CN105469368A - Interferometric phase filtering method - Google Patents

Abstract

The invention provides an interferometric phase filtering method. According to the technical schemes of the invention, the interferometric phase filtering method comprises the steps of frequency domain filtering and spatial domain filtering. According to the frequency domain filtering, an interferometric phase graph is converted to a complex field, so that a complex interferometric phase graph can be obtained; the complex interferometric phase graph is divided into square image blocks with overlapped areas; and frequency domain processing is performed on each image block, so that a frequency domain filtered complex interferometric phase graph can be obtained. According to the spatial domain filtering, the frequency domain filtered complex interferometric phase graph is subtracted from the complex interferometric phase graph, so that a residual complex interferometric phase graph can be obtained; the residual complex interferometric phase graph is filtered by using mean filtering, so that a spatial domain filtered residual complex interferometric phase graph can be obtained; the frequency domain filtered complex interferometric phase graph and the spatial domain filtered residual complex interferometric phase graph are added together, so that a filtered complex interferometric phase graph can be obtained, and phase selection is performed on the filtered complex interferometric phase graph, so that a filtered interferometric phase graph can be obtained. With the interferometric phase filtering method of the invention adopted, the detail information of interferometric phases can be reserved when noises are effectively filtered out.

Description

Interference phase filtering method

Technical Field

The invention belongs to the technical field of crossing of remote sensing and signal processing, and particularly relates to a filtering method of an interference phase.

Background

And (4) carrying out conjugate multiplication on the two synthetic aperture radar images, and taking the phase of the multiplication result to obtain an interference phase. The interference phase is an important physical quantity in the interferometry of the synthetic aperture radar, and the quality of the interference phase determines the precision of a final product, namely a digital elevation model or a terrain deformation quantity. However, due to the decorrelation factors, there is always severe space-variant noise in the interference phase. The space-variant noise not only introduces residual error points but also destroys the distribution of interference phases, thereby increasing the difficulty of subsequent phase unwrapping, and finally reducing the precision of products, so that the residual error points must be filtered through the interference phase filtering process.

The existing interference phase filtering methods are mainly classified into a spatial domain method and a transform domain method. The spatial domain method mainly adopts a self-adaptive window to filter according to the direction of interference fringes in an interference phase so as to achieve the effects of filtering noise and keeping details, and the methods mainly comprise a mean value method, a Lee method, a rotation method and the like. However, this method is not very effective for the low coherence region, and it is easy to destroy the detailed information of the region where the interference phase changes drastically.

The transform domain method can be classified into a frequency domain method and a wavelet domain method. The main basis of the transform domain method is: the interference phase and noise can be well separated in the transform domain. The frequency domain method mainly comprises a Goldstein method and an improved method thereof, and the wavelet domain method mainly comprises a discrete wavelet transform method and the like. The transform domain approach may result in over-filtering or under-filtering, since the interference phase and noise cannot be completely separated.

Disclosure of Invention

The invention provides an interference phase filtering method which can effectively filter noise and simultaneously keep detailed information of an interference phase.

The technical scheme of the invention is as follows: an interferometric phase filtering method, comprising the steps of:

first step, frequency filtering:

converting the interference phase diagram into a complex field to obtain a complex interference phase diagram, dividing the complex interference phase diagram into square image blocks with overlapping areas, wherein the following image blocks all refer to the square image block;

for each image block, the following processing is respectively carried out:

calculating a two-dimensional frequency spectrum of the image block by using two-dimensional Fourier forward transform;

performing absolute value taking, smoothing, normalization and power exponent operation on the two-dimensional frequency spectrum of the image block to obtain weight, wherein the power exponent is determined by using a noise standard deviation of a complex interference phase diagram and a normalized inverse phase derivative variance diagram of the interference phase diagram;

weighting the two-dimensional frequency spectrum of the image block by using the obtained weight so as to realize filtering;

performing two-dimensional inverse Fourier transform on the weighted two-dimensional frequency spectrum of the image block to obtain a frequency-domain filtered image block;

smoothing the overlapped area of the image blocks after the frequency domain filtering by using an averaging method so as to obtain a complex interference phase diagram after the frequency domain filtering;

step two, spatial filtering:

subtracting the complex interference phase image after frequency domain filtering by using the complex interference phase image to obtain a residual complex interference phase image, and filtering the residual complex interference phase image by using mean value filtering to obtain a residual complex interference phase image after spatial domain filtering; and adding the frequency-domain filtered complex interference phase diagram and the residual complex interference phase diagram after spatial-domain filtering to obtain a filtered complex interference phase diagram, and taking the phase of the filtered complex interference phase diagram to obtain the filtered interference phase diagram.

