CN101915901A - Magnetic resonance imaging method and device - Google Patents
Magnetic resonance imaging method and device Download PDFInfo
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Abstract
The invention relates to a magnetic resonance imaging method comprising the following steps of: correcting and scanning a visual field to obtain a plurality of composite images, summing the absolute values of the plurality of composite images to obtain a summation image, and computing a sensitivity coefficient according to the plurality of composite images and the summation image; and correcting the sensitivity coefficient, and generating a reconstructed image. The magnetic resonance imaging method and device sum the absolute values of the plurality of composite images to obtain the summation image and compute the sensitivity coefficient through the summation image, thereby effectively enhancing the uniformity of the sensitivity coefficient; and after the sensitivity coefficient is corrected, the reconstructed image is generated, thereby effectively eliminating artifacts caused by a motion factor and other factors on the images in the scanning process, enhancing the resolution of the artifact-free composite images generated after reconstruction and reinforcing the robustness of the reconstructed image.
Description
[technical field]
The present invention relates to mr imaging technique, particularly relate to a kind of MR imaging method and device.
[background technology]
Magnetic resonance imaging has higher soft tissue contrast and spatial resolution, can select imaging parameters and imaging aspect as required flexibly, be widely used in clinical in.Traditional magnetic resonance imaging usually occurs owing to data acquisition time causes the slower problem of image taking speed than length.This is because the gradient field intensity has seriously restricted the sweep velocity of magnetic resonance imaging near the limit.Therefore, adopted the multi-channel parallel imaging technique in traditional magnetic resonance imaging, promptly multichannel collecting and parallel imaging algorithm make magnetic resonance imaging can be no longer dependent on the also collection of expedited data greatly of raising of gradient field intensity.The multi-channel parallel imaging technique is to utilize the phased-array coil spatial information to replace the gradient coded message, and each coil unit is owed sampling to the K space simultaneously, and the K spacing wave quantity that makes each coil unit gather significantly reduces, and image taking speed improves greatly.This formation method had both improved the speed of imaging, can improve the contrast of image again, therefore had wide practical value in the very high inspection of imaging requirements such as heart, dynamically enhancing, blood vessel imaging.
But, in the multi-channel parallel imaging technique,, each coil gathers the K spatial data, and according to nyquist sampling theorem because all owing sampling, and the data that each coil unit is gathered are directly carried out image reconstruction aliasing can be taken place, and cause overlapping pseudo-shadow.Overlapping pseudo-shadow can pass through sensitivity coefficient, and (Sensitivity Encoding, SENSE) technology is removed.
Yet; in traditional sensitivity encoding technology; it is too poor the sensitivity coefficient homogeneity to occur; the defective that the sensitivity map air spots that obtains according to sensitivity coefficient is sliding; and in the process of data acquisition; because it is unusual that motion usually can make data take place, thereby image is produced very large pseudo-shadow, and picture quality is produced significant impact.
[summary of the invention]
Based on this, be necessary to provide a kind of inhomogeneity MR imaging method of sensitivity that improves.
In addition, also be necessary to provide a kind of inhomogeneity MR imaging apparatus of sensitivity that improves.
A kind of MR imaging method comprises the steps: visual field calibration scan is obtained a plurality of combination pictures, a plurality of combination pictures is carried out the absolute value summation obtain the image of suing for peace, and obtain sensitivity coefficient according to described a plurality of combination pictures and summation image calculation; Proofread and correct described sensitivity coefficient, and generate reconstructed image.
Preferably, state and proofread and correct described sensitivity coefficient, and also comprise the step of proofreading and correct described combination picture deviation field before the step of generation reconstructed image.
Preferably, the step of the deviation field in the described combination picture of described correction is: to the combination picture pre-service, obtain mask; Described mask is acted in the combination picture extracting tissue part's image, and described tissue part image is carried out log-transformation, obtain adding the sexual deviation field; According to adding sexual deviation field and mask, obtain according to a preliminary estimate deviation field by gauss low frequency filter and normalization convolution; The deviation field that the B spline-fitting is accurately estimated is carried out in deviation field according to a preliminary estimate, and the combination picture that obtains proofreading and correct of the ratio by the gradation of image that measures and the deviation field of described accurate estimation.
