CN105204010A - Ground object target detection method of low signal-to-clutter ratio synthetic aperture radar image - Google Patents

Abstract

The invention relates to a low signal-to-clutter ratio two-dimensional radar image target detection method. The method is characterized by through profile transformation, selecting a decomposition coefficient characteristic, restraining an influence of an inherent speckle noise of a SAR image and increasing a signal to noise ratio of the SAR image; extracting characteristic information of different directions and acquiring a target edge details and geometrical information; extracting the different decomposition coefficient characteristics so as to carry out fusion processing, improving a gap between a target characteristic value and a background characteristic value and increasing a target detection capability and a false alarm resistance capability. The invention discloses the target detection method which can be used to effectively process a low signal-to-clutter ratio SAR image; a direction decomposition number of each decomposition scale can be designed arbitrarily; detail information of a low-frequency characteristic sub-graph and a plurality of high-frequency characteristic sub-graphs can be acquired so that a small target, a hidden target and a weak scattering target which can not be detected by using a general method can be easily detected; a high false alarm resistance capability is possessed so that an inspection effect of the target is effectively increased.

Description

The ground object target detection method of low signal to noise ratio diameter radar image

Technical field

The invention belongs to Signal and Information Processing technical field, relate to the two-dimensional radar image object detection method of a kind of low signal to noise ratio that profile ripple (Contourlet) converter technique in multi-scale geometric analysis combines with synthetic aperture radar image-forming technology.

Background technology

Synthetic-aperture radar (SyntheticApertureRadar, hereinafter referred to as SAR), since eighties of last century birth at the beginning of the fifties, has obtained in civilian and military field and has applied widely.Due to the microwave Coherent Imaging RADAR that SAR is a kind of active, typical feature has round-the-clock, that round-the-clock obtains data ability, therefore, be collectively referred to as two large remote sensing Disciplinary Frontiers in the present age with high-spectrum remote-sensing, it has become earth observation systems and the indispensable important Detection Techniques of space-based reconnaissance and surveillance system.SAR has very good prospect in the application of military field, and it is not only the important technical of military target information detection, or the important sources of battle space awareness.But SAR imaging is by the impact of the factor such as radar system parameters and ground object target surface geometry, especially the speckle noise that coherent imaging mechanism is intrinsic and the susceptibility in orientation, they bring great difficulty to the decipher of SAR image and application, and particularly further become more meticulous application.Scout with counterreconnaissance, detect and instead detect, identify and camouflage etc. always interweaves and develops, all the time along with the evolution of war.Modern war is the IT-based warfare of in the high-tech, and how accurately, quick obtaining information is a very the key link.Nearly several local wars fully show, no matter be the military information scouting of prewar or the battlefield recruitment evaluation of war posture prediction and postwar, the information source of more than 80% is in military imaging reconnaissance satellite and Commercial Remote Sensing Satellites.But modern battlefield environment becomes increasingly complex, traditional optics and infrared remote sensing cannot meet modern war requirement, and SAR Imaging remote sensing technology compensate for their defect, have played irreplaceable effect, as " lacrosse " series of the U.S..In the application of SAR, the acquisition of the detection of SAR target, classification and identification and change information is the important content of target intelligence reconnaissance and surveillance and battlefield dynamic sensing all the time.

Modern battlefield and target intelligence reconnaissance are mainly derived from various remote sensing images, such as SAR image, infrared image and optical imagery.Simultaneously some are important, high pay-off target is often pretended or hidden, or coat some absorbing materials.Therefore, what in remote sensing images, these targets often presented is weak scattering or weak reflecting body, often disturb by background clutter signal and cover, be difficult to be detected or detect.The basic reason producing this phenomenon be reflection between object and background or scattering strength closely, namely their gray-scale value is very close, causes the signal to noise ratio of whole image also very very low.This is not used in the detection and indentification of target very much.And existing object detection method is difficult to obtain desirable effect, therefore, in order to effectively detect these hidden targets, transonic target and less target, the present invention is from SAR imaging mechanism, utilize profile wave convert principle in multi-scale geometric analysis theory, propose a kind of low signal to noise ratio (LowSignalClutterRatio, LSCR) object detection method newly.

