JP2004005017A - Method for correcting aliasing in power spectrum and apparatus using it - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To perform corrections while using as a correction factor the ratio of the power spectrum components of pure signals contained in the power spectra of actual signal data to power spectrum components including components produced by the effects of aliasing, thereby eliminating aliasing components included in the power spectra of signal (image) data. <P>SOLUTION: Based on signal data having a greater number of samples than the signal data to be corrected, pseudo signal data with smaller sampling intervals are created (S100). The aliasing components and the power spectrum components are obtained from the signal data (S101). The average ratio of the aliasing components to the power spectrum components of the signal data is used as the correction factor (S103) to correct the power spectra. <P>COPYRIGHT: (C)2004,JPO

Description

の関係が成り立っており、また、実ナイキスト周波数をｎｑ、仮想ナイキスト周波数をｎｑ´とすれば、
【数２】

となっている。またｕ、ｖの間には、
【数３】

の関係が成り立っている。
【００１９】
図１に示した処理方法の概念を、処理フローとして示したのが図２である。
図２に示すように、本発明の処理の手順は、先ず、実際の信号データから実際より小さな仮想サンプリング間隔の信号データをＭＴＦの補正をして作成する（ステップＳ１００）。
次に、仮想サンプリング間隔のスペクトルデータから、実際のサンプリング間隔の単純サンプリングのスペクトルデータと理想のスペクトルデータを作成する（ステップＳ１０１）。
【００２０】
次に、全信号データについて単純サンプリングのスペクトルデータの平均と理想のスペクトルデータの平均を求める（ステップＳ１０２）。
次に、パワースペクトルの補正係数を求める（ステップＳ１０３）。
次に、パワースペクトルを補正する（ステップＳ１０４）。
となっている。この手順にしたがって詳細に説明していく
【００２１】
（１）実際の信号データから実際より小さな仮想サンプリング間隔の信号データをＭＴＦの補正をして作成する。
実信号データｆ（ｓ_ｊ）のサンプリング間隔を、実際よりも小さな仮想サンプリング間隔にした信号データが仮想信号データｆ（ｔ_ｊ）である。この各々の信号データを、フーリエ変換して得られるスペクトルデータが、Ｆ（ｕ_ｊ）、Ｆ（ｖ_ｊ）であり、Ｆ（ｖ_ｊ）にＭＴＦの補正をしたものが擬似スペクトルデータＨ（ｖ_ｊ）である。
【００２２】
Ｆ（ｕ_ｊ）の振幅には、ＭＴＦ（ｕ_ｊ）がかかっており、Ｈ（ｖ_ｊ）の振幅にはＭＴＦ（ｖ_ｊ）がかかっていなければならない。これより、Ｈ（ｖ_ｊ）は、
【数４】

によってＭＴＦの補正を行なう。
【００２３】
（２）仮想サンプリング間隔のスペクトルデータから、実際のサンプリング間隔の単純サンプリングのスペクトルデータと理想のスペクトルデータを作成する。
擬似スペクトルデータを逆フーリエ変換した擬似信号データを、実際のサンプリング間隔で単純にサンプリングしたものを、ｇ（ｓ_ｋ）、ｇ（ｓ_ｋ）をフーリエ変換して得られるスペクトルデータが、Ｇ（ｖ_ｋ）である。
【００２４】
Ｇ（ｖ_ｋ）は、Ｈ（ｖ_ｊ）を使って、
（ｊ＞０）では、
Ｇ（ｖ_ｋ）＝Ｈ（ｖ_ｋ）＋Ｈ（ｖ_{−Ｎ＋ｋ−１}）………（７）
（ｊ＝０）では、
Ｇ（０）＝Ｈ（０）………（８）
（ｊ＜０）では、
Ｇ（ｖ_ｋ）＝Ｈ（ｖ_ｋ）＋Ｈ（ｖ_{Ｎ−ｋ＋１}）………（９）
と表わすことができる。
【００２５】
これをグラフで示したのが図３である。上記式（７）及び式（８）における第２項がエイリアシングのスペクトルデータ成分であり、これを取り除いた第１項が理想のスペクトルデータ成分となっている。
【００２６】
（３）全信号データについて、単純サンプリングのスペクトルデータの平均と理想のスペクトルデータの平均を求める。
全信号データについて、単純サンプリングのスペクトルデータＧ（ｖ_ｋ）及び理想のスペクトルデータＨ（ｖ_ｋ）を求めて、それぞれの平均を、
【数５】

