CN105069753A - Mobile-terminal-oriented method for restoring blurred image caused by jitter - Google Patents

Abstract

The invention discloses a mobile-terminal-oriented method for restoring a blurred image caused by jitter, and includes: (1) obtaining a blurred image when a mobile terminal jitters; (2) obtaining an output sequence of a gyroscope related with a jitter trajectory of the mobile terminal within opening time of a camera shutter; (3) obtaining a rotation angle of the mobile terminal after performing integration processing on the output sequence, and performing coordinate mapping on the rotation angle, thereby obtaining a jitter PSF template; and (4) according to the blurred image and the jitter PSF template, adopting an image restoration algorithm to perform restoration processing, thereby obtaining a restored image. The mobile-terminal-oriented method for restoring the blurred image caused by jitter estimates the jitter trajectory of a built-in camera of the mobile terminal within the opening time of the shutter according to the built-in gyroscope of the mobile terminal; integration is performed on the output sequence value of the gyroscope to obtain the rotation angle of the mobile phone, and coordinates are mapped to an image plane coordinate system, thereby obtaining the jitter PSF template, and the blurred image can be effectively restored by utilization of the PSF template and the corresponding image restoration algorithm.

Description

A kind of shake Restoration method of blurred image of facing moving terminal

Technical field

The invention belongs to technical field of image processing, more specifically relate to a kind of shake Restoration method of blurred image of facing moving terminal.

Background technology

The built-in camera of mobile terminal, in pictures taken process, inevitably causes image to produce fuzzy due to the shake of a variety of causes, and time most, moment has non-repeated, therefore carries out recovery to the blurred picture of shooting and is just extremely necessary.The all built-in gyroscope of mobile terminal of the overwhelming majority on market, this makes to obtain the movable information of mobile terminal within the camera shutter opening time becomes possibility, the shake PSF template in this time just can be obtained according to the movable information of mobile terminal, then according to Image Restoration Algorithm and above-mentioned shake PSF template, restoration disposal is carried out to this blurred picture, just can obtain restored image.

Image restoration is extremely important in image processing field, its recuperation is actually a kind of estimation procedure, builds corresponding restoration model according to image blurring factor, thus takes corresponding Image Restoration Algorithm to restore blurred picture, improve the sharpness of image, improve its visual effect.

Blur image restoration is study hotspot and the difficult point of image processing field always, whether known according to PSF, blur image restoration is divided into blind recovery and non-blind to restore, and non-blind is restored and compared the estimation procedure that blind recovery mainly has more PSF, the difficult point of this image restoration often.Have the method for a lot of extracting directly PSF from blurred picture at present, this class methods complexity is high, and computing time is longer, and extraction effect affects comparatively large by picture material, adaptability is general.

Summary of the invention

For the defect of prior art, the invention provides a kind of shake Restoration method of blurred image of facing moving terminal, its object is to utilize the gyroscope of terminal built-in to obtain PSF, then apply it in non-blind restoration algorithm and blurred picture is restored, improve the sharpness of image.

The invention provides a kind of shake Restoration method of blurred image of facing moving terminal, comprise the steps:

(1) blurred picture during width mobile terminal shake is obtained;

(2) obtained in the camera shutter opening time by gyroscope, shake the relevant output sequence of track to mobile terminal;

Wherein, output sequence is m × n group data, and data layout is (G _xi, G _yi, G _zi, t _i), m is gyrostatic sample frequency, and n is the shutter opening time of camera, and subscript i represents output sequence number, and value is 1,2 ..., m × n, G _xirepresent i-th group of angular velocity rotated around X-axis, G _yirepresent i-th group of angular velocity rotated around Y-axis, G _zirepresent i-th group of angular velocity rotated around Z axis, t _irepresent the sampling instant of i-th group of data, X-axis is the optical axis of camera, and Y-axis is the longitudinal axis of picture plane, and Z axis is the transverse axis of picture plane;

(3) Integral Processing is carried out to described output sequence, obtain the rotational angle of camera Y-axis and Z axis in its place XYZ coordinate system, and described rotational angle is carried out virtual borderlines, obtain shake PSF template;

(4) according to described blurred picture and described shake PSF template, adopt Image Restoration Algorithm to carry out restoration disposal, obtain restored image.