Summary of the invention

For above-mentioned prior art situation, the object of the invention is to: the ground object target detection method that a kind of low signal to noise ratio diameter radar image is provided, be called for short LSCR detection method.The method effectively can suppress the impact of SAR image speckle noise on the one hand, on the other hand, by the extraction of feature, can adjust the gray scale dynamic range between the feature of target area or area-of-interest in SAR image and background clutter feature.The more important thing is the multiple dimensioned multidirectional feature utilizing profile wave convert, the information of acquisition is more accurate.Therefore, the method can significantly improve the verification and measurement ratio of target, SAR target can effectively be detected, can obtain abundanter target information simultaneously.

Now design of the present invention and technical solution are described below:

Because SAR imaging mechanism is very complicated, be different from optical imagery, therefore, the detection of target needs to process SAR image in advance, as filtering, Edge contrast, histogram treatment, various conversion process, object improves the signal to noise ratio of SAR image, is conducive to the detection of target.They are difficult to reach desirable effect usually.SAR imaging is the mapping of ground object target feature space to image space, and the interaction of electromagnetic wave and ground object target is very complicated, and the signal of returning from ground object target scattering is non-stationary, nonlinear properties.Profile wave convert is better than wavelet transformation, there is many its own advantages: as multiple dimensioned characteristic, good time-frequency local characteristics, multi-direction characteristic, anisotropic properties, expand at the direction number of each yardstick simultaneously, allow the decomposition direction each yardstick with different number.Profile wave convert can carry out rarefaction representation curve with less basis function, a kind of superior rarefaction representation mode to image, be widely used in image co-registration, image denoising, image enhaucament, Iamge Segmentation, image object detection, recognition of face, image watermark process, Medical Image Processing etc., wavelet transformation is also a kind of extraordinary nonstationary random response method, is widely used.According to the feature of SAR image-forming principle and profile wave convert, and Small object, hide target and the feature of weak scattering target in SAR image, the present invention proposes a kind of low signal to noise ratio SAR image ground object target detection method, pass through profile wave convert, especially different profile Wave Decomposition coefficient characteristics is selected, the impact of the speckle noise that SAR image can be suppressed intrinsic, improves the signal to noise ratio (S/N ratio) of SAR image, is conducive to the inspection of target; In profile Wave Decomposition process, each decomposition layer different decomposition directions can be set, by extracting the characteristic information of different directions, abundanter object edge detailed information and geological information can be obtained; By extracting different profile Wave Decomposition coefficient characteristics, and carrying out fusion treatment, improving the gap between object feature value and background characteristics value, thus target detection capabilities and anti-false-alarm ability can be improved.Experiment shows that the method is a kind of very effective object detection method, has great application potential.

According to foregoing invention design and actual experimental result, the present invention proposes a kind of ground object target detection method of low signal to noise ratio diameter radar image, mainly comprises the following steps: (see Fig. 1):

Step 1: input SAR image;

Step 2: the Scale Decomposition of input profile wave convert and Directional Decomposition parameter;

Step 2.1: determine profile wave convert decomposition scale number:

Step 2.2: determine that each yardstick upper position that profile wave convert decomposes is to number:

Step 3: the conversion of profile Wave Decomposition is carried out to the SAR image of input; ;

Step 3.1: according to decomposition scale determined in step 2.1, the level number that namely will decompose, then carries out each Scale Decomposition to SAR;

Step 3.2: decompose number according to the orientation on each decomposition scale determined in step 2.2, orientation decomposition is carried out to each layer of the SAR image after Scale Decomposition;

Step 4: extract each Scale Decomposition coefficient characteristics figure of profile Wave Decomposition, and select corresponding feature;

Step 5: the method determining target detection;

Mechanism due to SAR imaging is coherent imaging, so coherence's constant false alarm rate (hereinafter referred to as the CCFAR) detection method selecting our seminar to propose detects target.CCFAR detection method reaches by the gap increasing object and background clutter reflection strength the object detecting target, no matter be Weak target or vanishing target, all can detect, and Detection results is good, under same constant false alarm rate, the false-alarm of generation is minimum;

Step 6: determine detection threshold T;

Step 7: target detection is carried out to characteristic pattern, and obtains testing result.

