAILED DESCRIPTION OF EMBODIMENTS

Fig. 1 shows schematically a system 2 for processing a plurality of signals. The system 2 receives as an input n analog signals S₁(O to S_n(t) having similar signal to noise ratios and outputs n digital signals S'i(t,) to S'_n(t_j). The n analog signals S₁(O to

S_n(t) are input to an analog signal adder 4. The analog signal adder 4 outputs n analog signals σ^t) to σ_n(t), where each of the analog signals σi(t) to σ_n(t) is a linear combination of the n input signals S₁(O to S_n(t). The signals σ^t) to σ_n(t), being a linear combination of the signals S₁(Q to S_n(O, will have a higher signal to noise ratio than the signals Si(t) to S_n(t). The n-dimensional vector of input signals (Si(t),...S_k(t),...S_n(t)) can thus be related to the n-dimensional output vector of the adder 4

(_σi(t),...σ_k(t),...σ_n(t)) by

ntf SKt)

where A is a non-singular nXn matrix.

In a preferred embodiment of the invention, the entries of the matrix A are selected from -1, 0 and 1. In a more preferred embodiment, the entries of the matrix A are selected from 0 and 1. In another preferred embodiment, each row of the matrix A contains exactly 1 0. In this case, each of the signals σ^t) to σ_n(t) is a linear combination of a unique combination of n-1 of the n signals S₁(O to S_n(t).

The analog signal adder 4 may be implemented by permanent electrical connections between the input signals Si(t) to S_n(t). Alternatively, the adder 4 may be implemented by temporarily electrical connections between the input signals by means of switching devices. Alternatively, the adder 4 maybe implemented by multiple encoding of the input signals, so that all of the input signals having a particular code are summed together. The multiple encoding may be, for example, frequency encoding,as disclosed in PCT.

Each of the signals σ₁(t),...σi_c(t),...σ_n(t) is amplified by means of an analog signal amplifier 6. Each of the n signals σi(t),...σ_k(t),...σ_n(t) may be amplified by a separate amplifier 6, as shown in Fig. 1. Alternatively, a single amplifier 6 may be used, where amplification of the signals σ₁(t),...σi_c(t),...σ_n(t) occurs via multiplexing of the n signals through a common amplifier 6 (not shown). Since the signals σ₁(t),...σ_k(t),...σ_n(t) have a higher signal to noise ratio than the signals S₁Ct) to S_n(t), amplifier or amplifiers 6 may be used having a lower sensitivity than would be required to amplify the signals S₁Ct) to S_n(t).

The result of the amplification is an n-dimensional vector of amplified analog signals ∑i(t),...∑_k(t),...∑_n(t). Each of the amplified signals ∑₁(t),...∑_k(t),...∑_n(t) is converted to a digital signal ∑'i(tj),...Σ'_kOj),.. -∑'_nO_j), respectively, by means of an analog to digital converter 8. Each of the n analog signals ∑i(t),...∑_k(t),...∑_n(t) may be digitized by a separate analog to digital converter 8, as shown in Fig. 1. Alternatively, a single analog to digital converter 8 may be used, where amplification of the signals Σ j (t), ... ∑_k(t), ... ∑_n(t) occurs via multiplexing of the n signals through a common analog to digital converter 8 (not shown). The multiplexing may be time multiplexing or may coding multiplexing in which each of the signals ∑₁(t),...∑_k(t),...∑_n(t) is, for example, frequency encoded as disclosed in PCT....

The n-dimensional vector of digital signals ∑'₁(t),...∑'_k(t),...∑'_n(t). is input to a digital signal adder 10. The digital signal adder 10 is a signal processing module that executes a signal recovery algorithm which generates the n digital signals S'i(t) to S'_n(t) from the n digital signals ∑'₁(t),...∑'_k(t),...∑'_n(t). The signal vector ∑'i(t),...∑^lk(t),...∑^f _n(t) that is input to the digital signal adder 10 is multiplied by the matrix A^"1, where A^"1 is the inverse of the matrix A:

Example In an implementation of the invention for the processing of 9 signals, the 9X9 non-singular matrix A may be used, where

In the matrix A, the entry

if the input signal S_j(t) is not. a component of σj(t). Thus, for example, σ₁(t)=S₁(t)+ S₂(t)+ S₃(t)+ S₈(t) and σ₂(t)=S₄(t)+ S₅(t)+ S₆(t). The signal-to-noise ratio of σi(t) would be about equal to l/V-4 = 0.5 times that of the input signals, while the signal-to-noise ratio of σ2(t) would be about equal to 1/ -Jϊ = 0.58 times that of the input signals.

A^" is given by: 0.57 0.29 0.14 0.14 0.86 0.57 0.57 0.29 0.14

1.14 1.57 1.29 1.29 1.71 1.14 0.14 0.43 0.29

0.57 0.29 0.14 0.14 0/14 0.43 0.43 0.71 0.14

0.29 0.14 0.57 0.57 0.43 0.29 0.29 0.14 0.57

A = 0.14 0.57 0.29 0.29 0.29 0.14 0.14 0.57 0.29

0.14 0.57 0.29 0.29 0.71 0.14 0.14 0.57 0.29

0.29 0.14 0.43 0.57 0.43 0.29 0.29 0.14 0.43

1.00 1.00 1.00 1.00 1.00 1.00 0.00 0.00 0.00

0.71 0.86 0.43 0.43 0.57 0.71 0.29 0.14 0.43

The invention also provides a method to produce a magnet. A U-shaped magnet may be made by combining pre-magnetized NdFeB sectors and assembling them piecewise in such manner that all North poles are pointing in parallel and thus a collection of such small magnets creates a larger magnet of a desired arc length and thickness. (See Fig. 2).

