WO2013157299A1 - 信号処理装置、信号処理方法およびプログラム - Google Patents
信号処理装置、信号処理方法およびプログラム Download PDFInfo
- Publication number
- WO2013157299A1 WO2013157299A1 PCT/JP2013/054596 JP2013054596W WO2013157299A1 WO 2013157299 A1 WO2013157299 A1 WO 2013157299A1 JP 2013054596 W JP2013054596 W JP 2013054596W WO 2013157299 A1 WO2013157299 A1 WO 2013157299A1
- Authority
- WO
- WIPO (PCT)
- Prior art keywords
- sequence
- phase
- function
- signal
- polynomial
- Prior art date
Links
Images
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
- G01R33/565—Correction of image distortions, e.g. due to magnetic field inhomogeneities
- G01R33/56545—Correction of image distortions, e.g. due to magnetic field inhomogeneities caused by finite or discrete sampling, e.g. Gibbs ringing, truncation artefacts, phase aliasing artefacts
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/88—Radar or analogous systems specially adapted for specific applications
- G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
- G01S13/90—Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
- G01S13/9021—SAR image post-processing techniques
- G01S13/9023—SAR image post-processing techniques combined with interferometric techniques
Definitions
- the present invention relates to signal processing for determining the phase of a set of signal sequences.
- phase unwrapping problem Signal processing such as remote sensing and magnetic resonance imaging (MRI) requires phase information, and it is important to obtain phase information accurately. In such signal processing, it is necessary to obtain a phase (interference signal or the like) between two signals as a continuous value, and this problem is referred to as a “phase unwrapping problem”.
- Patent Document 1 discloses a phase compensation circuit that compensates for a change in the phase of a reflected wave accompanying the movement of the target in order to transmit a radio wave to the moving target and receive a reflected wave from the target to obtain a target image.
- a range bin determining means for extracting a data string of a specific range bin from the received signal string of the reflected wave, and calculating a temporal change in phase from the extracted data string, and of the calculated temporal changes in phase
- Phase unwrapping means for removing aliasing and fitting using the least square method to the data indicating the time change of the phase from which the aliasing of the phase is eliminated, and detecting the second or higher order change component of the phase temporal change
- a phase compensation amount calculating means for calculating a phase compensation amount for reducing a second-order or higher-order change component from the detection result, and a phase compensation means for compensating the received signal sequence of the reflected wave according to the obtained phase compensation amount; Phase compensation circuit having is described.
- Patent Document 2 a 3D MR imaging sequence including 3D temperature distribution information is executed, a 3D phase distribution is calculated from the obtained 3D complex MR image, and then 3D phase unwrap processing is performed.
- a three-dimensional temperature measurement method using an MRI apparatus is described in which a three-dimensional temperature distribution is calculated from a later three-dimensional phase distribution, a volume rendering process is performed on the calculation result, and a three-dimensional temperature image is generated and displayed. ing.
- Patent Document 3 discloses a method for canceling a narrowband interference signal in a receiver, the step of subtracting a reference signal from a received input signal, and the step of calculating the phase of the result of subtraction based on an arc tangent function; Performing an unwrap function on the output signal from the arc tangent function by excluding the modulo 2 ⁇ restriction caused by the arc tangent function, thereby generating an absolute value phase representation; and for a predetermined time
- a method is described that includes determining a frequency offset by comparing shifted phase representation values and canceling narrowband interferers based on the result of the determined frequency offset.
- phase ⁇ (r) which is a continuous function, is obtained by calculating the two real polynomial functions B (0) (r), B (1) (r) by expanding the Euclidean algorithm.
- ) Tan ⁇ 1 (B (1) (r) / B (0) (r)) is described as an algebraic solution.
- An object of the present invention is to improve the stability of numerical calculation for obtaining a continuous phase of a set of signal sequences.
- the value of the indefinite portion of an integral multiple of ⁇ of the phase of a set of signal sequences at any point based on the number of times the sign of the sequence value changes between two adjacent terms in the sequence. May be determined.
- the first calculation unit may calculate, for each set of signal sequences, a piecewise polynomial that passes through each sample point of the signal sequence and in which polynomials in adjacent sections smoothly continue.
- the second calculation unit obtains from the polynomial residue sequence based on the determinants of the plurality of partial termination formula matrices that are sub-matrices of the termination formula matrix for the first function and the second function in each of the plurality of sections. Instead of the number sequence, a number sequence obtained by multiplying each term of the number sequence by a positive constant may be calculated.