The present invention further provides a kind of diameter radar image object detection method based on profile wave convert, it is characterized in that: described in step 2 profile Wave Decomposition carries out to the SAR image of input time determined Scale Decomposition number and the concrete steps determined to parameters such as point skills of orientation be:

Step 2.1: determine profile wave convert decomposition scale number:

Arranging of profile Wave Decomposition parameter has larger impact to testing result, and these parameters mainly comprise Scale Decomposition sum of series orientation to decomposition direction number; Scale Decomposition sum of series orientation is arranged to the value of decomposing direction number can not be too high, can not be too low; If Scale Decomposition value of series is too high, for SAR image, mean in high yardstick a large amount of speckle noise comprised, they can flood the geometric detail of target area and marginal information, be unfavorable for the detection of target on the contrary, therefore, the value of Scale Decomposition progression is generally 3 to 5 proper.

Step 2.2: determine that each yardstick upper position that profile wave convert decomposes is to number:

Determining with decomposition scale number, orientation is also extremely important to the determination of resolution parameter, the extraction that all can affect azimuth information bigger than normal or less than normal of its value; Orientation can not infinitely increase to resolution parameter, this is because along with orientation is to the increase of resolution parameter, calculated amount can be multiplied, if direction number is too many, target area continuous information will isolate process, the extraction of unfavorable target information on the contrary.Therefore, orientation is no more than 5 usually to the value of resolution parameter.

The present invention further provides a kind of diameter radar image object detection method based on profile wave convert, it is characterized in that: described in step 3 to the concrete steps that SAR image carries out profile wave convert decomposition be;

Step 3.1: according to decomposition scale determined in step 2.1, the level number that namely will decompose, then carries out each Scale Decomposition to SAR, and decomposition scale should within 5.

Step 3.2: decompose number according to the orientation on each decomposition scale determined in step 2.2, carry out orientation decomposition to each layer of the SAR image after Scale Decomposition, the direction set by each decomposition scale is followed successively by 2 ⁴, 2 ³, 2 ², 2 ¹, namely 16,8,4 and 2, decomposition scale by thick yardstick to thin yardstick.

The present invention further provides a kind of diameter radar image object detection method based on profile wave convert, it is characterized in that: the extraction profile Wave Decomposition coefficient characteristics described in step 4 concrete steps of carrying out feature selecting are:

Step 4.1: the feature obtaining all directions on each decomposition scale, according to orientation each in step 3 to decomposition situation, extract each orientation to feature subimage;

Step 4.2: the information of different directions on obtained each yardstick is merged, just can obtain this Scale Decomposition coefficient characteristics subimage.

Step 4.3: select different decomposition scale features.Scale coefficient feature after decomposition comprises low frequency coefficient characteristic pattern and each high frequency coefficient characteristic pattern, but the information that each feature sub-picture pack contains is different, therefore, in actual applications, need concrete which feature subimage of selection, such as select whole high-frequency characteristic subimage, still select part high-frequency characteristic subimage, in the present invention, select characteristics of low-frequency subimage and two high-frequency characteristic subimages.

Step 4.4: feature subimage merges.Feature subimage selected by step 4.3 merges, and obtains final for target detection feature image.

The present invention's advantage is compared with prior art:

The present invention be a kind of newly, very effective algorithm of target detection, the particularly SAR image of low signal to noise ratio, its advantage clearly, is embodied in following three aspects:

(1) advantage of method design

Select profile wave convert theory to decompose SAR image, the Directional Decomposition number on each decomposition scale can design arbitrarily, from different multiple directions obtaining informations, the information of acquisition can be made more accurate, more approach the actual conditions of target like this.Simultaneously, after utilizing profile wave convert to decompose, low frequency subcharacter figure and multiple high frequency subcharacter figure can be obtained, and along with the increase of decomposition scale, if the detailed information of the information spinner HFS obtained, but also mainly there is HFS in noise, and therefore the ratio of the composition of Noise is also more and more higher simultaneously.Can select according to embody rule or strengthen certain part coefficient in actual applications, reach the object of Enhanced feature, if high yardstick does not affect processing intent, and the noise comprised is more, can consider directly to remove high yardstick part, the effect removed or suppress SAR image speckle noise can be reached like this.

(2) advantage of data processing

Characteristics of low-frequency and part high-frequency characteristic is selected to merge, both take into account the susceptibility of SAR imaging to orientation, considered again the suppression to SAR image speckle noise, and made acquisition information more accurate like this, and improve the signal to noise ratio of characteristic image, thus effectively improve the Checking on effect of target.