とする。
【００２７】
（４）パワースペクトルの補正係数を求める。
単純サンプリング信号データのパワースペクトルをＰ（ｖ_ｋ）とすると、
【数６】

となる。（ここで＊は共役複素数を表わす。）
【００２８】
また、理想のパワースペクトルＰ´（ｖ_ｋ）は、
Ｐ´（ｖ_ｋ）＝｜Ｈ（ｖ_ｋ）｜^２………（１３）
となる。
【００２９】
したがって、単純サンプリング信号データのパワースペクトルを理想のパワースペクトルに補正する補正係数を、Ｃ（ｖ_ｋ）とすれば、
【数７】

となる。
【００３０】
（５）パワースペクトルを補正する。
（１）〜（４）で求めた補正係数を用いて、処理したい信号データのパワースペクトルを補正する。
処理したい信号データのパワースペクトルをＡ（ｖ_ｋ）とすれば、
Ａ´（ｖ_ｋ）＝Ｃ（ｖ_ｋ）×Ａ（ｖ_ｋ）………（１７）
によって補正を行なう。
【００３１】
以上のようにして、パワースペクトルのエイリアシングを補正することができるが、次にこのエイリアシング補正したパワースペクトルを用いたウィーナーフィルター或いはパラメトリックウィーナーフィルターの求め方について説明する。
【００３２】
パラメトリックウィーナーフィルターの評価基準Ｉ_ｐは次式で表わされる。

ここで、γは復元度とノイズの増幅の抑制度を調整するためのパラメータであり、γ＝１としたときウィーナーフィルターとなる。
【００３３】
Ａは劣化行列、Ｑはノイズ相関行列、Ｒ_ｆｆは原画像（信号）相関行列であり、Ｍ＋１個の変数ｈ_０、ｈ_１、…、ｈ_Ｍ−１、ｈ_Ｍの左右対称型フィルターを、Ｈ＝（ｈ_Ｍ、ｈ_Ｍ−１、…、ｈ_１、ｈ_０、ｈ_１、…、ｈ_Ｍ−１、ｈ_Ｍ）とおけば、Ｂはこれを巡回させた、
【数８】

のように定義する。
【００３４】
これらの行列を式（１８）のＩ_ｐに代入すれば、Ｉ_ｐはｈ_０、ｈ_１、…、ｈ_Ｍ−１、ｈ_ＭのＭ＋１個の変数の関数となる。これを、
Ｉ_ｐ（ｈ_０、ｈ_１、…、ｈ_Ｍ−１、ｈ_Ｍ）………（２０）
と表わす。
【００３５】
また、このフィルターには直流成分を変えないという条件を付け加えるのが望ましい。
この条件は、
【数９】