- the signal output unit may output a signal sequence having a phase in which two adjacent points having a phase difference larger than ⁇ are included in the points determined by the phase determination unit.
- the present invention also includes a step of acquiring a set of signal sequences, a first function that is a piecewise polynomial obtained by approximating each of the acquired set of signal sequences with a polynomial for each of a plurality of sections, and a second function A step of calculating a function; and in each of the plurality of intervals, any point in the interval is added to the polynomial residue sequence obtained by applying the Euclidean algorithm to the calculated first function and second function.
- the present invention it is possible to improve the stability of numerical calculation for obtaining a continuous phase of a set of signal sequences as compared with the case where the configuration of the present invention is not provided.
- FIG. 10 is a graph of the wrap phase of the input signal of FIGS. 8 and 9.
- FIG. 10 is a graph of an unwrapped phase of the input signal of FIGS. 8 and 9. It is the graph which showed the result of the numerical experiment which performed the phase unwrap about the input signal of FIG. 8 and FIG.
- This phase ⁇ is indefinite in m ⁇ (m is an integer) and cannot be determined uniquely, but defining an appropriate integer value m that makes ⁇ continuous is called “phase unwrapping”.
- the signal processing apparatus of this embodiment performs this phase unwrapping.
- FIG. 1 is a diagram for explaining the principle of a method for measuring the ground altitude by interference SAR.
- R 1 and R 2 are the distances from the radars of the trajectories 1 and 2 to the object on the ground surface
- B is the distance between the radars of the trajectories 1 and 2
- H is the altitude of the radar
- h is the altitude of the measurement target.
- the angles ⁇ , ⁇ , and ⁇ are determined as shown in FIG.
- the unknowns are R 1 , R 2 , h, ⁇ .
- FIG. 2 (a) is an image of two-dimensional phase data before performing phase unwrapping.
- the magnitude of the phase is shown by black and white shading, and in FIG. 2A, the phase is limited to between ⁇ and ⁇ . For this reason, there are points at which the value changes discontinuously from - ⁇ to ⁇ or from ⁇ to - ⁇ , so that there is a distinct white and black portion where the change in shading is discontinuous.
- a phase whose value (range) is limited to between ⁇ and ⁇ is hereinafter referred to as “wrapped phase”.
- FIG. 3 is a block diagram illustrating a functional configuration example of the signal processing device 10 according to the present embodiment.
- the signal processing apparatus 10 includes a signal acquisition unit 11, a section determination unit 12, a spline calculation unit 13, a function storage unit 14, a polynomial sequence calculation unit 15, a sequence generator 16, and a code count.
- the signal acquisition unit 11 acquires a set of signal sequences to be processed. For example, in the case of the above-described interference SAR, a real part and an imaginary part of A 1 A 2 * are set, and in the case of MRI, a real part and an imaginary part of s 0 * s 1 / s 0 s 1 * are each set of a signal sequence. Get as.
- each of the set of signal sequences acquired by the signal acquisition unit 11 is represented as F (x) and G (x). For example, when these signal sequences are time series signals, x represents time.
- a signal acquisition unit 11 acquires (step 10). Then, after the section determination unit 12 determines the sections [x 0 , x 1 ],..., [X N ⁇ 1 , x N ] of x, spline functions SF (x), The spline calculation unit 13 calculates S G (x) (step 20). The function storage unit 14 stores the calculated spline functions S F (x) and S G (x).
- step 80 If there is a next section, the process returns to step 30 (Yes in step 80).
- step 90 the process proceeds to step 90 (No in step 80).
- the signal output unit 19 outputs each unwrapped phase value obtained so far as a signal sequence (step 90).
- the spline calculation unit 13 calculates the spline functions S F (x) and S G (x) in step 20 of FIG. 4
- the sample values of the signal sequences F (x) and G (x) are used by the spline calculation unit 13 to approximate each of F (x) and G (x) with a spline function.
- the n-th order spline function S (x) is “a polynomial in which S (x) is n order or less in each section, and S (x) and its (n ⁇ 1) order derivative in the whole domain are Defined as a continuous function.
- the spline calculation unit 13 is not limited to the method of FIG. 5, and another existing calculation method may be used.
- FIG. 6 is a flowchart illustrating an operation example of the polynomial string calculation unit 15 according to the first embodiment.