Further, the step obtaining shake PSF template is specially:

(1) initialization empty chain table L, makes the initial value of output sequence i be 1;

(2) Integral Processing is carried out to described output sequence, obtain camera t within the shutter opening time _itime be engraved in the rotational angle θ of Y-axis in its place XYZ coordinate system _yiwith the rotational angle θ of Z axis _zi;

(3) by the rotational angle θ of camera in Y-axis _yiwith the rotational angle θ of Z axis _zibe mapped in photo coordinate system, obtain t in picture plane _ia location point (y in moment _i, z _i, △ t _i), and it is added in chained list L;

Wherein, y _ifor t _ithe deviation post of moment Y-axis, z _ifor t _ithe deviation post of moment Z axis, △ t _ifor camera attitude is in the retention time of this position, y _i=h × tan (θ _yi), z _i=h × tan (θ _zi), △ t _i=t _i+1-t _i, h represents camera lens focal length;

(4) judge whether i equals m × n, if so, then enter step (5); If not, then i adds 1, and is back to step (2);

(5) y is calculated _imaximum absolute value value and z _imaximum absolute value value ${\left|z\right|}_{max}={\mathrm{MAX}}_{i=1}^{m\×n}\left(\right|z_i\left|\right);$

(6) initialization one (2 × | y| _max+ 1) OK, (2 × | z| _max+ 1) the full 0 matrix M arranged, and make the initial value of data sequence number j be 1;

(7) the jth group data (y in chained list L is taken out _j, z _j, △ t _j), by (y in matrix M _j+ | y| _max) row (z _j+ | z| _max) element value that arranges adds △ t _j;

(8) judge whether j equals m × n, if so, then enter step (9); If not, then j adds 1, and is back to step (7);

(9) matrix M is normalized, namely obtains shake PSF template.

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

(1) the present invention is in order to improve the sharpness of blurred picture, carries out non-blind restoration disposal to it, can estimate the PSF of blurred picture; Gyroscope output sequence is utilized accurately to calculate the movement locus of camera within the shutter opening time particularly, then the PSF of blurred picture just can be estimated by virtual borderlines, again this PSF is applied in non-blind restoration algorithm and restoration disposal is carried out to mould lake image, obtain restored image, thus improve the sharpness of image.

(2) the present invention is only relevant with the state of terminal camera, and has nothing to do with the content of captured picture; And existing PSF extracting method is mostly after the content analyzing blurred picture, according to priori PSF estimated and extract, these method calculated amount are large and usable range has limitation more, the present invention only needs the PSF carrying out blurred picture according to the output sequence of terminal camera attitudes vibration to extract, have nothing to do with content of shooting, applicability is strong.

(3) the gyrostatic output sequence that the present invention is built-in according to mobile terminal directly calculates the PSF of blurred picture, and these data volumes are more limited, and therefore the present invention's complexity in PSF extraction is very low, and calculated amount is very little.

(4) pure digi-tal process, does not need to add extra hardware, with low cost.Can be found out by description above, the present invention only gyroscope built-in according to mobile terminal just can obtain desirable result, recovery operation pure digi-tal, does not need other auxiliary hardware devices completely, with low cost, has practical value widely.

Accompanying drawing explanation

Fig. 1 is the camera XYZ coordinate system figure that the embodiment of the present invention provides, and wherein X-axis is the optical axis of camera, and Y-axis is the longitudinal axis of picture plane, and Z axis is the transverse axis of picture plane;

Fig. 2 is the recovery process flow diagram that the embodiment of the present invention provides;

Fig. 3 is the coordinate graph of a relation of the output sequence that provides of the embodiment of the present invention to picture plane;

Fig. 4 is the extraction process flow diagram of the PSF that the embodiment of the present invention provides;

Fig. 5 is the actual recovery effect comparison diagram that the embodiment of the present invention provides, wherein figure (a), (b) are two width blurred pictures, figure (c) is the recovery effect figure of figure (a), schemes the recovery effect figure that (d) is figure (b).

Embodiment

In order to make object of the present invention, technical scheme and advantage clearly understand, below in conjunction with drawings and Examples, the present invention is further elaborated.Should be appreciated that specific embodiment described herein only in order to explain the present invention, be not intended to limit the present invention.

The shake of camera is divided into translation and rotation, and the impact of translation on picture quality is less, can not consider, rotating the impact of picture quality very large, is cause image blurring main cause.Fig. 1 is the camera XYZ coordinate system figure that the present embodiment provides, and wherein X-axis is the optical axis of camera, and Y-axis is the longitudinal axis of picture plane, and Z axis is the transverse axis of picture plane.The rotation of camera is exactly the rotation around X-axis, Y-axis and Z axis.And smaller around the impact of rotation on imaging of X-axis, so also can not consider.

