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

Abstract

The invention relates to an airborne electromagnetic data denoising method based on mathematical morphology. The airborne electromagnetic data denoising method includes: acquiring airborne electromagnetic detection data through an experiment, and combining triangular structure elements with semicircular structure elements to perform adaptive multiscale composite morphological filtering on the airborne electromagnetic date; determining a length range of the structure elements according to a minimum value and a maximum value of adjacent peak value intervals in original signals, and determining corresponding analysis scale K according to the length range; determining a height range according to a minimum value and a maximum value of signal peak values; adopting structure element sets for composite morphological operation on the original signals, and acquiring an average value as an output result. The adaptive multiscale composite morphological filtering method overcomes the defect of randomness in conventional selection of morphological filtering structure elements; by the airborne electromagnetic data denoising method, structure element type and scale can be selected adaptively according to local features and noise characteristics of signals for filtering airborne electromagnetic signals.

Description

Based on the aviation electromagnetic data de-noising method of mathematical morphology

Technical field

The present invention relates to a kind of data de-noising method of aviation electromagnetic field, especially time domain aviation electromagnetic field, specifically a kind of aviation electromagnetic data de-noising method based on mathematical morphology.

Background technology

Airborne eleectomagnetics is a kind of is carrier with aircraft, carries out the one prospecting detection method of geophysical exploration, is mainly used to quick census metal ore, large area geologic mapping, hydrogeology, the field such as engineering geologic investigation and environmental monitoring.

Mathematical morphology is a subject being based upon in strict mathematical theoretical foundation, now be successfully applied to the engineering practice fields such as image procossing, pattern analysis, pattern-recognition, computer vision, Power Disturbance, mechanical vibration and earthquake detection, and cause extensive attention.The method computing is simple, and its fundamental operation comprises that burn into expands, opening operation and closed operation and the form opening and closing of drawing on this basis and form make and break computing.Signal antinoise method based on mathematical morphology only depends on the local feature of pending signal, the geometric properties of structural element to signal is utilized to mate or revise, retain the principal shape of echo signal, to reach restraint speckle, to extract the object of useful information and reservation details composition simultaneously.

The main bugbear existed in mathematical morphology filter method is choosing of structural element, is the key factor affecting its filter effect on choosing of structural element type.Adopt dissimilar structural element shape facilities different in echo signal can be extracted, choosing of structural element will as much as possible close to the features of shape of pending signal itself, could reach best filter effect as far as possible like this, common structural element type has linear pattern, rectangle, collar plate shape, parabolic type, triangle and other polygons to combine.

Existing shape filtering method only adopts single scale structural element mostly, single scale morphology only selects a fixing structural element to carry out morphological analysis to signal, although this method is simple and be easy to realize, but the quality of its treatment effect relies on relevant priori greatly, and priori is often difficult to obtain accurately and effectively.In addition owing to usually comprising more than a kind of noise type in the signal, and noise in the signal often neither be equally distributed.

Existing shape filtering method all can not carry out complex morphological filtering to dissimilar in the structural element signal under different scale with the noise contribution of intensity.

Summary of the invention

Object of the present invention is just for the deficiencies in the prior art, provides a kind of while restraint speckle, extraction useful information, the aviation electromagnetic data de-noising method based on mathematical morphology of stick signal minutia better.

The object of the invention is to be achieved through the following technical solutions:

Main thought of the present invention is: for the multiple interference component comprised in aviation electromagnetic data, propose the morphologic filtering of self-adapting multi-dimension, have chosen triangular structure element and semicircular structure element, the positive and negative impulsive noise in filtered signal and random noise.

Based on the aviation electromagnetic data de-noising method of mathematical morphology, comprise the following steps:

A, by time domain helicopter electromagnetic detection experiment, through data acquisition hardware circuit, carry out timing equal interval sampling, collect original aerial electromagnetic data;

B, employing triangular structure element combine with semicircular structure element, aviation electromagnetic signal are carried out self-adapting multi-dimension complex morphological filtering process, the positive and negative impulsive noise in filtering echo signal and random noise.