Preferably, described to the combination picture pre-service, the step that obtains mask is: measure gray level image in combination picture, obtain the brightness maximal value of described gray level image mid point by described gray level image, setting threshold is the number percent of high-high brightness, is lower than threshold value and partly is made as 0, and tissue part is made as 1, form bianry image, obtain mask.
Preferably, the described sensitivity coefficient of described correction, and the step that generates reconstructed image is: the match by reference picture and the combination picture that obtains in the scanning of the visual field obtains residual error; Introduce annealing parameter, described residual error is imported in the strength of joint function, obtain the value of described strength of joint function, the value of described strength of joint function is as the element on the diagonal matrix diagonal line; Obtain not having pseudo-shadow combination picture by complex image, diagonal matrix and sensitivity coefficient.
A kind of MR imaging apparatus comprises at least: the phased array coil is used for visual field scanning is obtained a plurality of combination pictures and corresponding complex image; Calculation element is used for obtaining the image of suing for peace according to described a plurality of combination pictures, and obtains sensitivity coefficient according to described a plurality of combination pictures and summation image calculation; Equipment for reconstructing image is used to proofread and correct described sensitivity coefficient, and generates reconstructed image.
Preferably, also comprise: luminance correction device, the deviation field that is used for proofreading and correct described combination picture.
Preferably, described luminance correction device comprises at least: the mask process module is used for the combination picture pre-service is obtained mask; Organize conversion module, be used for described mask is acted on combination picture with extraction tissue part image, and described tissue part image is carried out log-transformation, obtain adding the sexual deviation field; The precorrection module is used for according to adding sexual deviation field and mask, obtains according to a preliminary estimate deviation field by gauss low frequency filter and normalization convolution; Level and smooth module is used for the deviation field that the level and smooth match of B batten is accurately estimated is carried out in deviation field according to a preliminary estimate, and the combination picture that obtains proofreading and correct of the ratio by the gradation of image that measures and the deviation field of described accurate estimation.
Preferably, described mask process module also is used for measuring gray level image at combination picture, obtain the brightness maximal value of described gray level image mid point by described gray level image, setting threshold is the number percent of high-high brightness, be lower than threshold value and partly be made as 0, tissue part is made as 1, forms bianry image, to obtain mask.
Preferably, described equipment for reconstructing image comprises at least: fitting module is used for obtaining residual error by the match of reference picture and described combination picture; Estimation module is used to introduce annealing parameter, and described residual error is imported in the strength of joint function, obtains the value of described strength of joint function, and the value of described strength of joint function is as the element on the diagonal line in the diagonal matrix; The image generation module is used for obtaining not having pseudo-shadow combination picture by complex image, diagonal matrix and sensitivity coefficient.Above-mentioned MR imaging method and device are sued for peace to the absolute value of combination picture and are obtained the image of suing for peace, and obtain sensitivity coefficient by this summation image calculation, thereby improved the homogeneity of sensitivity coefficient effectively, sensitivity coefficient is proofreaied and correct the back and is generated reconstructed image, effectively eliminated the pseudo-shadow that factor such as move in the scanning process causes image, improve the resolution of the pseudo-shadow combination picture of nothing of rebuilding the back generation, strengthened the robustness of reconstructed image.
Above-mentioned MR imaging method and device had at first been proofreaied and correct the deviation field in the combination picture before corrected sensitivity coefficient, thereby obtained the even brightness image, and had improved signal to noise ratio (S/N ratio), improved the accuracy that the observer analyzes visual image.
Above-mentioned MR imaging method and device gauss low frequency filter and normalization involve in capable filtering, have obtained deviation field according to a preliminary estimate, have removed the artefact between background area and the tissue image.
[description of drawings]
Fig. 1 is the process flow diagram of MR imaging method among the embodiment;
Fig. 2 is the process flow diagram of the deviation field in the positive combination picture of an embodiment lieutenant colonel;
Fig. 3 A is the brain original image;
Fig. 3 B be with the corresponding correction of brain original image after image;
Fig. 4 A is the line chart of brain original image;
Fig. 4 B be with the corresponding correction of brain original image after the line chart of image;
Fig. 5 is a corrected sensitivity coefficient and generate the process flow diagram of reconstructed image among the embodiment;
Fig. 6 is the synoptic diagram that generates reconstructed image among the embodiment;
Fig. 7 is the detailed block diagram of MR imaging apparatus among the embodiment;
Fig. 8 A is the reference picture of phantom;
Fig. 8 B is the phantom image by the classic method gained;
Fig. 8 C is the phantom image that the present invention generated;
Fig. 9 A is the reference picture of brain;
Fig. 9 B is the brain image by the classic method gained;
Fig. 9 C is the brain image that the present invention generated;
Figure 10 A is the reference picture of belly;
Figure 10 B is the abdomen images by the classic method gained;
Figure 10 C is the abdomen images that the present invention generated.