The invention provides a kind of shake Restoration method of blurred image of facing moving terminal, the shake PSF template in the camera shutter opening time can be estimated, and carry out by this PSF template the Digital Rehabilitation shaking blurred picture.The gyroscope that the present invention utilizes mobile terminal built-in obtains the output sequence that camera rotates around described X-axis, Y-axis and Z axis, then the shake track of camera within the shutter opening time is estimated, the PSF of blurred picture is obtained again by virtual borderlines, finally this PSF is applied in Image Restoration Algorithm and digital restoration is carried out to blurred picture, thus improve the sharpness of image, improve its visual effect.Because camera and gyroscope are all built in mobile terminal, therefore camera and gyroscope have identical shake track, so can obtain the movable information of camera with the output sequence of gyroscope within the camera shutter opening time.

In the shake Restoration method of blurred image of facing moving terminal provided by the invention, finally need shake PSF template to be applied in Image Restoration Algorithm and could to restore blurred picture, the Image Restoration Algorithm that the present embodiment is selected is Richardson-Lucy algorithm.Fig. 2 is the recovery process flow diagram that the embodiment of the present invention provides, and specifically comprises the steps:

(1) blurred picture during width mobile terminal shake is obtained;

(2) camera is obtained within the shutter opening time around the output sequence that described X-axis, Y-axis and Z axis rotate by gyroscope.

(3) Integral Processing is carried out to above-mentioned output sequence, obtain the rotational angle of each moment camera Y-axis and Z axis in the shutter opening time.

(4) rotational angle of trying to achieve in step (3) is mapped to photo coordinate system by coordinate conversion, obtains shake PSF template.

(5) Richardson-Lucy algorithm is utilized to restore blurred picture.

Richardson-Lucy restoration algorithm is a kind of Restoration method of blurred image adopting iterative manner, its core is the recovery utilizing the high s/n ratio PSF template obtained to carry out blurred picture, obtain the PSF of blurred picture in step (4), thus utilize Richardson-Lucy algorithm can realize the recovery of the blurred picture to mobile terminal shooting.

For optical imaging system, the system that PSF is defined as using two-dimensional impact function as input exports.Wherein two-dimensional impact function is defined as form as follows:

$\mathrm{\δ}(x,y)=\{\begin{array}{cc}\mathrm{\∞},& x^2+y^2=0\\ 0,& x^2+y^2\≠0\end{array}---\left(1\right)$

The shake of broad sense is defined as the random offset that optical imaging system PSF center changes generation in time.Concerning point target, shake to show as in image target picture point in each departing from its ideal position in efficiently sampling moment, and that is shake is the motion artifacts that a kind of Random Effect causes, and shows as the random offset of target location in picture frame.Discussed herein is dithered as sensu lato shake, and it should be noted that when the imaging camera shutter opening time enough in short-term, shake can not cause the random motion of PSF in picture frame, that is shakes the spatial distribution characteristic not affecting instantaneous PSF.Do not consider to defocus etc. that reason causes is image blurring, the image of shake is clearly at sampling instances, but time averaging result can cause the fuzzy of image.

Suppose that the opening and closing of shutter time used is very short, so optical imaging procedures can not be subject to the interference of flating.Original image f (x, y), by the effect of degenrate function H, obtains blurred picture g (x, y):

g(x,y)＝H[f(x,y)](2)

If degenrate function H is linear, space invariance, then degraded image is provided by following formula in spatial domain:

g(x,y)＝h(x,y)*f(x,y)(3)

Wherein h (x, the y) space representation that is degenrate function, also claim PSF, " * " represents convolution, and carrying out Fourier transform to above formula both sides can obtain

G(u,v)＝H(u,v)F(u,v)(4)

Wherein (u, v) is frequency domain coordinates, G (u, v), H (u, v) and F (u, v) corresponding blurred picture g (x respectively, y), the frequency domain value of degenrate function h (x, y) and original image f (x, y).