- ⁇ 0, ⁇ 1 i.e., spline function S F, 3 linear function of S G f k, g k
- S F spline function
- G f k 3 linear function of S G f k, g k
- each polynomial ⁇ j is factored by a power of x. 6 (that is, the 0th-order term becomes 0), the portion excluding the power should be redefined as ⁇ j and the process of FIG.
- the Euclidean mutual division method in the present embodiment includes such a modification.
- Non-Patent Documents 1 and 2 show that this correction term can be determined from the signs (+, ⁇ ) of (f (x), g (x)) before and after x where f (x) becomes 0. .
- the method of FIG. 6 makes it possible to correctly obtain a correction term even if there is no information on the position of x at which f (x) becomes 0 by using the property of the sturm sequence.
- the signal processing apparatus 10 of the present embodiment uses a mathematically exact method for determining the unwrapping phase from the polynomial. Therefore, if the input signal sequence can be approximated by a piecewise polynomial, phase unwrapping can be performed with high accuracy. Then, by approximating the input signal sequence with a spline function, a polynomial function that connects the sampling points can be obtained with high accuracy, leading to an improvement in the accuracy of phase unwrapping.
- the signal processing apparatus 10 executes the Euclidean mutual division method illustrated in FIG. 6 when calculating a polynomial string for determining an unwrapping phase.
- this method numerical instability cannot be avoided as the degree of the polynomial increases. This is due to the fact that there is a step of dividing the polynomial (step 34) in the process of FIG. 6 ( ⁇ j + 1 (x) is the remainder obtained by dividing ⁇ j-1 (x) by ⁇ j (x). -1 times). If the computer actually tries to execute the processing of FIG. 6, division of this polynomial may not be performed accurately.
- the answer of 1/3 divided by 1 is 3 with a remainder of 0, but since the computer cannot accurately represent 1/3, the remainder does not actually become 0.
- the coefficients are divided into a denominator and a numerator and each is stored as an integer, the digits of the coefficients of the polynomial become too large during the Euclidean algorithm, and cannot be stored accurately.
- the value of the coefficient of a certain polynomial will be inaccurate and repeat the step of creating the next polynomial using that inaccurate coefficient. Therefore, the coefficient of the polynomial will deviate from the actual one. Since accumulation of such numerical errors may affect the calculation result of phase unwrapping, it is desirable to generate a polynomial sequence without directly executing the Euclidean algorithm.
- Equation 13 A small matrix M j (f, g) as shown in Equation 13 is created.
- Equation 14 the elements in the rightmost column are expressed as f (x) x n ⁇ j ⁇ 1 , f (x) x n ⁇ j ⁇ 2 ,.
- f (x) x n ⁇ j ⁇ 2 the elements in the rightmost column are expressed as f (x) x n ⁇ j ⁇ 1 , f (x) x n ⁇ j ⁇ 2 ,.
- a matrix R j (f, g) as shown in Equation 14 is created.
- the determinant of this matrix is the j-th order partial termination formula of f (x) and g (x).
- the signal processing apparatus 10 obtains an unwrapping phase based on the number of sign changes of a number sequence formed from a polynomial sequence, and the difference of a positive constant multiple has an effect on counting the number of sign changes. Absent. Therefore, in the second embodiment, while calculating this polynomial sequence ⁇ 0 (x), ⁇ 1 (x),..., ⁇ q (x) ⁇ , the problem of instability in numerical calculation is avoided. Determine the continuous unwrapping phase.
- a polynomial sequence is calculated and then a value sequence is generated by substituting the value into the variable x.
- a value is set in the variable x before the partial termination formula is calculated. Is substituted, det (R j (f, g)) becomes a numerical determinant, and its numerical sequence is directly obtained. Since the numerical determinant can be easily calculated, the processing of the second embodiment is simplified from the processing of the first embodiment also in terms of calculation amount.
- FIG. 7 is a flowchart illustrating an operation example of the polynomial string calculation unit 15 according to the second embodiment.
- the polynomial sequence calculation unit 15 outputs the sequence ⁇ 0 (t),..., ⁇ j (t) ⁇ and passes it to the code count unit 17 (step 47). Thus, the operation of the polynomial sequence calculation unit 15 ends.
- the polynomial string calculation unit 15 calculates the power.