[embodiment]
Fig. 1 shows the method flow of magnetic resonance imaging among the embodiment, comprises the steps:
In step S10, visual field calibration scan is obtained a plurality of combination pictures, a plurality of combination pictures are carried out the absolute value summation obtain the image of suing for peace, and obtain sensitivity coefficient according to a plurality of combination pictures and summation image calculation.Among one embodiment, in the K space, calibration scan sampling in the visual field is obtained combination picture f
l(l=1,2 ..., L), by will be according to combination picture f
lThe absolute value images addition that generates and obtain the image of suing for peace
Thereby utilize following formula to calculate sensitivity coefficient C
l:
C
l＝f
l/Am
Wherein, l by in a plurality of phased array coils a certain phased array coil of correspondence.
By combination picture f
1The absolute value images addition and obtain sensitivity coefficient C
l, improved homogeneity effectively, make sensitivity coefficient C thus
lThe sensitivity image that produces has level and smooth surface.
In step S20, proofread and correct the deviation field in the described combination picture.In one embodiment, the deviation field is also referred to as the property the taken advantage of field of low frequency, is meant image in same physiological tissue or structure, the phenomenon that brightness slowly changes.When image data,, can cause the luminance non of gained image owing to the difference of susceptibility coefficient.Brightness image heterogeneous provides false contrast, has seriously hindered the observer this image is carried out correlativity and analysis of the accuracy.Based on this, as shown in Figure 2, in one embodiment, the detailed process of step S20 is:
In step S201,, obtain mask to the combination picture pre-service.The pre-service of combination picture is a mask process, refers to selected image, figure or object pending image (whole or local) is blocked, with the processing procedure of control image-region.The selected digital image, figure or the object that are covered on the pending image are called mask.The process of mask process is specifically: at combination picture f
1In measure gray level image, generate brightness histogram, find out the brightness maximal value of pixel in the gray level image by brightness histogram, setting threshold is the number percent of high-high brightness then, the part that is lower than threshold value can be regarded background area or noise as, be set to 0, tissue part is made as 1, thereby obtains a width of cloth bianry image as mask t.
In step S202, mask is acted in the combination picture extracting tissue part's image, and tissue part's image is carried out log-transformation, obtain adding the sexual deviation field.Among one embodiment, mask t is blocked in combination picture f
1On, extract the image v ' of tissue part
l, shown in the following formula, to the image v ' of tissue part
lCarry out log-transformation, add the sexual deviation field taking advantage of the sexual deviation field to be converted into.
V
l＝logv′
l＝logu′+logf′
l
Wherein, u ' is the true picture gray scale behind the mask, f '
lIt is the smooth variation deviation field behind the mask.
In step S203, according to adding sexual deviation field and mask, obtain according to a preliminary estimate deviation field by gauss low frequency filter and normalization convolution.Among one embodiment, carry out filtering, between background area and tissue image, produce in various degree artefact in meeting after the filtering, seriously influenced the quality of image by gauss low frequency filter.Therefore, also carry out filtering once more, remove the artefact between background area and the tissue image, obtain deviation field d according to a preliminary estimate by the method for normalization convolution
l
d
l＝exp(LPF[V
l]/LPF[t
l])
In step S204, the deviation field that the B spline-fitting is accurately estimated is carried out in deviation field according to a preliminary estimate, and the combination picture that obtains proofreading and correct of the ratio by the gradation of image that measures and the deviation field of accurate estimation.Among one embodiment, owing in the filtering of normalization convolution, be to think that the data of tissue image are known, the loss of data of background area to appearing at the not effect of artefact in the tissue image, is therefore carried out the B spline-fitting to deviation field according to a preliminary estimate.To carrying out the B spline-fitting and the process of the deviation field accurately estimated is in deviation field according to a preliminary estimate: in deviation field according to a preliminary estimate, select more smooth zone to carry out sub-sampling, the sample point of gained is as fitting nodes, use the resulting fitting nodes of B spline-fitting then, by interpolation, extrapolation image, obtain the deviation field f ' of level and smooth accurate estimation at last
l, B spline-fitting function can be expressed as:
Wherein, B
i, B
jBe one dimension B-spline function, θ
IjBe fitting parameter.
