CN108230274A - Multiresolution rapid denoising method and device under a kind of mixed noise model - Google Patents
Multiresolution rapid denoising method and device under a kind of mixed noise model Download PDFInfo
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Abstract
The invention discloses the multiresolution rapid denoising methods and device under a kind of mixed noise model, after obtaining noisy image, establish multilayer gaussian pyramid corresponding with noisy image and multilayer laplacian pyramid, utilize gradient descent method, successive ignition calculating is carried out successively and solves full variational regularization denoising object function respectively, so as to obtain denoising image in last time iterative calculation；Described device includes memory for storing at least one program and for loading at least one program to perform the processor of the method for the present invention.The present invention combines gaussian pyramid and the successive ignition of laplacian pyramid calculates, iterative calculation can correspond to different image resolution ratios respectively to solve object function every time, and the initial value iterated to calculate every time is from the result and laplacian pyramid of last iterative calculation, it can either ensure denoising effect, the calculation amount solved is reduced again, solving speed is improved, optimizes computational efficiency.
Description
Technical field
The present invention relates to technical field of image processing, the quick denoising of multiresolution under especially a kind of mixed noise model
Method and device.
Background technology
In industrial circle, radioscopic image detection is used as a kind of lossless, contactless and high-resolution defect inspection method,
It is an important means of integrated circuit defects detection, encapsulation component solder joint rosin joint, conducting wire in integrated circuit can be detected
The defects of crack of pressure welding, circuit between conducting wire, hole and bubble, effectively solves to encapsulate member during integrated antenna package
The problem of device inside defect is difficult to detect ensures the quality of production of integrated antenna package, has in integrated circuit defects detection
There are great application value and economic benefit.In medical domain, also lesion is detected commonly using X ray.X ray is examined
It surveys, is to penetrate object using X ray and received by video receiver, record X ray penetrates each different parts of object and occurs
Strength information after energy attenuation is so as to obtain radioscopic image.X ray penetrates the degree and warp that energy attenuation occurs during object
It is closely related to cross material, density, the thickness at object position etc..
However, X ray is in imaging process, it can be by the noise pollution of various sources complexity.Influencing maximum noise has X
Heat caused by free electron result of random thermal motion in the electronic circuits such as ray photons partition noise in itself and image capture device
Noise.X-ray photon statistically meets Poisson distribution, therefore the noise itself brought can be retouched with Poisson noise model
It states, and thermal noise can be described with Gaussian noise model.Therefore, the noise of radioscopic image cannot be simply with single noise model
It represents, it shows as Gauss-Poisson mixed noise.Common radioscopic image, such as micro- focusing X-ray image of integrated circuit
In strong Gauss-Poisson mixed noise presence, the detailed information particularly defect information that some in image can be caused crucial
Be difficult to differentiate, it is impossible to quick separating is carried out to defect and other non-defective parts, the defects of to integrated circuit detection bring tired
Difficulty, therefore denoising is carried out to focusing X-ray image and obtains that clear, the radioscopic image of high quality is particularly significant.
Common Traditional Space domain or transform domain denoising method such as medium filtering, mean filter etc. are generally directed to single specific
Noise, easily edge is made to thicken while smoothed image noise, to contain the radioscopic image of strong mixed noise without
Method obtains satisfactory denoising effect.For this problem, someone is based on Microfocus X-ray x-ray imaging process, makes an uproar from Gauss, Poisson
The mutually independent angle of sound establishes Poisson Gaussian mixed noise model under maximum a posteriori probability frame, and introduces full change
Point regularization term keeps image border, finally establishes the full variational regularization denoising mesh under Gauss-Poisson mixed noise model
Scalar functions.By solving full variational regularization denoising object function, good denoising effect can be reached.
Variational regularization denoising object function is entirely
First two of full variational regularization denoising object function are data fidelity item, last is full variational regularization
.F in object function is noisy artwork, and λ is regularization parameter, and k is the pixel serial number of image, and N is the pixel of image
Sum.Solution makes the u that J (u) is minimized, that is,Just denoising image is obtained.Usually using the method for iteration
More wheel iteration are carried out to this object function, wherein the result of t wheel iteration is ut, so as to solve u, i.e. denoising image.
The existing iterative solution method of object function is as follows：For in object function
The Hessian matrix of F (u) is in utPlace is approximately ηtE(ηt>0, E is unit matrix).To F (u) in utPlace carries out the second Taylor series can
To obtain F (u) in utThe Two-order approximation F at placek(u)：
Above formula is substituted into object function, the result of t+1 wheel iteration can be obtained：
Wherein,ηtIt can be determined with Barzilar-Borwein methods.