Step B comprises the following steps:

A, first determine to analyze scale size K accordingly with this according to the minimum value at adjacent peak interval in original signal and the length range of maximal value determination structural element;

B, again according to minimum value and the maximal value determination altitude range of signal peak;

C, then utilize little/large length correspondence little/highly determine greatly each structural element in multiscale analysis and form corresponding Multi-structure elements collection;

D, finally each structural element set pair original signal is adopted to carry out complex morphological computing and average as Output rusults.

Described to carry out complex morphological computing to original signal be first carry out erosion operation, dilation operation, opening operation and closed operation respectively to aviation electromagnetic signal, then carry out Opening-closing filter and form make and break filtering respectively:

Erosion operation: $\left(\mathrm{f\Θg}\right)\left(n\right)=\underset{m=\mathrm{0,1},...,M-1}{\min }\{f(n+m)-g\left(m\right)\},n=\mathrm{0,1},...,N+M-2$

Dilation operation: $(f\⊕g)\left(n\right)=\underset{m=\mathrm{0,1},...,M-1}{\max }\{f(n-m)+g\left(m\right)\},n=\mathrm{0,1},...,N-M$

Opening operation:

Closed operation: $(f\·g)\left(n\right)=\left[(f\⊕g)\mathrm{\Θg}\right]\left(n\right)$

Wherein, Θ represents erosion operation, represent dilation operation, ο represents opening operation, and represent closed operation, f is original aerial electromagnetic waveforms data, and g is selected morphological structuring elements, m and n is that the discrete sampling of input signal is counted, N > > M;

Carry out Opening-closing filter and form make and break filtering more respectively:

Opening-closing filter:

Form make and break filtering:

Finally, complex morphological wave filter is constructed:

Self-adaptation complex morphological wave filter: $z\left(n\right)=\frac{1}{2}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}[\mathrm{CFco}(f\left(n\right),G_i)+\mathrm{CFoc}(f\left(n\right),G_i)]$

Wherein, G=(g ₁, g ₂..., g _i), represent one group of Multi-structure elements collection, N is the number of types of structural element.

Beneficial effect: based on the aviation electromagnetic data de-noising method of mathematical morphology, make it not only be extracted useful information when denoising, also remain the detailed information of aviation electromagnetic signal simultaneously well, so that further to data analysis; The present invention proposes self-adapting multi-dimension complex morphological filtering method, overcome existing shape filtering structural element and choose random problem, according to signal local feature and the adaptive choice structure element type of noise behavior and size, then can carry out filtering to aviation electromagnetic signal.

Accompanying drawing illustrates:

Accompanying drawing 1 is based on the aviation electromagnetic data de-noising method flow diagram of mathematical morphology

Accompanying drawing 2 self-adaptation complex morphological filtering method figure

Accompanying drawing 3 aviation electromagnetic raw-data map

Accompanying drawing 4 aviation electromagnetic original signal and mathematical morphology filter effect contrast figure

Accompanying drawing 5 self-adaptation complex morphological filter effect figure

Embodiment:

Below in conjunction with drawings and Examples, the present invention is described in further detail.

Based on the aviation electromagnetic data de-noising method of mathematical morphology, comprise the following steps:

A, by time domain helicopter electromagnetic detection experiment, through data acquisition hardware circuit, carry out timing equal interval sampling, collect original aerial electromagnetic data;

B, employing triangular structure element combine with semicircular structure element, aviation electromagnetic signal are carried out self-adapting multi-dimension complex morphological filtering process, the positive and negative impulsive noise in filtering echo signal and random noise.

Step B comprises the following steps:

A, first determine to analyze scale size K accordingly with this according to the minimum value at adjacent peak interval in original signal and the length range of maximal value determination structural element;

B, again according to minimum value and the maximal value determination altitude range of signal peak;

C, then utilize little/large length correspondence little/highly determine greatly each structural element in multiscale analysis and form corresponding Multi-structure elements collection;

D, finally each structural element set pair original signal is adopted to carry out complex morphological computing and average as Output rusults.