The B spline-fitting is the optimizing process that makes J=E (θ)+ω R (θ) minimum, and in the formula, E (θ) is consistent degree, reflected B spline-fitting function and raw data s (x, degree of closeness y), promptly
ω is a weighting factor of rule of thumb selecting; R (θ) is a smoothness, the smooth degree of reflection B-spline function, promptly
According to the gradation of image v that measures
lAnd the deviation field f ' that accurately estimates
lThe combination picture that obtains proofreading and correct by following formula, promptly
u＝v
l/f′
l
Its brightness nonuniformity correction of the combination picture result who proofreaies and correct is shown in Fig. 3 A to Fig. 3 B, and the line chart of the brain original image of Fig. 3 A is shown in Fig. 4 A, and Fig. 3 B proofreaies and correct the correction result of the 60th row in the image of back shown in Fig. 4 B.In Fig. 4 A to Fig. 4 B, to compare with the line chart of brain original image, the line chart of proofreading and correct the back image is more level and smooth, and burr is less.
In step S30, corrected sensitivity coefficient, and generate reconstructed image.In one embodiment, when gathering raw data, be positioned over the influence that the coil at some position of human body is very easy to be moved or suffer the destruction of noise and take place unusual when image data, the destruction data that contain pseudo-shadow become the exceptional value that raw data is concentrated, moved or the pseudo-image data of noise corrupted for counting, to sensitivity coefficient C
lCarry out the AM Robust Estimation.As shown in Figure 5, in one embodiment, the process of step S30 specifically:
In step S301, the match by reference picture and the combination picture that obtains in visual field scanning obtains residual error.Be defined in the combination picture f that obtains in the scanning of the visual field
lWith the difference of reference picture be residual error r
lReference picture obtains fast by only scanning low-frequency data, and this reference picture resolution is higher.
In step S302, introduce annealing parameter, residual error is imported in the strength of joint function, obtain the value of strength of joint function, the value of strength of joint function is as the element on the diagonal matrix diagonal line.According to the discontinuous markov prior model of self-adaptation, the strength of joint function is
Wherein t is the annealing parameter that successively decreases gradually in the iterative process, and its cooling strategy passes through t
n=0.1 * t
N-1Finish, the initial value of annealing parameter t is 2.Obtain the element on the diagonal line, i.e. D=diag (d among the diagonal matrix row D by the strength of joint function calculation
1, d
2..., d
l), wherein l is that residual error is counted out.
In step S303, obtain not having pseudo-shadow combination picture by complex image, diagonal matrix and the sensitivity coefficient that in the scanning of the visual field, obtains.Carry out low coverage scanning and obtain complex image S
lThereby, with complex image S
l, diagonal matrix D and sensitivity coefficient C
lImport in the following image reconstruction formula
ρ
AM＝(C
l HDC
l)
-1C
l HDS
l
Wherein, ρ
AMBe the pseudo-shadow combination picture of the nothing that obtains after rebuilding, C
HBe the special transposition of the Hull rice of Matrix C.
As shown in Figure 6, by phased array coil Coil_l (l=1,2 ... L) carry out quick Fu Ye (fast fourier transform, FFT) conversion obtain corresponding complex image S after the scanning
lThereby, with complex image S
lWith susceptibility coefficient C
lAfter carrying out the AM Robust Estimation, obtain artifact-free combination picture.
