CN104793253A - Airborne electromagnetic data denoising method based on mathematical morphology - Google Patents

Abstract

The invention relates to a mathematical morphology-based airborne electromagnetic data denoising method, which obtains airborne electromagnetic detection data through experiments, uses a combination of triangular structural elements and semicircular structural elements, and performs self-adaptive multi-scale composite morphological filtering on airborne electromagnetic data : First determine the length range of the structural elements according to the minimum and maximum intervals between adjacent peaks in the original signal and then determine the corresponding analysis scale K; then determine the height range according to the minimum and maximum values of the signal peaks; use each structure The element set performs complex morphological operations on the original signal and takes the average value as the output result. The self-adaptive multi-scale compound morphological filtering method proposed by the present invention overcomes the problem of random selection of structural elements in traditional morphological filtering. The method can adaptively select the type and size of structural elements according to the local characteristics of the signal and the characteristics of noise, and then analyze the airborne electromagnetic signal to filter.

Description

Denoising method for airborne electromagnetic data based on mathematical morphology

technical field

The invention relates to a data denoising method in the field of aeronautical electromagnetics, especially in the field of time domain aeronautical electromagnetics, in particular to a method for denoising data in aeronautical electromagnetics based on mathematical morphology.

Background technique

Airborne electromagnetic method is a kind of survey and detection method that uses aircraft as a carrier to carry out geophysical exploration. It is mainly used for rapid survey of metal ore bodies, large-scale geological mapping, hydrogeology, engineering geological exploration and environmental monitoring and other fields.

Mathematical morphology is a discipline based on strict mathematical theory. It has been successfully applied in engineering practice fields such as image processing, graphic analysis, pattern recognition, computer vision, electrical energy disturbance, mechanical vibration and earthquake detection, and has attracted widespread attention. . The operation of this method is simple, and its basic operations include corrosion, expansion, opening and closing operations, and the morphological opening and closing and morphological closing and opening operations derived from them. The signal denoising method based on mathematical morphology only depends on the local characteristics of the signal to be processed, and uses structural elements to match or correct the geometric characteristics of the signal while retaining the main shape of the target signal to suppress noise, extract useful information and preserve Detail the purpose of the ingredients.

One of the main problems in the mathematical morphology filtering method is the selection of structural elements, and the selection of structural element types is the key factor affecting its filtering effect. Different types of structural elements can be used to extract different shape features in the target signal. The selection of structural elements should be as close as possible to the shape characteristics of the signal to be processed, so as to achieve the best filtering effect as possible. Common structural elements Types are linear, rectangular, disc, parabolic, triangular, and other combinations of polygons.

Most of the existing morphological filtering methods only use single-scale structural elements, and single-scale morphology only selects a fixed structural element for morphological analysis of the signal. Although this method is simple and easy to implement, its processing effect is extremely poor. However, accurate and effective prior knowledge is often difficult to obtain. In addition, since the signal usually contains more than one type of noise, and the noise is often not evenly distributed in the signal.

None of the existing morphological filtering methods can perform composite morphological filtering on different types and intensities of noise components in structural element signals at different scales.

Contents of the invention

The purpose of the present invention is to address the deficiencies of the prior art, and provide a mathematical morphology-based airborne electromagnetic data denoising method that better preserves signal detail features while suppressing noise and extracting useful information.

The purpose of the present invention is achieved through the following technical solutions:

The main idea of the present invention is: Aiming at various interference components contained in airborne electromagnetic data, an adaptive multi-scale morphological filter is proposed, and triangular structural elements and semicircular structural elements are selected to filter out positive and negative elements in the signal. Impulse noise and random noise.

The airborne electromagnetic data denoising method based on mathematical morphology includes the following steps:

A. Through the time-domain helicopter electromagnetic detection experiment, through the data acquisition hardware circuit, sampling at regular intervals is carried out, and the original aeronautical electromagnetic data is collected;

B. Using the combination of triangular structural elements and semicircular structural elements, the aeronautical electromagnetic signal is subjected to self-adaptive multi-scale compound shape filtering processing, and the positive and negative pulse noise and random noise in the target signal are filtered out.

Step B includes the following steps:

a. First, determine the length range of the structural elements according to the minimum and maximum values of the interval between adjacent peaks in the original signal, and then determine the corresponding analysis scale K;

b. Then determine the altitude range according to the minimum and maximum values of the signal peak value;

c. Then use the small/large length to correspond to the small/large height to determine each structural element in the multi-scale analysis and form a corresponding multi-structural element set;

d. Finally, each structural element set is used to perform compound morphological operations on the original signal and an average value is taken as the output result.