Described to carry out complex morphological computing to original signal be first carry out erosion operation, dilation operation, opening operation and closed operation respectively to aviation electromagnetic signal, then carry out Opening-closing filter and form make and break filtering respectively:

Erosion operation: $\left(\mathrm{f\Θg}\right)\left(n\right)=\underset{m=\mathrm{0,1},...,M-1}{\min }\{f(n+m)-g\left(m\right)\},n=\mathrm{0,1},...,N+M-2$

Dilation operation: $(f\⊕g)\left(n\right)=\underset{m=\mathrm{0,1},...,M-1}{\max }\{f(n-m)+g\left(m\right)\},n=\mathrm{0,1},...,N-M$

Opening operation:

Closed operation: $(f\·g)\left(n\right)=\left[(f\⊕g)\mathrm{\Θg}\right]\left(n\right)$

Wherein, Θ represents erosion operation, represent dilation operation, ο represents opening operation, and represent closed operation, f is original aerial electromagnetic waveforms data, and g is selected morphological structuring elements, m and n is that the discrete sampling of input signal is counted, N > > M;

Carry out Opening-closing filter and form make and break filtering more respectively:

Opening-closing filter:

Form make and break filtering:

Finally, complex morphological wave filter is constructed:

Self-adaptation complex morphological wave filter: $z\left(n\right)=\frac{1}{2}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}[\mathrm{CFco}(f\left(n\right),G_i)+\mathrm{CFoc}(f\left(n\right),G_i)]$

Wherein, G=(g ₁, g ₂..., g _i), represent one group of Multi-structure elements collection, N is the number of types of structural element.

Embodiment 1:

(1) original aerial electromagnetic data is obtained by time domain helicopter electromagnetic survey mission test.Be specially: utilize aviation electromagnetic detection system data acquisition hardware circuit to obtain result of detection Wave data, carry out timing equal interval sampling through data acquisition hardware circuit, collect aviation electromagnetic original signal data.

(2) triangular structure element is suitable for the positive and negative impulse noise interference of filtering, and semicircular structure element is suitable for filtering random noise disturbance.Therefore consider to adopt triangle and semicircular structure element to carry out complex morphological filtering to original signal.Detailed process is as follows:

(1) first, respectively erosion operation, dilation operation, opening operation and closed operation are carried out to signal:

Erosion operation: $\left(\mathrm{f\Θg}\right)\left(n\right)=\underset{m=\mathrm{0,1},...,M-1}{\min }\{f(n+m)-g\left(m\right)\},n=\mathrm{0,1},...,N+M-2$

Dilation operation: $(f\⊕g)\left(n\right)=\underset{m=\mathrm{0,1},...,M-1}{\max }\{f(n-m)+g\left(m\right)\},n=\mathrm{0,1},...,N-M$

Opening operation:

Closed operation: $(f\·g)\left(n\right)=\left[(f\⊕g)\mathrm{\Θg}\right]\left(n\right)$

(2) Opening-closing filter and form make and break filtering is carried out again respectively:

Opening-closing filter:

Form make and break filtering:

Construct a kind of self-adaptation complex morphological wave filter, thus improve filter effect.

The filtering of self-adaptation complex morphological: $z\left(n\right)=\frac{1}{2}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}[\mathrm{CFco}(f\left(n\right),G_i)+\mathrm{CFoc}(f\left(n\right),G_i)]$

Wherein

(3) mathematic(al) representation of triangular structure element and semicircular structure element is as follows respectively:

(1) triangular structure element

$g\left(i\right)=H\×[1-\frac{\left|i\right|}{L}],(i=-L,...,0,...,L)$

(2) semicircular structure element

$g\left(i\right)=H\×\left[\sqrt{1-{\left(\frac{i}{L}\right)}^2}\right],(i=-L,...,0,...,L)$

Wherein, the length of L representative structure element, the height of H representative structure element.

(4) determination of structural element length

If original signal is X={x _i| i=1,2 ..., N} (N is the number of data points of original signal), first calculates the local maximum value sequence of original signal, and has all carried out equalization process before the computation.If PE={PE _i| i=1,2 ..., N _pEbe the local maximum value sequence of original signal, N _pEfor the number of local maximum value sequence.If NE={NE _i| i=1,2 ..., N _nEbe the local minimum value sequence of original signal, N _nEfor the number of local minimum value sequence.Definition local maximum is spaced apart local minimum is spaced apart by the feature of the minimum interval of the local maximum obtained and triangle, semicircular structure element, the minimum value K of corresponding morphological structuring elements length dimension can be calculated _lminwith maximal value K _lmax.