- the removed part is redefined as ⁇ j (x) and the polynomial sequence ⁇ 0 (x), ⁇ 1 (x),..., ⁇ q (x) ⁇ may be calculated.
- the signal processing apparatus 10 uses a partial termination method when calculating a polynomial string for determining the unwrapping phase.
- the polynomial sequence is calculated numerically and stably.
- the method of the present embodiment can be realized stably regardless of whether it is a floating-point operation or a multiple-precision integer operation.
- FIG. 8 is a graph of one input signal f (x) used in the numerical experiment of phase unwrapping
- FIG. 9 is a graph of the other input signal g (x) used in the numerical experiment.
- 8 (a), 8 (b), and 8 (c) are graphs when signals are observed with sample intervals of 0.25, 0.4, and 0.55, respectively. The same applies to FIG. In each graph, the sample points are indicated by circles. In each graph, the solid lines are true f (x) and g (x).
- a chain line indicates a spline function acquired by the signal acquisition unit 11 using the signal at each sample point as a signal sequence and calculated by the spline calculation unit 13 based on the signal sequence. In this numerical experiment, adjacent sample points are approximated by a cubic function.
- FIG. 10 is a graph of the wrapping phase of the input signal of FIGS. 8 and 9, and FIG. 11 is a graph of the unwrapping phase of the input signal of FIGS.
- the unwrapped phase in Fig. 11 is a true unwrapped phase obtained from Equation 16, and the wrapped phase in Fig. 10 is a wrapped phase obtained by limiting its range to (- ⁇ , ⁇ ).
- 11 is discontinuous where the value changes from ⁇ to ⁇ or from ⁇ to ⁇ , but the unwrapped phase in Fig. 11 is a continuous function, and the graphs in Fig. 10 (a) to Fig. 10 (c) Since the graphs of FIGS. 11A to 11C are obtained by plotting Expression 16, they are all the same regardless of the size of the sample interval.
- FIG. 12 is a graph showing the results of a numerical experiment in which phase unwrapping was performed on the input signals of FIGS. 8 and 9.
- the solid line represents the estimated value of ⁇ (x) obtained by the comparison method
- the chain line represents the estimated value of ⁇ (x) obtained by the signal processing device 10.
- the graphs of FIGS. 11 (a) and 11 (b) are used for both the method of the signal processing apparatus 10 and the comparison method. Is almost the same.
- FIG. 12C where the sample interval is large, there is a difference from the graph of FIG.
- the phase signal output by the signal processing apparatus 10 may include sample points whose phase difference between adjacent sample points is larger than ⁇ , unlike the output result by the comparison method.
- the signal processing apparatus 10 of the present embodiment if the sampling interval of the input signal sequence is sufficiently small, the input signal sequence is approximated with sufficient accuracy by a spline function, and phase unwrapping is successful.
- FIG. 13 is a diagram illustrating a hardware configuration of the computer 90.
- the computer 90 includes a processor 91, a main memory 92, a storage device 93, a communication interface 94, a display mechanism 95, and an input interface 96.
- the processor 91 implements each function described above by executing a program stored in the storage device 93.
- the main memory 92 stores a program being executed by the processor 91, data temporarily used by the program, and the like.
- the storage device 93 stores a program executed by the processor 91, input / output data related to the program, and the like.
- the communication interface 94 transmits / receives data to / from an external device.
- the display mechanism 95 includes a video memory, a display, and the like, and displays data and the like to the user.
- the input interface 96 includes a keyboard, a mouse, and the like, and accepts input operations from the user.
- the function storage unit 14 is realized by, for example, the main memory 92 shown in FIG.
- program for realizing the present embodiment may be provided by communication means or may be provided by being stored in a recording medium such as a CD-ROM.