Another method of manufacturing a U-shaped magnet is to first assemble unmagnetized bricks of NdFeB sectors into a large U-shape of a desired shape and size. One then attaches a mirror U-shape solenois without an iron core.

Once attached to the NdFeB U-shape, a signiiicanlyt large current pulse is passed through the coil, thus creating a magnetic field strong enough to have the NdFeB U-shape magnetized in the desired direction.

Claims

CLAIMS:

1. A method for processing an n-dimensional vector of analog signals n analog signals (S₁(t),...S_k(t),...S_n(t)) comprising:

(a) applying a non-singular linear transformation A to the vector (S₁(Q₅... S_k(t),...S_n(t)) to generate an n-dimensional vector of analog signals (σ₁(t)₅...σ_k(t),...σ_n(t)); and

(b) amplifying each of the analog signals σi(t) to σ_n(t) to produce an n-dimensional vector of analog signals (∑i(t),...Σ _k(t),...∑_n(t)).

2. The method according to Claim 1 further comprising: (a) digitizing the analog signals ∑'i(t) to ∑'_n(t) to produce an n- dimensional vector of digital signals (∑'i(t),...∑^li_ζ(t),...∑'_n(t)); and (b) applying to the n-dimensional vector of digital signals

(∑'i (t), ... ∑'k(t), .. • ∑'_n(t)) the linear transformation A^"1.

3. The method according to Claim 1 or 2 wherein the signals S₁(O to S_n(t) have about the same signal to noise ratio.

4. The method according to any one of the previous claims wherein the signals S i (t), ... S_k(t), ... S_n(t) are uncorrelated.

5. The method according to Claim 1 wherein the step of amplifying each of the analog signals σi(t) to σ_n(t) is accomplished using a separate analog signal amplifier for each signal.

6. The method according to Claim 1 wherein the step of amplifying each of the analog signals σ^t) to σ_n(t) is accomplished using a single analog signal amplifier and multiplexing the signals to the amplifier.

7. The method according to Claim 6 wherein the multiplexing is time multiplexing.

8. The method according to Claim 6 wherein the multiplexing is signal encoded multiplexing.

9. The method according to Claim 8 wherein the signal encoding is frequency encoding.

10. The method according to any one of the previous claims wherein the signals Si(t) to S_π(t) are MRI signals.

11. The method according to any one of the previous claims wherein all entries of the matrix A are selected from -1, 0, and 1.

12. The method according to Claiml 1 wherein all entries of the matrix A are selected from 0, and 1.

5 13. The method according to any one of the previous claims wherein the matrix A has exactly one 0 in each row.

14. A system for processing an n-dimensional vector of analog signals n analog signals (S₁(Q₅... S_k(t),... S_n(O) comprising:

(a) an analog signal adder applying a non-singular linear 10 transformation A to the vector (S i(t), ... S_k(t), ... S_n(O) to generate an n-dimensional vector of analog signals (σi(t)₅...σ_k(t)₅...σ_n(t)); and

(b) one or more analog signal amplifiers amplifying the analog signals σi(t) to σ_n(t) to produce an n-dimensional vector of

15 analog signals (E₁(O,...Σ _k(t),...∑_n(t)).

15. The system according to Claim 1 further comprising:

(a) one or more analog to signal converters digitizing the analog signals ∑'^t) to ∑'_n(t) to produce an n-dimensional vector of digital signals (∑^l ₁(t),...∑^l _k(t),...∑^f _n(t)); and

20 (b) a digital signal adder applying to the n-dimensional vector of digital signals (∑'i(t),...∑'_k(t),...∑'_n(t)) the linear transformation A^"1.

16. The system according to Claim 14 or 15 wherein the signals S₁(O to S_n(t) have about the same signal to noise ratio.

25 17. The system according to any one of Claims 14 to 16 wherein the signals

S i (t), ... S_k(t), ... S_n(O are uncorrelated.

18. The system according to Claim 14 comprising a separate analog signal amplifier for each signal, each analog signal amplifier amplifying a different one of the analog signals σi(t) to σ_n(t). 30

19. The system according to Claim 14 comprising a single analog signal amplifier and a multiplexer multiplexing the signals σj(t) to σ_n(t) to the amplifier.

20. The system according to Claim 19 wherein the multiplexing is time multiplexing.

21. The system according to Claim 19 wherein the multiplexing is signal encoded multiplexing.

5 22. The system according to Claim 21 wherein the signal encoding is frequency encoding.

23. The system according to any one of Claimsl4 to 22 wherein the signals S₁(Q to S_n(t) are MRI signals.

24. The system according to any one of Claims 14 to 23 wherein all entries of the 10 matrix A are selected from —1, 0, and 1.

25. The system according to Claim24 wherein all entries of the matrix A are selected from 0, and 1.

26. The system according to any one of Claims 14 to 25 wherein the matrix A has exactly one 0 in each row.

15 27. A computer program comprising computer program code means for performing all the steps of Claim 1 when said program is run on a computer.

28. A computer program as claimed in Claim 28 embodied on a computer readable medium.