と表わされる。
【００３６】
この式（２１）のもとで、式（２０）を最小にするために、ラグランジュの未定乗数をλとして、
【数１０】

とおけば、（Ｍ＋２）個の式、
【数１１】

が導出される。
【００３７】
この（Ｍ＋２）次連立方程式を、ｈ_０、ｈ_１、…、ｈ_Ｍ−１、ｈ_Ｍ及びλについて解く事によって、評価基準Ｉ_ｐを最小にするパラメトリックウィーナーフィルターを求める事ができる。
この中で、原画像（信号）の相関行列Ｒ_ｆｆを用いているが、原画像（信号）相関行列を求めるのは困難である場合がほとんどであるから、原画像（信号）の代わりに実際に得られる観測画像（信号）から推定する方法が本出願人によって提案されている。
【００３８】
これは、観測画像（信号）の相関行列Ｒ_ｇｇとノイズの相関行列Ｑを用いて、
Ｒ_ｆｆ＝Ａ^−１（Ｒ_ｇｇ−Ｑ）（Ａ^−１）^ｔ………（２４）
によって原画像（信号）の相関行列Ｒ_ｆｆを推定するものである。
【００３９】
ここにおける観測画像（信号）の相関行列Ｒ_ｇｇは、観測画像（信号）をδ、観測画像（信号）に関する平均操作をＥ_ｇ［●］とすれば、
Ｒ_ｇｇ＝Ｅ_ｇ［δδ^ｔ］………（２５）
と表わされる。
【００４０】
また、フーリエ変換を表わす行列をＷ^−１、フーリエ逆変換を表わす行列をＷとして、δのスペクトルデータをεとおけば、
ε＝Ｗ^−１δ………（２６）
と表わされ、そのパワースペクトルは行列εε^ｔの対角成分として表わされる。
【００４１】
そして、パワースペクトルのエイリアシング補正係数ベクトルＣ（ｖ_ｋ）の平方根をとったベクトルをｃｃとしてｃｃを対角成分として、その他の成分を０とした対角行列をＣとすれば、パワースペクトルのエイリアシング補正は、
Ｃεε^ｔＣ^ｔ………（２７）
によって行なうことができる。
【００４２】
ここで、エイリアシング補正されたスペクトルデータをε´とおけば、
ε´＝Ｃε………（２８）
であり、そのエイリアシング補正された信号データをδ´とすれば、
δ´＝Ｗε´
である。
【００４３】
そこで、Ｃを用いて、
Ｃ_ｗ＝ＷＣＷ^−１………（３０）
と定義すれば、