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Remote Sensing (AREA)
- Radar, Positioning & Navigation (AREA)
- General Physics & Mathematics (AREA)
- Condensed Matter Physics & Semiconductors (AREA)
- Signal Processing (AREA)
- High Energy & Nuclear Physics (AREA)
- Health & Medical Sciences (AREA)
- Radiology & Medical Imaging (AREA)
- Nuclear Medicine, Radiotherapy & Molecular Imaging (AREA)
- General Health & Medical Sciences (AREA)
- Electromagnetism (AREA)
- Computer Networks & Wireless Communication (AREA)
- Magnetic Resonance Imaging Apparatus (AREA)
- Radar Systems Or Details Thereof (AREA)
Abstract
Description
位相決定部が、数列内の隣接する2項間で数列の値の符号が変化した回数に基づいて、いずれかの点における1組の信号列の位相がもつπの整数倍の不定部分の値を決定するものであってよい。
第1の算出部が、1組の信号列のそれぞれについて、信号列の各標本点を通過し、かつ隣り合う区間の多項式同士が滑らかに連続する区分的多項式を算出するものであってよい。
第2の算出部が、複数の区間のそれぞれにおいて、第1の関数と第2の関数に関する終結式行列の小行列である複数の部分終結式行列の行列式に基づいて、多項式剰余列から得られる数列に代えて、その数列の各項を正の定数倍した数列を算出するものであってよい。
位相決定部が位相を決定した点の中に位相差がπより大きい隣接する2点が含まれる位相の信号列を、信号出力部が出力するものであってよい。
また、本発明は、1組の信号列を取得するステップと、取得された1組の信号列のそれぞれを複数の区間ごとに多項式で近似した区分的多項式である第1の関数および第2の関数を算出するステップと、複数の区間のそれぞれにおいて、算出された第1の関数と第2の関数にユークリッドの互除法を適用することにより得られる多項式剰余列に区間内のいずれかの点を代入した値の数列を算出するステップと、算出された数列の各項の符号に基づいて、いずれかの点における1組の信号列の位相を決定するステップと、複数の区間のそれぞれにおいて決定された位相の信号列を出力するステップとを含む信号処理方法を提供する。
また、本発明は、コンピュータに、1組の信号列を取得する機能と、取得された1組の信号列のそれぞれを複数の区間ごとに多項式で近似した区分的多項式である第1の関数および第2の関数を算出する機能と、複数の区間のそれぞれにおいて、算出された第1の関数と第2の関数にユークリッドの互除法を適用することにより得られる多項式剰余列に区間内のいずれかの点を代入した値の数列を算出する機能と、算出された数列の各項の符号に基づいて、いずれかの点における1組の信号列の位相を決定する機能と、複数の区間のそれぞれにおいて決定された位相の信号列を出力する機能とを実現させるためのプログラムを提供する。
本実施形態の信号処理装置は、取得した1組の信号列F,Gから位相Θ=tan-1(G/F)を計算し、出力する。この位相Θはmπ(mは整数)の不定性があり一意に求まらないが、Θが連続になる適切な整数値mを定めることを「位相アンラップ」という。本実施形態の信号処理装置は、この位相アンラップを行う。
合成開口レーダ(Synthetic Aperture Radar:SAR)を用いて地表の情報を計測するシステムがある。SARは、飛行機や衛星に搭載されたレーダから地上に向けて電波を発射し、対象物から反射された電波を自身のアンテナで受信しており、アンテナ自身が飛行機や衛星によって移動することで仮想的に大きな開口面を実現したレーダである。合成開口レーダの1つである干渉合成開口レーダ(干渉SAR)は、同一地域について得られた2セットの複素画像を干渉させて生成される干渉縞から、地表高度や、地殻変動による地表高度の変化を計測する。
同位相(in-phase) s0=(W+F)exp(iθ0)
逆位相(out-phase) s1=(W-F)exp(i(θ0+φ))
ここで、W,F,θ0は定数である。すると、s0 *s1/s0s1 *=exp(i2φ)であるから、位相差φは以下のように求められる。
図3は、本実施形態の信号処理装置10の機能構成例を示したブロック図である。図示するように、信号処理装置10は、信号取得部11と、区間決定部12と、スプライン算出部13と、関数格納部14と、多項式列算出部15と、数列生成部16と、符号カウント部17と、アンラップ処理部18と、信号出力部19とを備える。
本実施形態では、信号列F(x),G(x)の標本値を用いて、スプライン算出部13がF(x),G(x)のそれぞれをスプライン関数で近似することにより、各標本点を通る2つの区分的多項式を求める。n次のスプライン関数S(x)は、「各区間においてS(x)がn次以下の多項式であり、かつ定義域全体でS(x)とその(n-1)次以下の導関数が連続な関数」と定義される。すなわち、スプライン関数は、複数の多項式を互いに接続した区分的多項式であって、多項式同士のつなぎ目(節点という)も含めて数学的な意味で滑らかな関数である。
第1の実施形態の信号処理装置10は、アンラップ位相を決定するための多項式列を算出する際に、図6に示したユークリッドの互除法を実行している。しかし、この方法では、多項式の次数が高くなると数値的な不安定性が回避できなくなる。これは、図6の処理に多項式の割り算をするステップ(ステップ34)があることに起因する(ψj+1(x)は、ψj-1(x)をψj(x)で割った余りを-1倍して求められる)。計算機で実際に図6の処理を実行しようとすると、この多項式の割り算が正確に行えない場合がある。例えば、1割る1/3の答えは3余り0であるが、計算機では1/3を正確に表すことができないため、実際には余りが0にならない。また、係数を分母と分子に分けてそれぞれを整数として保存した場合でも、ユークリッドの互除法の途中で多項式の係数の桁が大きくなりすぎてしまい、正確に保存できなくなる。つまり、計算機でユークリッドの互除法を素直に実装しようとすると、ある多項式の係数の値が途中で正確でなくなり、その正確でない係数を用いて次の多項式を作るというステップを繰り返してしまうので、途中から多項式の係数が実際のものとずれてしまう。このような数値計算上の誤差が蓄積すると位相アンラップの計算結果に影響を与えるおそれがあるため、ユークリッドの互除法を直接実行せずに多項式列が生成されるようにすることが望ましい。