The said complex morphological operation on the original signal is to firstly perform corrosion operation, expansion operation, opening operation and closing operation on the aeronautical electromagnetic signal, and then respectively perform morphological opening and closing filtering and morphological closing and opening filtering:

Corrosion operation: $\left(\mathrm{f\Θg}\right)\left(\mathrm{no}\right)=\underset{m=\mathrm{0,1},...,m-1}{\min }\{f(\mathrm{no}+m)-g\left(m\right)\},\mathrm{no}=\mathrm{0,1},...,N+m-2$

Expansion operation: $(f\⊕g)\left(\mathrm{no}\right)=\underset{m=\mathrm{0,1},...,m-1}{\max }\{f(\mathrm{no}-m)+g\left(m\right)\},\mathrm{no}=\mathrm{0,1},...,N-m$

Open operation:

Closing operation: $(f\&Center\; Dot;g)\left(\mathrm{no}\right)=\left[(f\⊕g)\mathrm{\Θg}\right]\left(\mathrm{no}\right)$

Among them, Θ represents the erosion operation, Represents expansion operation, ο represents opening operation, · represents closing operation, f is the original airborne electromagnetic waveform data, g is the selected morphological structure element, m and n are the discrete sampling points of the input signal, N>>M;

Then perform morphological opening and closing filtering and morphological closing and opening filtering respectively:

Morphological opening and closing filtering:

Morphological closed-open filter:

Finally, construct the compound morphological filter:

Adaptive complex morphological filter: $z\left(\mathrm{no}\right)=\frac{1}{2}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}[\mathrm{CFco}(f\left(\mathrm{no}\right),G_i)+\mathrm{CFoc}(f\left(\mathrm{no}\right),G_i)]$

Wherein, G=(g ₁ , g ₂ ,..., g _i ), represents a set of multiple structural elements, and N is the number of types of structural elements.

Beneficial effects: The denoising method of airborne electromagnetic data based on mathematical morphology not only extracts useful information during denoising, but also preserves the detailed information of airborne electromagnetic signals for further data analysis; The invention proposes an adaptive multi-scale compound morphological filtering method, which overcomes the problem of random selection of structural elements in the existing morphological filtering, and can adaptively select the type and size of structural elements according to the local characteristics of the signal and noise characteristics, and then perform airborne electromagnetic signal filtering.

Description of drawings:

Accompanying drawing 1 is the flow chart of airborne electromagnetic data denoising method based on mathematical morphology

Accompanying drawing 2 self-adaptive composite shape filtering method diagram

Attached Figure 3 is the original data map of airborne electromagnetic

Accompanying drawing 4 Comparison chart of airborne electromagnetic original signal and mathematical morphology filtering effect

Attached Figure 5 Effect diagram of self-adaptive composite morphological filtering

Detailed ways:

The present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments.

The airborne electromagnetic data denoising method based on mathematical morphology includes the following steps:

A. Through the time-domain helicopter electromagnetic detection experiment, through the data acquisition hardware circuit, sampling at regular intervals is carried out, and the original aeronautical electromagnetic data is collected;

B. Using the combination of triangular structural elements and semicircular structural elements, the aeronautical electromagnetic signal is subjected to self-adaptive multi-scale compound shape filtering processing, and the positive and negative pulse noise and random noise in the target signal are filtered out.

Step B includes the following steps:

a. First, determine the length range of the structural elements according to the minimum and maximum values of the interval between adjacent peaks in the original signal, and then determine the corresponding analysis scale K;

b. Then determine the altitude range according to the minimum and maximum values of the signal peak value;

c. Then use the small/large length to correspond to the small/large height to determine each structural element in the multi-scale analysis and form a corresponding multi-structural element set;

d. Finally, each structural element set is used to perform compound morphological operations on the original signal and an average value is taken as the output result.

The said complex morphological operation on the original signal is to firstly perform corrosion operation, expansion operation, opening operation and closing operation on the aeronautical electromagnetic signal, and then respectively perform morphological opening and closing filtering and morphological closing and opening filtering:

Corrosion operation: $\left(\mathrm{f\Θg}\right)\left(\mathrm{no}\right)=\underset{m=\mathrm{0,1},...,m-1}{\min }\{f(\mathrm{no}+m)-g\left(m\right)\},\mathrm{no}=\mathrm{0,1},...,N+m-2$

Expansion operation: $(f\⊕g)\left(\mathrm{no}\right)=\underset{m=\mathrm{0,1},...,m-1}{\max }\{f(\mathrm{no}-m)+g\left(m\right)\},\mathrm{no}=\mathrm{0,1},...,N-m$

Open operation:

Closing operation: $(f\&Center\; Dot;g)\left(\mathrm{no}\right)=\left[(f\⊕g)\mathrm{\Θ\; g}\right]\left(\mathrm{no}\right)$

Among them, Θ represents the erosion operation, Represents expansion operation, ο represents opening operation, · represents closing operation, f is the original airborne electromagnetic waveform data, g is the selected morphological structure element, m and n are the discrete sampling points of the input signal, N>>M;

Then perform morphological opening and closing filtering and morphological closing and opening filtering respectively:

Morphological opening and closing filtering:

Morphological closed-open filter:

Finally, construct the compound morphological filter:

Adaptive complex morphological filter: $z\left(\mathrm{no}\right)=\frac{1}{2}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}[\mathrm{CFco}(f\left(\mathrm{no}\right),G_i)+\mathrm{CFoc}(f\left(\mathrm{no}\right),G_i)]$

Wherein, G=(g ₁ , g ₂ ,..., g _i ), represents a set of multiple structural elements, and N is the number of types of structural elements.

Example 1:

(1) Raw airborne electromagnetic data obtained through the time-domain helicopter electromagnetic detection flight test. Specifically: use the data acquisition hardware circuit of the aeronautical electromagnetic detection system to obtain the waveform data of the detection result, and perform regular and equal interval sampling through the data acquisition hardware circuit to collect the original signal data of the aeronautical electromagnetic detection system.

(2) The triangular structural element is suitable for filtering positive and negative pulse noise interference, and the semicircular structural element is suitable for filtering random noise interference. Therefore, the use of triangular and semicircular structural elements is considered to perform complex morphological filtering on the original signal. The specific process is as follows:

(1) First, corrode, expand, open and close the signal respectively:

Corrosion operation: $\left(\mathrm{f\Θg}\right)\left(\mathrm{no}\right)=\underset{m=\mathrm{0,1},...,m-1}{\min }\{f(\mathrm{no}+m)-g\left(m\right)\},\mathrm{no}=\mathrm{0,1},...,N+m-2$

Expansion operation: $(f\⊕g)\left(\mathrm{no}\right)=\underset{m=\mathrm{0,1},...,m-1}{\max }\{f(\mathrm{no}-m)+g\left(m\right)\},\mathrm{no}=\mathrm{0,1},...,N-m$

Open operation:

Closing operation: $(f\·g)\left(\mathrm{no}\right)=\left[(f\⊕g)\mathrm{\Θg}\right]\left(\mathrm{no}\right)$

(2) Perform morphological opening and closing filtering and morphological closing and opening filtering respectively:

Morphological opening and closing filtering:

Morphological closed-open filter:

An adaptive composite morphological filter is constructed to improve the filtering effect.

Adaptive complex morphological filtering: $z\left(\mathrm{no}\right)=\frac{1}{2}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}[\mathrm{CFco}(f\left(\mathrm{no}\right),G_i)+\mathrm{CFoc}(f\left(\mathrm{no}\right),G_i)]$

in

(3) The mathematical expressions of triangular structural elements and semicircular structural elements are as follows:

(1) Triangular structural elements

$\mathrm{<span\; class="notranslate">\; g</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; \&times;</span><span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\frac{<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; |</span>}{\mathrm{<span\; class="notranslate">\; L</span>}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; ,</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; )</span>$

(2) Semicircular structural elements

$\mathrm{<span\; class="notranslate">\; g</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; \&times;</span><span\; class="notranslate">\; [</span>\sqrt{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; L</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; ,</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; )</span>$

Among them, L represents the length of the structural element, and H represents the height of the structural element.

(4) Determination of the length of structural elements

Assuming that the original signal is X={ _xi |i=1,2,...,N} (N is the number of data points of the original signal), first calculate the local maximum value sequence of the original signal, and all have been carried out before the calculation averaged processing. Let PE={PE _i |i=1,2,...,N _PE } be the local maximum value sequence of the original signal, and N _PE be the number of local maximum value sequences. Let NE={NE _i |i=1,2,...,N _NE } be the local minimum value sequence of the original signal, and N _NE be the number of local minimum value sequences. Define the local maximum interval as The interval between local minima is Based on the obtained local maximum and minimum intervals and the characteristics of triangular and semicircular structural elements, the minimum value K _lmin and maximum value K _lmax of the length scale of the corresponding morphological structural elements can be calculated.

In the formula, is the round up operator, is the floor operator.