In step (2), obtain mobile terminal around the angular velocity that described X-axis, Y-axis and Z axis rotate within the shutter opening time by gyroscope, output sequence is m × n group data, and data layout is (G _xi, G _yi, G _zi, t _i), m is gyrostatic sample frequency, and n is the shutter opening time of camera, and subscript i represents output sequence number, and value is 1,2 ..., m × n, G _xirepresent i-th group of angular velocity rotated around X-axis, G _yirepresent i-th group of angular velocity rotated around Y-axis, G _zirepresent i-th group of angular velocity rotated around Z axis, t _irepresent the sampling instant of i-th group of data.

In step (3), camera is less to Imaging around the rotation of X, so can not consider.Fig. 3 is the coordinate graph of a relation of the output sequence that provides of the embodiment of the present invention to picture plane, θ in this figure _y, θ _zbe the rotational angle of camera Y-axis, Z axis respectively, visible camera is the rotational angle θ of Z axis around Y-axis Effect of Rotation _z, camera is the rotational angle θ of Y-axis around Z axis Effect of Rotation _y.Definition θ _yit _ithe rotational angle of moment Y-axis, θ _zit _ithe rotational angle of moment Z axis, being calculated as follows of they

$\left.\begin{array}{c}{\mathrm{\θ}}_{yi}=\underset{j=1}{\overset{i}{\mathrm{\Σ}}}\frac{\left(G_{zj+1}+G_{zj}\right)\left(t_{j+1}-t_j\right)}{2}\\ {\mathrm{\θ}}_{zi}=\underset{j=1}{\overset{i}{\mathrm{\Σ}}}\frac{\left(G_{yj+1}+G_{yj}\right)\left(t_{j+1}-t_j\right)}{2}\end{array}\right\}---\left(5\right)$

In step (4), according to above-mentioned angle by virtual borderlines to photo coordinate system, obtain shake PSF template.In Fig. 3, a and b is respectively width and the length of shooting image, and h is camera lens focal length, y and z is respectively impulse function at θ _yand θ _zin the deviation post as Y-axis in plane YOZ and Z axis under impact.Definition y _ifor t _ithe deviation post of moment Y-axis, z _ifor t _ithe deviation post of moment Z axis, △ t _ifor camera attitude is in the retention time of this position.Picture plane YOZ mid point (y _i, z _i, △ t _i) computing formula as follows

$\left.\begin{array}{c}{y}_i=h\×\tan \left({\mathrm{\θ}}_{yi}\right)\\ z_i=h\×\tan \left({\mathrm{\θ}}_{zi}\right)\\ {\mathrm{\Δt}}_i=t_{i+1}-t_i\end{array}\right\}---\left(6\right)$

Initialization empty chain table L, by point (y _i, z _i, △ t _i) add to wherein, each group of Data duplication above-mentioned steps in the output sequence that gyroscope is obtained.After end, calculate y _imaximum absolute value value ${\left|y\right|}_{max}={\mathrm{MAX}}_{i=1}^{m\×n}\left(\right|y_i\left|\right)$ And z _imaximum absolute value value ${\left|z\right|}_{max}={\mathrm{MAX}}_{i=1}^{m\×n}\left(\right|z_i\left|\right),$ Reinitialize one (2 × | y| _max+ 1) OK, (2 × | z| _max+ 1) the full 0 matrix M arranged, takes out the point (y in chained list L successively _j, z _j, △ t _j), wherein j represents the data sequence number in chained list L, and value is 1,2 ..., m × n, and by (y in matrix M _j+ | y| _max) row (z _j+ | z| _max) element value that arranges adds △ t _j.After above-mentioned steps completes, matrix M is normalized, namely obtains shake PSF template.

Fig. 4 is the extraction process flow diagram of above-mentioned shake PSF template, specifically comprises the following steps:

(1) initialization empty chain table L, makes output sequence i be 1;

(2) Integral Processing is carried out to described output sequence, obtain camera t within the shutter opening time _itime be engraved in the rotational angle θ of Y-axis in its place XYZ coordinate system _yiwith the rotational angle θ of Z axis _zi;

(3) by the rotational angle θ of camera in Y-axis _yiwith the rotational angle θ of Z axis _zibe mapped in photo coordinate system, obtain t in picture plane _ilocation point (the y in moment _i, z _i, △ t _i), and it is added in chained list L;

(4) judge whether i equals m × n, if so, then enter step (5); If not, then i adds 1, and is back to step (2);

(5) y is calculated _imaximum absolute value value | y| _maxand z _imaximum absolute value value | z| _max;

(6) initialization one (2 × | y| _max+ 1) OK, (2 × | z| _max+ 1) the full 0 matrix M arranged, and make data sequence number j equal 1;

(7) the jth group data (y in chained list L is taken out _j, z _j, △ t _j), by (y in matrix M _j+ | y| _max) row (z _j+ | z| _max) element value that arranges adds △ t _j;

(8) judge whether j equals m × n, if so, then enter step (9); If not, then j adds 1, and is back to step (7);

(9) matrix M is normalized, namely obtains shake PSF template.