以下では、第1の実施形態の信号処理装置10を用いた位相アンラップの数値実験について説明する。この数値実験では、f(x)=cos(Θ(x)),g(x)=sin(Θ(x))でありΘ(x)が以下の数16で表される信号を一定の時間間隔にて観測し、観測した信号から元の信号f(x),g(x)の連続位相Θ(x)を推定する。この数値実験では、観測した信号から、信号処理装置10の位相アンラップ方法と別の位相アンラップ方法とにより、数16の位相を正しく求められるかどうかを調べる。
11 信号取得部
12 区間決定部
13 スプライン算出部
14 関数格納部
15 多項式列算出部
16 数列生成部
17 符号カウント部
18 アンラップ処理部
19 信号出力部
Claims (7)
- 1組の信号列を取得する信号取得部と、
前記信号取得部により取得された前記1組の信号列のそれぞれを複数の区間ごとに多項式で近似した区分的多項式である第1の関数および第2の関数を算出する第1の算出部と、
前記複数の区間のそれぞれにおいて、前記第1の算出部が算出した前記第1の関数と前記第2の関数にユークリッドの互除法を適用することにより得られる多項式剰余列に当該区間内のいずれかの点を代入した値の数列を算出する第2の算出部と、
前記第2の算出部により算出された前記数列の各項の符号に基づいて、前記いずれかの点における前記1組の信号列の位相を決定する位相決定部と、
前記複数の区間のそれぞれにおいて前記位相決定部により決定された位相の信号列を出力する信号出力部と
を備える信号処理装置。 - 前記位相決定部が、前記数列内の隣接する2項間で当該数列の値の符号が変化した回数に基づいて、前記いずれかの点における前記1組の信号列の位相がもつπの整数倍の不定部分の値を決定する、請求項1に記載の信号処理装置。
- 前記第1の算出部が、前記1組の信号列のそれぞれについて、当該信号列の各標本点を通過し、かつ隣り合う区間の多項式同士が滑らかに連続する区分的多項式を算出する、請求項1または2に記載の信号処理装置。
- 前記第2の算出部が、前記複数の区間のそれぞれにおいて、前記第1の関数と前記第2の関数に関する終結式行列の小行列である複数の部分終結式行列の行列式に基づいて、前記多項式剰余列から得られる前記数列に代えて、当該数列の各項を正の定数倍した数列を算出する、請求項1から3のいずれか1項に記載の信号処理装置。
- 前記位相決定部が位相を決定した点の中に位相差がπより大きい隣接する2点が含まれる位相の信号列を、前記信号出力部が出力する、請求項1から4のいずれか1項に記載の信号処理装置。
- 1組の信号列を取得するステップと、
取得された前記1組の信号列のそれぞれを複数の区間ごとに多項式で近似した区分的多項式である第1の関数および第2の関数を算出するステップと、
前記複数の区間のそれぞれにおいて、算出された前記第1の関数と前記第2の関数にユークリッドの互除法を適用することにより得られる多項式剰余列に当該区間内のいずれかの点を代入した値の数列を算出するステップと、
算出された前記数列の各項の符号に基づいて、前記いずれかの点における前記1組の信号列の位相を決定するステップと、
前記複数の区間のそれぞれにおいて決定された位相の信号列を出力するステップと
を含む信号処理方法。 - コンピュータに、
1組の信号列を取得する機能と、
取得された前記1組の信号列のそれぞれを複数の区間ごとに多項式で近似した区分的多項式である第1の関数および第2の関数を算出する機能と、
前記複数の区間のそれぞれにおいて、算出された前記第1の関数と前記第2の関数にユークリッドの互除法を適用することにより得られる多項式剰余列に当該区間内のいずれかの点を代入した値の数列を算出する機能と、
算出された前記数列の各項の符号に基づいて、前記いずれかの点における前記1組の信号列の位相を決定する機能と、
前記複数の区間のそれぞれにおいて決定された位相の信号列を出力する機能と
を実現させるためのプログラム。
Priority Applications (2)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
JP2014511131A JP6041325B2 (ja) | 2012-04-19 | 2013-02-22 | 信号処理装置、信号処理方法およびプログラム |
US14/395,087 US20150134712A1 (en) | 2012-04-19 | 2013-02-22 | Signal processing device, signal processing method, and program |
Applications Claiming Priority (2)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
JP2012095589 | 2012-04-19 | ||
JP2012-095589 | 2012-04-19 |
Publications (1)
Publication Number | Publication Date |
---|---|
WO2013157299A1 true WO2013157299A1 (ja) | 2013-10-24 |
Family
ID=49383268
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
PCT/JP2013/054596 WO2013157299A1 (ja) | 2012-04-19 | 2013-02-22 | 信号処理装置、信号処理方法およびプログラム |
Country Status (3)
Country | Link |
---|---|
US (1) | US20150134712A1 (ja) |
JP (1) | JP6041325B2 (ja) |
WO (1) | WO2013157299A1 (ja) |
Cited By (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