Fig. 7 shows the MR imaging apparatus among the embodiment, and this MR imaging apparatus comprises phased array coil 20, calculation element 40, luminance correction device 60 and equipment for reconstructing image 80, wherein:
C
l＝f
l/Am
Organize conversion module 602, be used for mask is acted on combination picture with extraction tissue part image, and tissue part's image is carried out log-transformation, obtain adding the sexual deviation field.This tissue conversion module 602 blocks mask t in combination picture f
lOn, extract the image v ' of tissue part
l, by following formula with the image v ' of tissue part
lCarry out log-transformation, add the sexual deviation field taking advantage of the sexual deviation field to be converted into, promptly
v
l＝logv′
l＝logu′+logf′
l
Wherein, u ' is the true picture gray scale behind the mask, f '
lIt is the smooth variation deviation field behind the mask.
d
l＝exp(LPF[V
l]/LPF[t
l])
Level and smooth module 604 is used for the deviation field that the B spline-fitting is accurately estimated is carried out in deviation field according to a preliminary estimate, and the combination picture that obtains proofreading and correct of the ratio by the gradation of image that measures and the deviation field of accurate estimation.This level and smooth module 604 selects more smooth zone to carry out sub-sampling in deviation field according to a preliminary estimate, with resulting sample point as fitting nodes, use the resulting fitting nodes of B spline-fitting then,, obtain the deviation field f ' of level and smooth accurate estimation at last by interpolation, extrapolation image
l, B spline-fitting function can be expressed as:
Wherein, B
i, B
jBe one dimension B-spline function, θ
IjBe fitting parameter.
The B spline-fitting is the optimizing process that makes J=E (θ)+ω R (θ) minimum, and in the formula, E (θ) is consistent degree, reflected B spline-fitting function and raw data s (x, degree of closeness y), promptly
ω is a weighting factor of rule of thumb selecting; R (θ) is a smoothness, the smooth degree of reflection B-spline function, promptly
According to the gradation of image v that measures
lAnd the deviation field f ' that accurately estimates
lThe combination picture that obtains proofreading and correct by following formula, promptly
u＝v
l/f′
l
Equipment for reconstructing image 80 is used for corrected sensitivity coefficient, and generates reconstructed image.Among one embodiment, 80 couples of sensitivity coefficient C of equipment for reconstructing image
lCarry out the AM Robust Estimation, comprising:
ρ
AM＝(C
l HDC
l)
-1C
l HDS
l
Wherein, ρ
AMBe the pseudo-shadow combination picture of the nothing that obtains after rebuilding, C
HBe the special transposition of the Hull rice of Matrix C.
Shown in Fig. 8 A to Fig. 8 C, by the comparison that resulting no pseudo-shadow combination picture was sought and installed in reference picture, classic method gained image and above-mentioned magnetic resonance imaging in phantom data reconstructed results, it is more clear not have pseudo-shadow combination picture as can be seen.
Shown in Fig. 9 A to Fig. 9 C, by in the reconstructed results of true brain data, resulting no pseudo-shadow combination picture is sought and is installed in contrast reference picture, classic method gained image and above-mentioned magnetic resonance imaging, in the indicated position of the arrow of classic method, it is clear and do not have a pseudo-shadow not have pseudo-shadow combination picture.
Shown in Figure 10 A to Figure 10 C, by in the reconstructed results of belly data, resulting no pseudo-shadow combination picture is sought and is installed in contrast reference picture, classic method gained image and above-mentioned magnetic resonance imaging, in the indicated position of the arrow of classic method, it is clear and do not have a pseudo-shadow not have pseudo-shadow combination picture.
Above-mentioned MR imaging method and device are sued for peace to the absolute value of combination picture and are obtained the image of suing for peace, and obtain sensitivity coefficient by this summation image calculation, thereby improved the homogeneity of sensitivity coefficient effectively, sensitivity coefficient is proofreaied and correct the back and is generated reconstructed image, effectively eliminated the pseudo-shadow that factor such as move in the scanning process causes image, improve the resolution of the pseudo-shadow combination picture of nothing of rebuilding the back generation, strengthened the robustness of image reconstruction.
Above-mentioned MR imaging method and device had at first been proofreaied and correct the deviation field in the combination picture before corrected sensitivity coefficient, thereby obtained the even brightness image, and had improved signal to noise ratio (S/N ratio), improved the accuracy that the observer analyzes visual image.
Above-mentioned MR imaging method and device gauss low frequency filter and normalization involve in capable filtering, have obtained deviation field according to a preliminary estimate, have removed the artefact between background area and the tissue image.
The above embodiment has only expressed several embodiment of the present invention, and it describes comparatively concrete and detailed, but can not therefore be interpreted as the restriction to claim of the present invention.Should be pointed out that for the person of ordinary skill of the art without departing from the inventive concept of the premise, can also make some distortion and improvement, these all belong to protection scope of the present invention.Therefore, the protection domain of patent of the present invention should be as the criterion with claims.