In formula, for the operational symbol that rounds up, for downward rounding operation accords with.

The length dimension sequence K of structural element can be obtained thus _lfor:

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

(5) determination of structural element height

Due to the amplitude of the height respective signal of structural element, therefore determine the height of structural element according to the minimizing amplitude size of signal local maximum.If maximal value and the minimum value of local maximum sequence are respectively p _{p max}and p _{p min}, then the minimizing height value of local maximum and local of signal is respectively H _pe=p _{p max}-p _{p min}and H _ne=p _{n max}-p _{n min}.For making full use of the height local feature information of signal, the height value of the local extremum of definition signal is H _e

H _e＝max(H _pe,H _ne)

In order to make height value sequence H _lwith structural element length dimension K _lcorresponding, definable structural element high degree of sequence H _lfor:

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 formula, α is height ratio coefficient, and the present embodiment gets 0.05.

(6) definition of unit structure element

For triangular structure element, the structural element selecting three data points is unit structural element B, and (K-1 dilation operation), during yardstick K=1, KB={0, 1, 0}, during yardstick K=2, KB={0,1, 2, 1,0}, the like, underscore represents the position of initial point.

(7) determination of each mesostructure element

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

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

Wherein, B _tand B _sbe respectively unit triangle structural element and unit semicircular structure element.

Claims (3)

1., based on an aviation electromagnetic data de-noising method for mathematical morphology, it is characterized in that, comprise the following steps:

A, by time domain helicopter electromagnetic detection experiment, through data acquisition hardware circuit, carry out timing equal interval sampling, collect original aerial electromagnetic data;

B, employing triangular structure element combine with semicircular structure element, aviation electromagnetic signal are carried out self-adapting multi-dimension complex morphological filtering process, the positive and negative impulsive noise in filtering echo signal and random noise.

2., according to the aviation electromagnetic data de-noising method based on mathematical morphology according to claim 1, it is characterized in that, step B comprises the following steps:

A, first determine to analyze scale size K accordingly with this according to the minimum value at adjacent peak interval in original signal and the length range of maximal value determination structural element;

B, again according to minimum value and the maximal value determination altitude range of signal peak;

C, then utilize little/large length correspondence little/highly determine greatly each structural element in multiscale analysis and form corresponding Multi-structure elements collection;

D, finally each structural element set pair original signal is adopted to carry out complex morphological computing and average as Output rusults.

3. according to the aviation electromagnetic data de-noising method based on mathematical morphology according to claim 2, it is characterized in that, described to carry out complex morphological computing to original signal be first carry out erosion operation, dilation operation, opening operation and closed operation respectively to aviation electromagnetic signal, then carry out Opening-closing filter and form make and break filtering respectively:

Erosion operation: $\left(\mathrm{f\Θg}\right)\left(n\right)=\underset{m=\mathrm{0,1},...,M-1}{\min }\{f(n+m)-g\left(m\right)\}$ n＝0,1,...,N+M-2

Dilation operation: $(f\⊕g)\left(n\right)=\underset{m=\mathrm{0,1},...,M-1}{\min }\{f(n-m)+g\left(m\right)\}$ n＝0,1,...,N-M

Opening operation:

Closed operation: $(f\·g)\left(n\right)=\left[(f\⊕g)\mathrm{\Θg}\right]\left(n\right)$

Wherein, Θ represents erosion operation, represent dilation operation, ο represents opening operation, and represent closed operation, f is original aerial electromagnetic waveforms data, and g is selected morphological structuring elements, m and n is that the discrete sampling of input signal is counted, N > > M;

Carry out Opening-closing filter and form make and break filtering more respectively:

Opening-closing filter: Foc (f (n))=f ο gg

Form make and break filtering: Fco (f (n))=fg ο g

Finally, complex morphological wave filter is constructed:

Self-adaptation complex morphological wave filter: $z\left(n\right)=\frac{1}{2}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}[\mathrm{CFco}(f\left(n\right),G_i)+\mathrm{CFoc}(f\left(n\right),G_i)]$

Wherein, G=(g ₁, g ₂..., g _i), represent one group of Multi-structure elements collection, N is the number of types of structural element.