The invention can achieve the following technical effects:

the method comprises one-step frequency domain filtering and one-step spatial domain filtering, wherein the frequency domain filtering has the advantage of keeping dense interference fringes while filtering noise, the spatial domain filtering has the advantage of further filtering noise and keeping partial detail information, and the method integrates the advantages of the two filtering processes; in addition, another innovation point of the invention is that the power exponent is determined by adopting the noise standard deviation of the complex interference phase diagram and the normalized inverse phase derivative variance diagram of the interference phase diagram during the first step of frequency domain filtering, thereby improving the filtering precision; meanwhile, the detail information of the interference phase is kept through mean value filtering.

Drawings

FIG. 1 is a schematic flow chart of an interference phase filtering method according to the present invention;

FIG. 2 is an interference phase diagram to be filtered;

FIG. 3 is a filtered interference phase diagram obtained by the Goldstein method;

FIG. 4 is a filtered interference phase diagram obtained by Lee method;

FIG. 5 is a diagram of the interference phase after filtering according to the present invention;

fig. 6 is a graph comparing the performance of fig. 3, fig. 4 and fig. 5.

Detailed Description

The present invention will be described in detail with reference to fig. 1.

The method comprises the following steps: converting and blocking the interference phase map into a complex interference phase map:

wherein,the method comprises the steps of partitioning a complex interference phase image, wherein the size of an image block is a square of 32 × 32 pixels, the partition and the partition are overlapped, each direction is overlapped by 14 pixel points, and then the step ② is completed for each image block.

Step two: image block filtering

Step (1), calculating a two-dimensional frequency spectrum of the image block:

B＝FFT2(P)

where P is an image block, B is the two-dimensional spectrum of the image block, and FFT2(·) is a two-dimensional fourier transform.

Step (2): and performing absolute value taking, smoothing, normalization and power exponent operation on the two-dimensional frequency spectrum of the image block to obtain the weight.

Calculating the absolute value A of the two-dimensional frequency spectrum of the image block:

A＝abs(B)

where abs (. circle.) represents the absolute value. The a value is then smoothed:

S＝smooth(A)

where S is an absolute value of the two-dimensional spectrum of the smoothed image block, smooth (·) is a two-dimensional gaussian filter, and the window size of the two-dimensional gaussian filter is determined according to actual conditions, and is 7 × 7 pixels in the embodiment of the present invention. Then, S is normalized:

N＝normalization(S)

wherein normalization () is a normalization operator. And finally, obtaining a weight W by exponentiating the N:

W＝N^α

wherein:

α＝(1.1σ)^β

where σ is the noise standard deviation of the complex interference phase image block,is interference phase pattern corresponding to filter windowThe mean value of the medium normalized inverse phase derivative variogram is calculated by the following formula:

σ＝1.4826median(|▽P-median(▽P)|)

$\▿P=\frac{1}{\sqrt{6}}vec\left(P*\left[\begin{array}{cc}2& -1\\ -1& 0\end{array}\right]\right)$

$\stackrel{\‾}{V}=mean\left(normalization\left(\frac{1}{PDV}\right)\right)$

PDV is a phase derivative variance graph of an interference phase graph corresponding to a filtering window, and mean (-) is an averaging operator.

Step (3): weighting the two-dimensional spectrum of the image block:

B_W＝B·W

B_Wis the weighted image block two-dimensional spectrum.