となり、これによってエイリアシング補正された信号データδ´の相関行列に補正することができる。
【００４４】
尚、式（２４）における観測画像（信号）からの推定では、Ｒ_ｇｇ―Ｑが使われているが、式（３１）におけるＲ_ｇｇは、ノイズの補正された観測画像（信号）の相関行列とみなして、Ｒ_ｇｇ―Ｑに対して式（３１）によるエイリアシング補正を行なって原画像（信号）の相関行列の推定を行なえば良い。
【００４５】
これによって、エイリアシングの影響を排除したより正確な推定にすることができる。このように推定した原画像（信号）の相関行列を式（１８）のＲ_ｆｆに代入して、ウィーナーフィルター或いはパラメトリックウィーナーフィルターを求めれば、より正確な原画像に近づけるフィルターにすることができる。
【００４６】
【発明の効果】
以上説明したように本発明によれば、統計的に補正係数を求めて補正を行なうため安定してパワースペクトルのエイリアシング補正を行なうことができる。またこの補正されたパワースペクトルを用いてウィーナーフィルターを求めれば、より精度の高いフィルターを求めることができる。
また、この補正されたパワースペクトルを用いて、ウィーナーフィルターを求めれば、より精度の高いフィルターを求めることができる。。
【図面の簡単な説明】
【図１】本発明によるエイリアシング補正によって得られる信号データの生成過程（エイリアシング補正処理方法）をあらわした図である。
【図２】図１に示した処理方法の流れを示すフローチャートである。
【図３】本発明のシステムにおけるスペクトルデータにおけるエイリアシングを説明する概念図である。
【符号の説明】
１　　実信号データ
２　　仮想信号データ
３　　再サンプリング信号データ
４　　再サンプリング信号データ
５　　仮想スペクトルデータ
６　　再サンプリングスペクトルデータ
７　　ＭＴＦデータ
８　　ＭＴＦデータ
９　　擬似スペクトルデータ[0001]
TECHNICAL FIELD OF THE INVENTION
The present invention, for example, belongs to the field of digital signal processing, and more particularly to a correction method for eliminating the effect of aliasing in a power spectrum and an apparatus using the same.
[0002]
[Prior art]
In the field of digital signal processing or digital image processing, it is often necessary to determine the power spectrum of signal data or image data. A typical example is a Wiener filter.
The Wiener filter requires a correlation matrix of an original signal or an original image to be restored. Since this correlation matrix becomes a power spectrum when Fourier-transformed, the power spectrum of the original signal or original image is required.
[0003]
Usually, it is difficult to directly obtain the power spectrum of the original signal or the original image, and the present applicant has proposed a method of estimating the correlation matrix (power spectrum) of the original image from the correlation matrix (power spectrum) of the observed image. Have been.
[0004]
However, when the signal data or image data is digital data, if the original signal or image contains a frequency component higher than the Nyquist frequency determined by the size of the sampling interval, the frequency component is folded back as an aliasing component. Frequency components. This aliasing component cannot be distinguished from the original frequency line segment, and it has been difficult to perform effective aliasing correction.
[0005]
[Problems to be solved by the invention]
When an aliasing component is included in the signal data or the image data, if the power spectrum is obtained using the signal data or the image data as it is, an incorrect power spectrum results due to the aliasing component.
[0006]
In addition, when a Wiener filter is obtained using this incorrect power spectrum, for example, it is not a very good filter. In particular, when estimating the correlation matrix (power spectrum) of the original image from the correlation matrix (power spectrum) of the observed image, the sampling interval of the observed image is often not sufficiently small, and the power spectrum has aliasing. It is considered that many components are contained, and the accuracy of the filter derived therefrom is low.
Therefore, it is necessary to eliminate aliasing components contained in the power spectrum of the signal data or the image data as much as possible.
[0007]
Therefore, an object of the present invention is to solve the above-described problems. For example, a power spectrum component of a pure signal included in a power spectrum of actual signal data and a power spectrum including a component due to aliasing are included. The ratio of the spectral components is statistically obtained, and the ratio is corrected as a correction coefficient.
[0008]
More specifically, in order to separate and obtain the power spectrum component of the pure signal included in the power spectrum of the signal data and the component due to the effects of aliasing, the number of samples having a larger number of samples than the signal data to be actually corrected is determined. The signal data is prepared, and the signal data of a smaller sampling interval is created in a pseudo manner.
[0009]
The power spectrum when this virtual signal data is resampled at the actual sampling interval contains a component due to the effect of aliasing, and the power spectrum component of the pure signal is obtained from the virtual signal data. The statistical ratio is used as a correction coefficient.
[0010]
The correction coefficient thus obtained is a statistical aliasing correction coefficient created from a plurality of digital signal data or digital image data, and can correct the power spectrum aliasing with high accuracy.
[0011]
[Means for Solving the Problems]
For this purpose, the present invention provides a signal data generating step of pseudo-generating second signal data at a smaller sampling interval based on first signal data having a larger number of samples than signal data to be corrected. Obtaining an aliasing component and a power spectrum component of the signal data based on the second signal data generated by the signal data generating step; and the aliasing component and the second signal obtained by the obtaining step. And correcting the power spectrum using the ratio of the power spectrum components of the signal data as a correction coefficient.
[0012]
Further, the present invention is a signal processing device or an image processing device in which a plurality of devices are communicably connected to each other, wherein at least one device among the devices is the device according to any one of claims 1 to 4. It has a function based on the steps of the aliasing correction method.
[0013]
BEST MODE FOR CARRYING OUT THE INVENTION
Hereinafter, embodiments of the present invention will be described with reference to the drawings.
FIG. 1 shows a process of generating signal data (aliasing correction processing method) obtained by the aliasing correction according to the present invention.
In FIG. 1, (a) shows actual signal data of a larger number of samples than the signal data to be actually corrected, and (b) shows a sampling interval of the actual signal data of (a) reduced. Based on this, correction is performed using the MTF data of (g) and (h), and signal data at a small sampling interval is created in a pseudo manner. This is the pseudo spectrum data of (i).
[0014]
From this pseudo-spectral data, (f) re-sampled spectrum data, which is the spectrum data of the signal data (c) re-sampled at the actual sampling interval, can be obtained, and a component due to aliasing can also be obtained.
[0015]
Here, the definition of each symbol in FIG. 1 will be described.
The actual signal data is f, the resampled signal data is g, the spectrum data is F and G, the pseudo spectrum data is H, and the MTF data is MTF.
[0016]
Also, let s be a sample point at the actual sampling interval in the signal space and t be a sample point at a virtual sampling interval smaller than the actual sampling interval.
Also, let u be a spectrum sample point in the frequency space corresponding to the sample point s at the actual sampling interval in the signal space, and let v be a spectrum sample point in the frequency space corresponding to t.
[0017]
Also, assuming that the number of samples of the signal data of (a) larger than the signal data to be actually corrected is 2N + 1, the number of samples of the signal data to be actually corrected is 2M + 1, and the index j is -N to N and k is -M to M And
[0018]
At this time, between s and t,
(Equation 1)