JP2016041384A (ja) * | 2016-01-04 | 2016-03-31 | 株式会社日立メディコ | 磁気共鳴イメージング装置、時系列画像作成方法及びプログラム |
CN111308327A (zh) * | 2019-12-02 | 2020-06-19 | 电子科技大学 | 模拟电路故障定位与故障元件参数辨识方法 |
Families Citing this family (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US9880277B2 (en) * | 2014-05-01 | 2018-01-30 | Utah State University Research Foundation | Synthetic aperture radar processing |
US10998984B2 (en) * | 2018-05-04 | 2021-05-04 | Massachuusetts Institute of Technology | Methods and apparatus for cross-medium communication |
Citations (5)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
JPH0575476A (ja) * | 1991-09-10 | 1993-03-26 | Nippon Hoso Kyokai <Nhk> | 位相情報圧縮装置 |
JPH1090112A (ja) * | 1996-09-11 | 1998-04-10 | Sony Corp | 干渉計による2次元位相データのアンラップ方法および装置 |
JP2003070763A (ja) * | 2001-08-28 | 2003-03-11 | Ge Medical Systems Global Technology Co Llc | 位相矛盾検出方法および装置、位相矛盾解消方法および装置、並びに、磁気共鳴撮影装置 |
JP2007333583A (ja) * | 2006-06-15 | 2007-12-27 | Mitsubishi Electric Corp | 画像レーダ装置 |
JP2010252331A (ja) * | 2009-04-16 | 2010-11-04 | Advantest Corp | 検出装置、算出装置、測定装置、検出方法、算出方法、伝送システム、プログラム、および、記録媒体 |
Family Cites Families (1)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US6703835B2 (en) * | 2002-04-11 | 2004-03-09 | Ge Medical Systems Global Technology Co. Llc | System and method for unwrapping phase difference images |
-
2013
- 2013-02-22 JP JP2014511131A patent/JP6041325B2/ja not_active Expired - Fee Related
- 2013-02-22 WO PCT/JP2013/054596 patent/WO2013157299A1/ja active Application Filing
- 2013-02-22 US US14/395,087 patent/US20150134712A1/en not_active Abandoned
Patent Citations (5)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
JPH0575476A (ja) * | 1991-09-10 | 1993-03-26 | Nippon Hoso Kyokai <Nhk> | 位相情報圧縮装置 |
JPH1090112A (ja) * | 1996-09-11 | 1998-04-10 | Sony Corp | 干渉計による2次元位相データのアンラップ方法および装置 |
JP2003070763A (ja) * | 2001-08-28 | 2003-03-11 | Ge Medical Systems Global Technology Co Llc | 位相矛盾検出方法および装置、位相矛盾解消方法および装置、並びに、磁気共鳴撮影装置 |
JP2007333583A (ja) * | 2006-06-15 | 2007-12-27 | Mitsubishi Electric Corp | 画像レーダ装置 |
JP2010252331A (ja) * | 2009-04-16 | 2010-11-04 | Advantest Corp | 検出装置、算出装置、測定装置、検出方法、算出方法、伝送システム、プログラム、および、記録媒体 |
Cited By (3)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
JP2016041384A (ja) * | 2016-01-04 | 2016-03-31 | 株式会社日立メディコ | 磁気共鳴イメージング装置、時系列画像作成方法及びプログラム |
US9714999B1 (en) | 2016-01-04 | 2017-07-25 | Hitachi, Ltd. | Magnetic resonance imaging apparatus, time-series image generation method, and program |
CN111308327A (zh) * | 2019-12-02 | 2020-06-19 | 电子科技大学 | 模拟电路故障定位与故障元件参数辨识方法 |
Also Published As
Publication number | Publication date |
---|---|
US20150134712A1 (en) | 2015-05-14 |
JPWO2013157299A1 (ja) | 2015-12-21 |
JP6041325B2 (ja) | 2016-12-07 |
Similar Documents
Publication | Publication Date | Title |
---|---|---|
Lentati et al. | TEMPONEST: a Bayesian approach to pulsar timing analysis | |