In the step (5) of restoring flow process, Richardson-Lucy algorithm is specially:

Richardson-Lucy algorithm is a kind of algorithm for blur image restoration jointly proposed by Richardson and Lucy.At first for the lens deviation corrected due to Hubble Telescope cause image blurring, this algorithm is a kind of widely used Image Restoration Algorithm at present.

The basic thought of Richardson-Lucy algorithm makes to export a maximum likelihood value for ideal data by continuous iteration.During by this algorithm application to blur image restoration, prerequisite is PSF must be known, or at least can estimate to obtain, and then by certain iterations, make output image converge to the close maximum likelihood image of same true picture, thus improve the display effect of blurred picture.

Richardson-Lucy algorithm hypothesis picture noise obeys Poisson distribution, and blurred picture g=h*f+ β, f and g represents original picture rich in detail and blurred picture respectively, and h represents PSF, and β represents picture noise, and " * " represents convolution algorithm.There is β=g-h*f after transposition, obtain the likelihood probability p (g|f) of image f identical with the probability distribution of the likelihood probability p (β) of noise, all obey Poisson distribution, when solving with maximal possibility estimation, conditional probability distribution:

$p\left(g\right|f)=\underset{x,y}{\Π}\frac{{\left((f*h)(x,y)\right)}^{g(x,y)}{e}^{-(f*h)(x,y)}}{g(x,y)!}---\left(7\right)$

In order to ask for maximal value, according to maximum Likelihood, after being taken the logarithm by above formula, two ends make it be zero to f (x, y) differentiate, then have:

$\frac{\∂\ln p\left(g\right|f)(x,y)}{\∂f(x,y)}=0---\left(8\right)$

$\[\frac{g}{f*h}*h^{*}\](x,y)=1---\left(9\right)$

Wherein h ^*for the adjoint matrix of h, i.e. h ^*(x, y)=h (-x ,-y).F (x, y) is multiplied by above formula two ends simultaneously, can obtain:

$f(x,y)\[\frac{g}{f*h}*h^{*}\](x,y)=f(x,y)---\left(10\right)$

Add iterative algorithm to solve it:

$f^{\mathrm{\α}+1}(x,y)=f^{\mathrm{\α}}(x,y)\[\frac{g}{f^{\mathrm{\α}}*h}*h^{*}\](x,y)---\left(11\right)$

Wherein, α represents iterations.It is as follows that above formula transforms to frequency domain:

$F^{\mathrm{\α}+1}(u,v)=F^{\mathrm{\α}}(u,v)\[\frac{G(u,v)}{F^{\mathrm{\α}}(u,v)H(u,v)}{H}^{*}(u,v)\]---\left(12\right)$

Wherein (u, v) is frequency domain coordinates, F ^α(u, v) is the frequency domain value of the restored image after α-1 iteration, F ^α+1(u, v) is the frequency domain value of restored image after the α time iteration, the frequency domain value of the corresponding blurred picture g (x, y) of G (u, v), H (u, v) difference, PSFh (x, y), H ^*(u, v) is the conjugate matrices of H (u, v), and F ⁰(u, v)=G (u, v).

Here it is standard Richardson-Lucy algorithm, the method does not provide stopping criterion for iteration, and along with the increase of iterations α, restored image converges on original picture rich in detail gradually.This algorithm is when using small size PSF, and usually less iterations just can reach stable solution.As known PSF but picture noise information is unknown time, also can be undertaken there is efficient recovery by this restoration methods.

The feature utilizing Richardson-Lucy algorithm to carry out blur image restoration have following some:

(1) a given width original image, if PSF selects suitably, only to need less iterations, just can obtain good recovery effect;

(2) as long as the pixel non-negative of PSF and input picture, then the value of the pixel of the restored image obtained after iterative processing is also non-negative;

(3) if blurred picture and original image have larger deviation, as long as provide PSF accurately, can be restored with less iterations equally.