(3) advantage of target detection

Target is detected with the characteristic pattern after this method process, the verification and measurement ratio of target can not only be improved, and the Small object making originally cannot to detect with conventional method, hide target and weak scattering target becomes easy detection, the false-alarm probability of target is very low simultaneously, has strong anti-false-alarm ability.

Accompanying drawing explanation

Fig. 1: the ground object target detection method schematic diagram of low signal to noise ratio diameter radar image

Fig. 2: CCFAR detection method process flow diagram

Fig. 3: LSCR is used for tank T72 testing result figure

Wherein: a original image, b all thin characteristic coefficient figure, c low frequency and thin characteristic patterns of part

Fig. 4: LSCR is used for ship detection result figure

Wherein: a original image, b all thin characteristic coefficient figure, c low frequency and thin characteristic patterns of part

Embodiment

Now the present invention be described further, to survey SAR image, the present invention is further elaborated in conjunction with the embodiments:

Step 1: input original SAR image

Step 2: multiple dimensioned profile Wave Decomposition is carried out to SAR image.Select profile wave convert theoretical to the determination of the gordian technique decomposition scale that SAR image is decomposed and the determination of each yardstick upper position point skill, because yardstick is too high be, the inside comprises a large amount of speckle noises, according to actual conditions, sub-sample resolution yardstick is 4, equally, the decomposition direction of each yardstick can not be too many, is no more than 2 ⁵, otherwise process can be isolated to directional information, calculated amount also can be multiplied, the orientation point skill of every decomposition layer can be arranged arbitrarily, according to the precision of acquisition of information and the size of calculated amount, select the direction number on each decomposition scale not identical, be namely set to 2 from thick yardstick respectively to fine dimension ⁴, 2 ³, 2 ², 2 ^1,, because along with the increase of yardstick, information content is more and more less, so there is no need to arrange more orientation point skill on high-precision yardstick.

Step 3: obtain each Scale Decomposition coefficient characteristics figure, and choosing coefficient merges, after profile Wave Decomposition is carried out to SAR image, according to the setting of resolution parameter above, obtain a low frequency subgraph as characteristic pattern and 4 high frequency subimage characteristic patterns, another gordian technique after these feature subimages obtain how to select feature, in this experiment, low frequency subgraph picture and two details yardstick high frequency subimages are selected to merge, to obtain final target detection feature figure.

Step 4: select CCFAR detection algorithm to detect target;

Along with improving constantly of SAR image resolution, how from SAR image, extracting useful information rapidly, is focus and the difficult point of research at present, Target detection and identification in especially strong reflection clutter background; In the identification of SAR target, first need to determine potential target area from scene, be called area-of-interest (ROI); Under normal conditions, people use constant false alarm rate (CFAR) operator to complete the Detection task of target, constant false alarm rate detects and is often applied to radar and the communications field, its algorithm research has the history of more than 30 year, in this respect, U.S.'s Lincoln laboratory achieves a large amount of achievements in research, and representative is the DP-CFAR rate algorithm based on Gaussian distribution that Novak proposes.At present, widely used object detection method is still based on CFAR detection algorithm, it is developed so far existing many branches, as cell-average CA-CFAR (Cell-AverageCFAR), minimum selection SO-CFAR (SmallestofCFAR), Ordered Statistic OS-CFAR (OrderStatisticCFAR) and MAXIMUM SELECTION GO-CFAR (GreatestofCFAR) etc., their key distinction is different clutter Estimation of Mean algorithms.Detecting the shortcoming of target with CFAR, to be that requirement target and background clutter is distributed with obvious reflection strength poor, that is, is directly difficult to faint, little and hiding target be detected with CFAR algorithm.So of the present invention group etc. proposes coherence CFAR (CCFAR) SAR algorithm of target detection from SAR imaging mechanism, overcomes the weakness of CFAR algorithm.CCFAR not only can improve the signal to noise ratio of SAR image, but also the reflection strength that can expand object and background clutter is poor, is very beneficial for the detection of SAR image target.Fig. 2 is the process flow diagram of CCFAR detection algorithm.