Claims (10)
1. a MR imaging method comprises the steps:
Visual field calibration scan is obtained a plurality of combination pictures, a plurality of combination pictures are carried out the absolute value summation obtain the image of suing for peace, and obtain sensitivity coefficient according to described a plurality of combination pictures and summation image calculation;
Proofread and correct described sensitivity coefficient, and generate reconstructed image.
2. MR imaging method according to claim 1 is characterized in that, the described sensitivity coefficient of described correction, and also comprise the step of proofreading and correct described combination picture deviation field before the step of generation reconstructed image.
3. MR imaging method according to claim 2 is characterized in that, the step of the deviation field in the described combination picture of described correction is:
To the combination picture pre-service, obtain mask;
Described mask is acted in the combination picture extracting tissue part's image, and described tissue part image is carried out log-transformation, obtain adding the sexual deviation field;
According to adding sexual deviation field and mask, obtain according to a preliminary estimate deviation field by gauss low frequency filter and normalization convolution;
The deviation field that the B spline-fitting is accurately estimated is carried out in deviation field according to a preliminary estimate, and the combination picture that obtains proofreading and correct of the ratio by the gradation of image that measures and the deviation field of described accurate estimation.
4. MR imaging method according to claim 3 is characterized in that, described to the combination picture pre-service, the step that obtains mask is:
Measure gray level image in combination picture, obtain the brightness maximal value of described gray level image mid point by described gray level image, setting threshold is the number percent of high-high brightness, be lower than threshold value and partly be made as 0, tissue part is made as 1, forms bianry image, obtains mask.
5. MR imaging method according to claim 3 is characterized in that, the described sensitivity coefficient of described correction, and the step of generation reconstructed image is:
Match by reference picture and the combination picture that obtains in visual field scanning obtains residual error;
Introduce annealing parameter, described residual error is imported in the strength of joint function, obtain the value of described strength of joint function, the value of described strength of joint function is as the element on the diagonal matrix diagonal line;
Obtain not having pseudo-shadow combination picture by complex image, diagonal matrix and sensitivity coefficient.
6. a MR imaging apparatus is characterized in that, comprises at least:
The phased array coil is used for visual field scanning is obtained a plurality of combination pictures and corresponding complex image;
Calculation element is used for obtaining the image of suing for peace according to described a plurality of combination pictures, and obtains sensitivity coefficient according to described a plurality of combination pictures and summation image calculation;
Equipment for reconstructing image is used to proofread and correct described sensitivity coefficient, and generates reconstructed image.
7. MR imaging apparatus according to claim 6 is characterized in that, also comprises:
Luminance correction device, the deviation field that is used for proofreading and correct described combination picture.
8. MR imaging apparatus according to claim 7 is characterized in that, described luminance correction device comprises at least:
The mask process module is used for the combination picture pre-service is obtained mask;
Organize conversion module, be used for described mask is acted on combination picture with extraction tissue part image, and described tissue part image is carried out log-transformation, obtain adding the sexual deviation field;
The precorrection module is used for according to adding sexual deviation field and mask, obtains according to a preliminary estimate deviation field by gauss low frequency filter and normalization convolution;
Level and smooth module is used for the deviation field that the level and smooth match of B batten is accurately estimated is carried out in deviation field according to a preliminary estimate, and the combination picture that obtains proofreading and correct of the ratio by the gradation of image that measures and the deviation field of described accurate estimation.
9. MR imaging apparatus according to claim 8, it is characterized in that, described mask process module also is used for measuring gray level image at combination picture, obtain the brightness maximal value of described gray level image mid point by described gray level image, setting threshold is the number percent of high-high brightness, is lower than threshold value and partly is made as 0, and tissue part is made as 1, form bianry image, to obtain mask.
10. MR imaging apparatus according to claim 8 is characterized in that, described equipment for reconstructing image comprises at least:
Fitting module is used for obtaining residual error by the match of reference picture and described combination picture;
Estimation module is used to introduce annealing parameter, and described residual error is imported in the strength of joint function, obtains the value of described strength of joint function, and the value of described strength of joint function is as the element on the diagonal line in the diagonal matrix;
The image generation module is used for obtaining not having pseudo-shadow combination picture by complex image, diagonal matrix and sensitivity coefficient.
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