To obtain the PSF of mobile terminal shooting blurred picture in the method to step (4) according to the step (2) of restoring flow process after, first set iterations α by f in iterative equation ⁰(x, y) g (x is set to, y), initializes by first iteration is blurred picture self, then the PSF template that the step (4) h in formula (11) being set to recovery flow process is tried to achieve, finally carries out iteration according to formula (11) and obtains restored image.

Fig. 5 illustrates the effect contrast figure implementing said method, wherein Fig. 5 (a), (b) are two width blurred pictures, figure (c) is the recovery effect figure of figure (a), figure (d) is the lower right corner in the recovery effect figure of figure (b), figure (c), (d) is the PSF that this method is extracted.By Fig. 5 we can see use the present invention obtain the PSF of blurred picture after adopt Richardson-Lucy algorithm to carry out recovery can to obtain details restored image clearly, image definition is improved.

Those skilled in the art will readily understand; the foregoing is only preferred embodiment of the present invention; not in order to limit the present invention, all any amendments done within the spirit and principles in the present invention, equivalent replacement and improvement etc., all should be included within protection scope of the present invention.

Claims (2)

1. a shake Restoration method of blurred image for facing moving terminal, is characterized in that, comprise the steps:

(1) blurred picture during width mobile terminal shake is obtained;

(2) obtained in the camera shutter opening time by attitude sensor, shake the relevant output sequence of track to mobile terminal;

Wherein, output sequence is m × n group data, and data layout is (G _x, G _y, G _z, t), m is the sample frequency of attitude sensor, and n is the shutter opening time of camera, G _xrepresent the output valve of X-axis in the XYZ coordinate system of camera place, G _yrepresent the output valve of Y-axis, G _zrepresent the output valve of Z axis, t represents sampling instant, and wherein X-axis is the optical axis of camera, and Y-axis is the longitudinal axis of picture plane, and Z axis is the transverse axis of picture plane; Sampling instant t _icorresponding output sequence is (G _xi, G _yi, G _zi, t _i), i is the sequence number of sampling instant, and the value of i is 1,2 ..., m × n;

(3) carry out processing the rotational angle obtaining mobile terminal to described output sequence, and described rotational angle is carried out virtual borderlines, obtain shake PSF template;

(4) according to described blurred picture and described shake PSF template, adopt Image Restoration Algorithm to carry out restoration disposal, obtain restored image.

2. shake Restoration method of blurred image as claimed in claim 1, it is characterized in that, obtain shake PSF template step and be specially:

(1) initialization empty chain table L, definition wherein each element is tlv triple (y, z, △ t), and makes the initial value of output sequence i be 1;

Y, z represent the position coordinates shaking the point on track in shake PSF template, and △ t represents the retention time of the attitude of mobile terminal at this point;

(2) camera t within the shutter opening time is obtained _itime be engraved in the rotational angle θ of X-axis in XYZ coordinate system _xi, the rotational angle θ of Y-axis _yiwith the rotational angle θ of Z axis _zi;

(3) by the rotational angle θ of camera Y-axis _yiwith the rotational angle θ of Z axis _zibe mapped in photo coordinate system, obtain t in picture plane _ia location point (y of moment PSF _i, z _i, △ t _i), and it is added in chained list L;

Wherein, y _ifor t _ithe deviation post of moment Y-axis, z _ifor t _ithe deviation post of moment Z axis, △ t _ifor camera attitude is in the retention time of this position, y _i=h × tan (θ _yi), z _i=h × tan (θ _zi), △ t _i=t _i+1-t _i, h is camera lens focal length;

(4) judge whether i equals m × n, if so, then enter step (5); If not, then i=i+1, and be back to step (2);

(5) y is obtained _imaximum absolute value value and z _imaximum absolute value value ${\left|z\right|}_{max}={\mathrm{MAX}}_{i=1}^{m\×n}\left(\right|z_i\left|\right);$

(6) initialization one (2 × | y| _max+ 1) OK, (2 × | z| _max+ 1) the full 0 matrix M arranged, and make data sequence number j equal 1;

(7) the jth group data (y in chained list L is taken out _j, z _j, △ t _j), by (y in matrix M _j+ | y| _max) row (z _j+ | z| _max) element value that arranges adds △ t _j;

(8) judge whether j equals m × n, if so, then enter step (9); If not, then j adds 1, and is back to step (7);

(9) matrix M is normalized rear acquisition described shake PSF template.