In target detection, the determination of threshold value T is the key issue of CFAR algorithm of target detection, and it and background clutter distributed model have relation closely; Suppose the probability density function (PDF) that p (x) is radar clutter distributed model, then

$F\left(x\right)={\∫}_0^{x}p\left(t\right)\mathrm{dt}---\left(1\right)$

Visible F (x) [0 ,+∞) on be increasing function, pass through solving equation

$1-P_{\mathrm{fa}}={\∫}_0^{T}p\left(x\right)\mathrm{dx}---\left(2\right)$

Can threshold value T be obtained, wherein, P _fafor false-alarm probability, different P _fadifferent threshold value T can be obtained; Background clutter distribution mainly contains: lognormality (Log-normal) distribution, Rayleigh (Rayleigh) distribution, Wei Buer (Weibull) distribution, K distribution, Gamma distribution, Pearson came (Pearson) distribution etc., wherein rayleigh distributed is the special case of Wei Buer distribution.Land clutter is generally Wei Buer distribution, and sea clutter is generally K distribution, sometimes in order to simplify calculating, adopts Gauss (Gaussian) distribution, as typical two-parameter CFAR detection algorithm.

Step 5: obtain object detection results

By CCFAR detection method, the characteristic image after final coefficient fusion is detected, just can obtain the testing result figure of target; If I _f(x, y) representation feature figure, T represents the threshold value of acquisition, D _f(x, y) represents the result detected, and so can detect pixel with formula (3), judge whether to belong to interested pixel.

$D_F(x,y)=\left\{\begin{array}{cc}{I}_F(x,y);& \left|I_F(x,y)\right|\&GreaterEqual;T\\ 0;& \left|I_F(x,y)\right|<T\end{array}\right.---\left(3\right)$

If the value of pixel (x, y) is more than or equal to threshold value T, the target pixel points that need detect so exactly; If the value of pixel (x, y) is less than threshold value T, so just not think it is target pixel points.

Now according to experimental result of the present invention, accompanying drawing is described in further detail:

In order to verify the validity and reliability of the ground object target detection method (i.e. LSCR algorithm of target detection) of low signal to noise ratio diameter radar image proposed by the invention, we compare experiment by different SAR image and diverse ways, and experimental result as shown in Figure 3 and Figure 4.

The experimental data of Fig. 3 display derives from MSTAR (MovingandStationaryTargetAcquisitionandRecognition) database, and the target comprised is T72 tank, imaging background thick grass and bushes.Wherein, Fig. 3 (a) is original image, Fig. 3 (b) is the reconstructed image of all thin scale coefficient features after profile Wave Decomposition, Fig. 3 (c) is the reconstructed image of profile Wave Decomposition rear section scale coefficient feature, and Fig. 3 (A), Fig. 4 (B) and Fig. 3 (C) are the testing result figure of Fig. 3 (a), Fig. 3 (b) and Fig. 3 (c) respectively.In whole testing process, the detection algorithm of utilization is identical, and testing conditions is also identical, the detection algorithm CCFAR algorithm selected here.Known from Fig. 3 (a), the signal to noise ratio of original SAR image is lower, namely the gray-scale value of target area and background gray levels similar, therefore, be difficult to detect target area information accurately by general method.Profile wave convert is that one has multi-resolution characteristics, time-frequency local characteristics, multi-direction characteristic and anisotropic multiscale analysis geometric theory, is applicable to the treatment and analyses of SAR image.The Detection results of Fig. 3 (C) is obviously better than Fig. 3 (A) and Fig. 3 (B), and under identical condition, the false alarm rate in Fig. 3 (A) is apparently higher than Fig. 3 (C).So the result of Fig. 3 shows LSCR very effective algorithm of target detection.

The SAR image that Fig. 4 shows is data from the ERS-2 of European Space Agency, and wherein Fig. 4 (a) is original image, and the target comprised in image is ship, and background is ocean.During due to SAR imaging at that time, wave is larger, defines strong jamming pattern clutter, thus ship be scattering into weak scattering target, be usually difficult to detect, but effectively target can be detected by LSCR method.Icon in Fig. 4 illustrates identical with Fig. 3.As can see from Figure 4, under identical condition, the effect of Fig. 4 (C) is better than other two kinds of situations, and false alarm rate in Fig. 4 (C) is minimum, and this shows a kind of very effective SAR target detection method of LSCR algorithm further.Fig. 3 and Fig. 4 absolutely prove LSCR algorithm can not only effectively detect little, faint, hide target, and false dismissed rate and false alarm rate all very low.Under same constant false alarm rate (ConstantFalseAlarmRatio, CFAR) condition, be better than other algorithm of target detection, as wavelet transformation, CFAR detection algorithm, two-parameter detection method etc.The significant advantage of another one is the speckle noise that LSCR algorithm effectively can suppress SAR image, is conducive to the development facilitating SAR image Interpretation Technology and application prospect.