Step three, calculating the complex interference phase diagram after frequency domain filtering

After obtaining the weighted two-dimensional frequency spectrums of all the image blocks, calculating the weighted complex interference image blocks P by two-dimensional inverse Fourier transform_W：

P_W＝IFFT2(B_W)

Where IFFT2(·) is a two-dimensional inverse fourier transform. The frequency domain filtering results of the overlapping regions come from different image blocks, so that the method of averaging the frequency domain filtering results of all the overlapping regions is adopted, and the complex interference phase diagram psi subjected to frequency filtering is obtained_frequency。

Step IV: computing a spatial filtered residual complex interference phase map

Step (1), calculating residual complex interference phase diagram psi_residual：

ψ_residual＝ψ-ψ_frequency

Step (2), calculating a residual complex interference phase diagram psi after spatial filtering_spatial：

ψ_spatial＝meanfilter(ψ_residual)

Where, meanfilter (-) is an average filter, and the window size is determined according to actual conditions, which is 5 × 5 pixels in the embodiment of the present invention.

Step five: computing a filtered interference phase map

Step (1), calculating the filtered complex interference phase diagram psi_filtered：

ψ_filtered＝ψ_spatial+ψ_frequency

And (2) calculating a filtered interference phase diagram:

wherein angle (·) is a phase operator.

Detailed description with respect to fig. 2-6:

fig. 2 is an interference phase diagram to be filtered. The interference phase is intercepted from the measured data of Italian Etna volcano, the size is 500 x 500 pixels, wherein the abscissa is a column index, and the unit is a pixel; the ordinate is the row index and the unit is the pixel.

Fig. 3 is a filtered interference phase diagram obtained by the Goldstein method. It can be seen that although the interference fringes are well preserved, part of the noise is still present.

Fig. 4 is a filtered interference phase diagram obtained by the Lee method. It can be seen that the noise is well filtered, but the interference fringes are destroyed, especially in the areas where the interference fringes are dense.

Fig. 5 is a diagram of the interference phase after filtering according to the present invention. It can be seen that the noise is effectively filtered and the interference fringes are well maintained.

Fig. 6 is a graph comparing the performance of fig. 3, fig. 4 and fig. 5. The performance comparison graph comprises a performance index: residual points. The residual point is calculated by the following method: for any 4 adjacent pixel points in the filtered interference phase image:we calculate the winding gradient values of two pixels respectively:

wherein, C {. is a winding operator, and the value range is [ -pi, pi) ], delta₁，Δ₂，Δ₃，Δ₄Is the winding gradient value. The 4 wrap gradient values are then summed:

Δ_total＝Δ₁+Δ₂+Δ₃+Δ₄

if Δ_totalAnd (4) not equal to 0, the pixel points (i, j) are called residual points, and the smaller the number of the residual points is, the better the quality of the interference phase diagram after filtering is. Compared with the Goldstein method and the Lee method, the method greatly reduces the number of residual points in the interference phase diagram, and is more favorable for subsequent phase unwrapping.

Claims (1)

1. An interferometric phase filtering method, comprising the steps of:

first step, frequency filtering:

converting the interference phase diagram into a complex field to obtain a complex interference phase diagram, dividing the complex interference phase diagram into square image blocks with overlapping areas, wherein the following image blocks all refer to the square image block;

for each image block, the following processing is respectively carried out:

calculating a two-dimensional frequency spectrum of the image block by using two-dimensional Fourier forward transform;

performing absolute value taking, smoothing, normalization and power exponent operation on the two-dimensional frequency spectrum of the image block to obtain weight, wherein the power exponent is determined by using a noise standard deviation of a complex interference phase diagram and a normalized inverse phase derivative variance diagram of the interference phase diagram;

weighting the two-dimensional frequency spectrum of the image block by using the obtained weight;

performing two-dimensional inverse Fourier transform on the weighted two-dimensional frequency spectrum of the image block to obtain a frequency-domain filtered image block;

smoothing the overlapped area of the image blocks after the frequency domain filtering by using an averaging method to obtain a complex interference phase diagram after the frequency domain filtering;

step two, spatial filtering:

subtracting the complex interference phase image after frequency domain filtering by using the complex interference phase image to obtain a residual complex interference phase image, and filtering the residual complex interference phase image by using mean value filtering to obtain a residual complex interference phase image after spatial domain filtering; and adding the frequency-domain filtered complex interference phase diagram and the residual complex interference phase diagram after spatial-domain filtering to obtain a filtered complex interference phase diagram, and taking the phase of the filtered complex interference phase diagram to obtain the filtered interference phase diagram.