Lackey et al. | Effective-one-body waveforms for binary neutron stars using surrogate models | |
Liu et al. | Precision calibration of radio interferometers using redundant baselines | |
Nakano et al. | Perturbative extraction of gravitational waveforms generated with numerical relativity | |
Noël et al. | Frequency-domain subspace identification for nonlinear mechanical systems | |
JP6503418B2 (ja) | 周波数解析装置、当該周波数解析装置を用いた信号処理装置、および、当該信号処理装置を用いた高周波測定装置 | |
Xu et al. | A refined strategy for removing composite errors of SAR interferogram | |
JP6041325B2 (ja) | 信号処理装置、信号処理方法およびプログラム | |
Repetti et al. | Non-convex optimization for self-calibration of direction-dependent effects in radio interferometric imaging | |
Beyer et al. | Numerical evolutions of fields on the 2-sphere using a spectral method based on spin-weighted spherical harmonics | |
Asli et al. | New discrete orthogonal moments for signal analysis | |
JP2014013180A (ja) | レーダ処理装置 | |
Gu et al. | A trimmed moving total least-squares method for curve and surface fitting | |
Granados et al. | Regularization of nearly hypersingular integrals in the boundary element method | |
Kitahara et al. | Algebraic phase unwrapping along the real axis: extensions and stabilizations | |
Deng et al. | Optimal interpolation and prediction in pulsar timing | |
CN105549010B (zh) | 频域合成孔径雷达成像方法 | |
US10769801B2 (en) | Fast multi-spectral image registration by modeling platform motion | |
EP1862913A2 (en) | Spectrum interpolation method, spectrum interpolation apparatus, and spectrum interpolation program storage medium | |
Beyer et al. | A spectral method for half-integer spin fields based on spin-weighted spherical harmonics | |
Fukuhara et al. | Stability of boundary element methods for the two dimensional wave equation in time domain revisited | |
Reutskiy | A new numerical method for solving high-order fractional eigenvalue problems | |
Wang et al. | Precise and fast phase wraps reduction in fringe projection profilometry | |
Brown et al. | Fast simulation of Gaussian-mode scattering for precision interferometry | |
Zhang et al. | Phase unwrapping based on accumulation of residual maps with local denoising |
Legal Events
Date | Code | Title | Description |
---|---|---|---|
121 | Ep: the epo has been informed by wipo that ep was designated in this application |
Ref document number: 13778895 Country of ref document: EP Kind code of ref document: A1 |
|
ENP | Entry into the national phase |
Ref document number: 2014511131 Country of ref document: JP Kind code of ref document: A |
|
WWE | Wipo information: entry into national phase |
Ref document number: 14395087 Country of ref document: US |
|
NENP | Non-entry into the national phase |
Ref country code: DE |
|
122 | Ep: pct application non-entry in european phase |
Ref document number: 13778895 Country of ref document: EP Kind code of ref document: A1 |