From this, the length scale sequence K _l of the structural elements can be obtained as:

K _l ＝{K _lmin ,K _lmin +1,K _lmax -1,K _lmax }

(5) Determination of the height of structural elements

Since the height of the structural element corresponds to the amplitude of the signal, the height of the structural element is determined according to the amplitude of the local maximum and minimum values of the signal. Suppose the maximum value and minimum value of the local maximum value sequence are p _{p max} and p _{p min} respectively, then the height values of the local maximum value and local minimum value of the signal are H _pe =p _{p max} -p _{p min} and H _ne =p _{n max} -p _{n min} . In order to make full use of the height local feature information of the signal, the height value of the local extremum of the signal is defined as _He

H _e =max(H _pe ,H _ne )

In order to make the height value sequence _Hl correspond to the structural element length scale _Kl , the structural element height sequence _Hl can be defined as:

H _l ＝{α·[H _e /(K _max -K _min +1)+(j-1)·H _e /(K _max -K _min +1)]}

j=1,2,...,K _max -K _min +1

In the formula, α is the height proportional coefficient, which is taken as 0.05 in this embodiment.

(6) Definition of unit structure elements

Taking the triangular structure element as an example, select the structure element of three data points as the unit structure element B, and (K-1 expansion operation), when the scale K=1, KB={ 0 , 1,0}, when the scale K=2, KB={ 0,1,2,1,0 }, and so on, underlined The location of the origin.

(7) Determination of structural elements of each scale

G ₁ ＝H _l (i)·K _l (i)B _T i＝1,2,...,K _max -K _min +1

G ₂ ＝H _l (i)·K _l (i)B _S i＝1,2,...,K _max -K _min +1

Among them, B _T and B _S are the unit triangle structure element and the unit semicircle structure element respectively.

Claims (3)

1. A method for denoising airborne electromagnetic data based on mathematical morphology, characterized in that, comprising the following steps: A. Through the time-domain helicopter electromagnetic detection experiment, through the data acquisition hardware circuit, sampling at regular intervals is carried out, and the original aeronautical electromagnetic data is collected; B. Using the combination of triangular structural elements and semicircular structural elements, the aeronautical electromagnetic signal is subjected to adaptive multi-scale compound shape filtering processing, and the positive and negative pulse noise and random noise in the target signal are filtered out. 2. according to the airborne electromagnetic data denoising method based on mathematical morphology according to claim 1, it is characterized in that step B comprises the following steps: a. First, determine the length range of the structural element according to the minimum and maximum values of the interval between adjacent peaks in the original signal, and then determine the corresponding analysis scale K; b. Then determine the altitude range according to the minimum and maximum values of the signal peak value; c. Then use the small/large length to correspond to the small/large height to determine each structural element in the multi-scale analysis and form a corresponding multi-structural element set; d. Finally, each structural element set is used to perform compound morphological operations on the original signal and an average value is taken as the output result. 3. according to the airborne electromagnetic data denoising method based on mathematical morphology according to claim 2, it is characterized in that, the described original signal is carried out composite form operation is to carry out corrosion operation, dilation operation, opening respectively earlier to airborne electromagnetic signal Operation and closing operation, and then perform morphological opening and closing filtering and morphological closing and opening filtering respectively: Corrosion operation: $\left(\mathrm{f\&Theta;g}\right)\left(\mathrm{no}\right)=\underset{m=\mathrm{0,1},...,m-1}{\min }\{f(\mathrm{no}+m)-g\left(m\right)\}$ n=0,1,...,N+M-2 Expansion operation: $(f\&CirclePlus;g)\left(\mathrm{no}\right)=\underset{m=\mathrm{0,1},...,m-1}{\min }\{f(\mathrm{no}-m)+g\left(m\right)\}$ n=0,1,...,NM Open operation: Closing operation: $(f\&Center\; Dot;g)\left(\mathrm{no}\right)=\left[(f\&CirclePlus;g)\mathrm{\&Theta;g}\right]\left(\mathrm{no}\right)$ Among them, Θ represents the erosion operation, Represents expansion operation, ο represents opening operation, · represents closing operation, f is the original airborne electromagnetic waveform data, g is the selected morphological structure element, m and n are the discrete sampling points of the input signal, N>>M; Then perform morphological opening and closing filtering and morphological closing and opening filtering respectively: Morphological opening and closing filtering: Foc(f(n))=fοg·g Morphological closed-open filter: Fco(f(n))=f·gog Finally, construct the compound morphological filter: Adaptive complex morphological filter: $z\left(\mathrm{no}\right)=\frac{1}{2}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}[\mathrm{CFco}(f\left(\mathrm{no}\right),G_i)+\mathrm{CFoc}(f\left(\mathrm{no}\right),G_i)]$ Wherein, G=(g ₁ , g ₂ ,..., g _i ), represents a set of multiple structural elements, and N is the number of types of structural elements.