And the real Nyquist frequency is nq and the virtual Nyquist frequency is nq ′,
(Equation 2)

It has become. Also, between u and v,
[Equation 3]

The relationship holds.
[0019]
FIG. 2 shows the concept of the processing method shown in FIG. 1 as a processing flow.
As shown in FIG. 2, in the processing procedure of the present invention, first, signal data at a virtual sampling interval smaller than the actual one is created from the actual signal data by correcting the MTF (step S100).
Next, from the spectrum data at the virtual sampling interval, the spectrum data of the simple sampling at the actual sampling interval and the ideal spectrum data are created (step S101).
[0020]
Next, the average of the simple sampling spectrum data and the average of the ideal spectrum data are obtained for all the signal data (step S102).
Next, a correction coefficient of the power spectrum is obtained (step S103).
Next, the power spectrum is corrected (step S104).
It has become. Details will be described according to this procedure.
(1) Signal data at a virtual sampling interval smaller than the actual one is created from the actual signal data by correcting the MTF.
The signal data in which the sampling interval of the real signal data f (s _j ) is a virtual sampling interval smaller than the actual one is the virtual signal data f (t _j ). The spectrum data obtained by Fourier-transforming each of the signal data is F (u _j ) and F (v _j ), and the F (v _j ) corrected for MTF is the pseudo-spectral data H (v _j ). _j ).
[0022]
MTF (u _j ) must be applied to the amplitude of F (u _j ), and MTF (v _j ) must be applied to the amplitude of H (v _j ). From this, H (v _j ) is
(Equation 4)

To correct the MTF.
[0023]
(2) From the spectrum data at the virtual sampling interval, create the simple sampling spectrum data and the ideal spectrum data at the actual sampling interval.
The pseudo signal data obtained by inverse Fourier transform of the pseudo spectrum data is simply sampled at an actual sampling interval, and the spectrum data obtained by Fourier transforming g (s _k ) and g (s _k ) is represented by G (v _k ).
[0024]
G (v _k ) is _calculated by using H (v _j )
(J> 0)
G (v _k ) = H (v _k ) + H (v− _{N + k−1} ) (7)
(J = 0),
G (0) = H (0) (8)
(J <0),
G (v _k ) = H (v _k ) + H (v _{N−k + 1} ) (9)
Can be expressed as
[0025]
FIG. 3 shows this in a graph. The second term in the above equations (7) and (8) is an aliasing spectrum data component, and the first term excluding this is an ideal spectrum data component.
[0026]
(3) With respect to all the signal data, the average of simple sampling spectrum data and the average of ideal spectrum data are obtained.
For all the signal data, the spectrum data G (v _k ) of the simple sampling and the ideal spectrum data H (v _k ) are obtained, and the respective averages are calculated as
(Equation 5)