Claims (4)

1. the ground object target detection method of low signal to noise ratio diameter radar image, it is characterized in that: pass through profile wave convert, select different profile Wave Decomposition coefficient characteristics, the impact of the speckle noise suppressing diameter radar image (hereinafter referred to as SAR) intrinsic, improves the signal to noise ratio (S/N ratio) of SAR image; By extracting the characteristic information of different directions, obtain abundant object edge detailed information and geological information; Carrying out fusion treatment by extracting different profile Wave Decomposition coefficient characteristics, improving the gap between object feature value and background characteristics value, improve target detection capabilities and anti-false-alarm ability, specifically comprise the following steps:

Step 1: input SAR image;

Step 2: the Scale Decomposition of input profile wave convert and Directional Decomposition parameter;

Step 2.1: determine profile wave convert decomposition scale number;

Step 2.2: determine that each yardstick upper position that profile wave convert decomposes is to number;

Step 3: the conversion of profile Wave Decomposition is carried out to the SAR image of input;

Step 3.1: according to decomposition scale determined in step 2.1, the level number that namely will decompose, then carries out each Scale Decomposition to SAR;

Step 3.2: decompose number according to the orientation on each decomposition scale determined in step 2.2, orientation decomposition is carried out to each layer of the SAR image after Scale Decomposition;

Step 4: extract each Scale Decomposition coefficient characteristics figure of profile Wave Decomposition, and select corresponding feature;

Step 5: the method determining target detection: select coherence's constant false alarm rate detection method to detect target;

Step 6: determine detection threshold T: select the Likelihood estimation that mathematical expectation is maximum, comprise one and ask expectation value and maximizing two steps, these two steps repeat, until convergence.

Step 7: target detection is carried out to characteristic pattern, and obtains testing result.

2. the ground object target detection method of low signal to noise ratio diameter radar image according to claim 1, is characterized in that: described in step 3.1 each Scale Decomposition is carried out to SAR should within 5; Described in step 3.2,2 are followed successively by the direction that each layer of SAR image carries out set by orientation decomposition scale ⁴, 2 ³, 2 ², 2 ¹, namely 16,8,4 and 2, decomposition scale by thick yardstick to thin yardstick.

3. the ground object target detection method of low signal to noise ratio diameter radar image according to claim 1, is characterized in that: the extraction profile Wave Decomposition coefficient characteristics described in step 4 concrete steps of carrying out feature selecting are:

Step 4.1: the feature obtaining all directions on each decomposition scale, according to orientation each in step 3 to decomposition situation, extract each orientation to feature subimage;

Step 4.2: the information of different directions on obtained each yardstick is merged, obtains this Scale Decomposition coefficient characteristics subimage;

Step 4.3: select different decomposition scale features: specifically select characteristics of low-frequency subimage and two high-frequency characteristic subimages;

Step 4.4: feature subimage merges: the feature subimage selected by step 4.3 merges, obtains final for target detection feature image.

4. the ground object target detection method of low signal to noise ratio diameter radar image according to claim 1, is characterized in that: the Likelihood estimation that the method selection mathematical expectation of the determination detection threshold T described in step 6 is maximum, is specially:

Suppose the probability density function (PDF) that p (x) is radar clutter distributed model, then

$F\left(x\right)={\&Integral;}_0^{x}p\left(t\right)\mathrm{dt}---\left(1\right)$

F (x) [0 ,+∞) on be increasing function, pass through solving equation

$1-P_{\mathrm{fa}}={\&Integral;}_0^{T}p\left(x\right)\mathrm{dt}---\left(2\right)$

Can threshold value T be obtained, wherein, P _fafor false-alarm probability, different P _fadifferent threshold value T can be obtained; Background clutter is distributed with: lognormality (Log-normal) distribution, Rayleigh (Rayleigh) distribution, Wei Buer (Weibull) distribution, K distribution, Gamma distribution, Pearson came (Pearson) distribution.