And
[0027]
(4) Find a correction coefficient for the power spectrum.
Assuming that the power spectrum of the simple sampling signal data is P (v _k ),
(Equation 6)

It becomes. (Here, * represents a conjugate complex number.)
[0028]
The ideal power spectrum P ′ (v _k ) is
P ′ (v _k ) = | H (v _k ) | ² (13)
It becomes.
[0029]
Therefore, if the correction coefficient for correcting the power spectrum of the simple sampling signal data to the ideal power spectrum is C (v _k ),
(Equation 7)

It becomes.
[0030]
(5) Correct the power spectrum.
The power spectrum of the signal data to be processed is corrected using the correction coefficients obtained in (1) to (4).
If the power spectrum of the signal data to be processed is A (v _k ),
A ′ (v _k ) = C (v _k ) × A (v _k ) (17)
The correction is performed by
[0031]
As described above, the aliasing of the power spectrum can be corrected. Next, a method of obtaining a Wiener filter or a parametric Wiener filter using the aliased power spectrum will be described.
[0032]
The evaluation criterion _Ip of the parametric Wiener filter is expressed by the following equation.

Here, γ is a parameter for adjusting the degree of restoration and the degree of suppression of noise amplification. When γ = 1, it becomes a Wiener filter.
[0033]
A is a degradation matrix, Q is a noise correlation matrix, R _ff is an original image (signal) correlation matrix, and a left-right symmetric filter of M + 1 variables h ₀ , h ₁ ,..., H _M−1 , h _{M H = (h M, h M} -1, ..., h 1, h 0, h 1, ..., h M-1, h M) if put and, B is allowed to cycle through this,
(Equation 8)

Is defined as
[0034]
Substituting these matrix _{I p} of the formula (18), _{I p} is _{h 0, h 1, ...,} a function of M + 1 single variable _{h M-1, h M.} this,
I _p (h ₀ , h ₁ ,..., H _M−1 , h _M ) (20)
It is expressed as
[0035]
It is desirable to add a condition that the DC component is not changed in this filter.
This condition
(Equation 9)

Is represented by
[0036]
Under this equation (21), in order to minimize equation (20), Lagrange's undetermined multiplier is defined as λ,
(Equation 10)

Then, (M + 2) expressions,
[Equation 11]

Is derived.
[0037]
By solving this (M + 2) -order simultaneous equation for h ₀ , h ₁ ,..., H _M−1 , h _M and λ, a parametric Wiener filter that minimizes the evaluation criterion I _p can be obtained.
In this, the correlation matrix R _ff of the original image (signal) is used. However, in most cases, it is difficult to obtain the original image (signal) correlation matrix. Has been proposed by the present applicant.
[0038]
This is obtained by using the correlation matrix R _gg of the observed image (signal) and the correlation matrix Q of the noise,
R _ff = A ⁻¹ (R _gg −Q) (A ⁻¹ ) ^t (24)
_{Is used} to estimate the correlation matrix R _ff of the original image (signal).
[0039]
Here, the correlation matrix R _gg of the observed image (signal) can be expressed by: δ for the observed image (signal) and E _g [●] for the averaging operation for the observed image (signal).
R _gg = E _g [δδ ^t ] (25)
Is represented by
[0040]
Also, if the matrix representing the Fourier transform is W ⁻¹ , the matrix representing the inverse Fourier transform is W, and the spectral data of δ is ε,
ε = W ⁻¹ δ (26)
Expressed and, the power spectrum is expressed as diagonal elements of the matrix εε ^t.
[0041]
If the vector obtained by taking the square root of the aliasing correction coefficient vector C (v _k ) of the power spectrum is cc, cc is the diagonal component, and the diagonal matrix with the other components being 0 is C, the aliasing of the power spectrum is obtained. The correction is
Cεε ^t C ^t ............ (27)
Can be done by
[0042]
Here, if the aliasing-corrected spectrum data is denoted by ε ′,
ε '= Cε (28)
And if the aliased signal data is δ ′,
δ '= Wε'
It is.
[0043]
So, using C,
C _w = WCW ^-1 (30)
If you define

Thus, the correlation matrix of the aliased signal data δ ′ can be corrected.
[0044]
In the estimation from the observed image (signal) in Expression (24), R _gg -Q is used. However, R _gg in Expression (31) is a correlation matrix of the observed image (signal) corrected for noise. In this case, the correlation matrix of the original image (signal) may be estimated by performing an aliasing correction on R _gg -Q by Expression (31).
[0045]
As a result, it is possible to obtain a more accurate estimation excluding the influence of aliasing. By substituting the correlation matrix of the original image (signal) estimated in this way into R _ff in equation (18) and obtaining a Wiener filter or a parametric Wiener filter, it is possible to obtain a more accurate filter close to the original image.
[0046]
【The invention's effect】
As described above, according to the present invention, since the correction coefficient is statistically obtained and corrected, the aliasing correction of the power spectrum can be performed stably. Further, if a Wiener filter is obtained using the corrected power spectrum, a filter with higher accuracy can be obtained.
Further, if a Wiener filter is obtained using the corrected power spectrum, a filter with higher accuracy can be obtained. .
[Brief description of the drawings]
FIG. 1 is a diagram showing a process of generating signal data (aliasing correction processing method) obtained by aliasing correction according to the present invention.
FIG. 2 is a flowchart showing a flow of the processing method shown in FIG. 1;
FIG. 3 is a conceptual diagram illustrating aliasing in spectrum data in the system of the present invention.
[Explanation of symbols]
1 real signal data 2 virtual signal data 3 resampled signal data 4 resampled signal data 5 virtual spectrum data 6 resampled spectrum data 7 MTF data 8 MTF data 9 pseudo spectrum data

Claims (5)

A signal data generating step of pseudo-generating second signal data at a smaller sampling interval based on the first signal data having a larger number of samples than the signal data to be corrected;
An acquisition step of acquiring an aliasing component and a power spectrum component of the signal data based on the second signal data generated by the signal data generation step;
A correction step of correcting the power spectrum using a ratio between the aliasing component obtained in the obtaining step and the power spectrum component of the second signal data as a correction coefficient. The correction coefficient used in the correction step is
A signal data generating step of generating second signal data having a small sampling interval from the first signal data;
An MTF (Modulation Transfer Function) correction step of performing MTF (Modulation Transfer Function) correction on the second signal data;
A first obtaining step of obtaining a power spectrum component of the second signal data;
A power spectrum generation step of generating simple power spectrum data and ideal power spectrum data at a sampling interval of the first signal data from the power spectrum data obtained in the first acquisition step;
A second acquisition step of acquiring an average of each of the simple power spectrum data and the ideal power spectrum data obtained in the power spectrum generation step;
2. The aliasing correction method according to claim 1, wherein the third acquisition step is for acquiring an average ratio between the simple power spectrum data obtained in the second acquisition step and the ideal power spectrum data. The aliasing correction method according to claim 1, further comprising a filter acquisition step of acquiring at least one of a Wiener filter and a parametric Wiener filter based on the power spectrum obtained in the acquisition step. The filter acquisition step corrects a power spectrum obtained from a matrix obtained by subtracting a noise correlation matrix from a correlation matrix of an observed image (signal), and estimates a signal of an original image (signal) based on the corrected power spectrum. The aliasing correction method according to claim 3, wherein: A signal processing device or an image processing device in which a plurality of devices are communicably connected to each other,
A signal processing device or an image processing device, wherein at least one of the devices has a function based on the steps of the aliasing correction method according to claim 1.

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