The number of full variational regularization object function under Gauss-Poisson mixed noise model it can be seen from the above process
Non-linear serious, the existing denoising method based on full variational regularization object function according to fidelity item, it is necessary to iterate, and every
Secondary iteration will include two processes of outer iteration and inner iteration, and each iteration will update stWith ηtTwo coefficients, in ut+1It is excellent
Change in object function and fix stWith ηtAfterwards, solution u could be carried outt+1Inner iteration, it is also necessary to carry out complicated two-dimensional matrix and calculate,
Therefore need that the iterations carried out are more, and computationally intensive, calculating speed is slow, and algorithm operational efficiency is low.Even if to original noisy
Image directly carries out down-sampled processing so as to reduce image resolution ratio, then passes through corresponding full variational regularization denoising method again
Solution is iterated, can reduce the solution run time of algorithm totality, improves solution efficiency, but when using this method,
The marginal information of image key has just been lost when down-sampled so that is subsequently gone forward side by side using full variational regularization denoising method
After row solves, the fringe region in denoising image occurs apparent fuzzy, it is impossible to obtain satisfactory denoising effect.
Invention content
In order to solve the above-mentioned technical problem, the first object of the present invention is to provide more points under a kind of mixed noise model
Resolution rapid denoising method, a kind of the second quick denoising device of the multiresolution being designed to provide under mixed noise model.
The first technical solution for being taken of the present invention is：
A kind of multiresolution rapid denoising method under mixed noise model, including：
S1. after obtaining noisy image, multilayer gaussian pyramid corresponding with noisy image and multilayer Laplce gold are established
Word tower；
S2. using gradient descent method, successive ignition calculating is carried out successively and solves full variational regularization denoising target letter respectively
Number, so as to obtain denoising image in last time iterative calculation；The input picture iterated to calculate each time is respectively from Gauss gold
The tomographic image chosen in word tower；The initial value of iterative calculation is the tomographic image chosen from gaussian pyramid for the first time, remaining
The initial value iterated to calculate each time is calculated according to the iteration result and laplacian pyramid of last time iterative calculation.
Further, the number of the iterative calculation is three times, the step S2 is specifically included：
S21. one layer of initial value and input picture respectively as first time iterative calculation is chosen from gaussian pyramid, is utilized
Gradient descent method carries out iterative calculation for the first time and solves full variational regularization denoising object function, so as to obtain being tied among first
Fruit；
S22. according to the first intermediate result and laplacian pyramid, the initial value of second of iterative calculation is calculated, from
One layer of input picture as second of iterative calculation is chosen in gaussian pyramid, using gradient descent method, carries out second repeatedly
Generation, which calculates, solves full variational regularization denoising object function, so as to obtain the second intermediate result；
S23. according to the second intermediate result and laplacian pyramid, the initial value of third time iterative calculation is calculated, from
One layer of input picture as third time iterative calculation is chosen in gaussian pyramid, using gradient descent method, third time is carried out and changes
Generation, which calculates, solves full variational regularization denoising object function, so as to obtain denoising image.
Further, the method for building up of the gaussian pyramid is：
Using following formula, the gray value of pixel in each tomographic image of gaussian pyramid is calculated according to noisy image, from
And establish gaussian pyramid：
In formula, f (x, y) be noisy image, Ii(x, y) is the i-th tomographic image of gaussian pyramid IiAt middle pixel (x, y)
Gray value, Reduce () represent down-sampled operation, and g is the Gaussian template that a size is k × k, and k is custom parameter, and i is height
The serial number of each layer of this pyramid, m and n are sum of parameters.
Further, the number of plies of the laplacian pyramid is three layers, the method for building up of the laplacian pyramid
For：
Using following formula, to the multi-layer image of gaussian pyramid respectively into row interpolation, according to interpolation result, Laplce is obtained
Pyramidal each tomographic image, so as to establish laplacian pyramid：
In formula, Ti(x, y) is to the interpolation result of gaussian pyramid i+1 layer, LiFor i-th layer of figure of laplacian pyramid
Picture, Expand () represent image interpolation operation, and i is the serial number of gaussian pyramid and each layer of laplacian pyramid, and m and n are
Sum of parameters.
Further, in the step S21, the initial value of iterative calculation for the first time is set especially by following formula：
In formula,For the initial value of first time iterative calculation, I2The 2nd tomographic image for gaussian pyramid；
It is as follows that iterative formula used is iterated to calculate for the first time：
In formula, J () is full variational regularization denoising object function, and t is current iteration round, and d is decline step-length,For introduce after small constant α it is complete become subitem, o' is the addition Item for preventing denominator zero passage, and A is unit matrix, iteration
The u of gained2For the first intermediate result.
Further, in the step S22, especially by the initial value of following formula second of iterative calculation of setting：
In formula,The initial value iterated to calculate for second,For u2By bilinear interpolation as a result, u2Among first
As a result, β1For weight coefficient, L1For the 1st layer of edge image of laplacian pyramid；
Second of iterative calculation iterative formula used is as follows：
In formula, J () is full variational regularization denoising object function, and t is current iteration round, and d is decline step-length,For introduce after small constant α it is complete become subitem, o' is the addition Item for preventing denominator zero passage, and A is unit matrix, I1For height
This pyramidal 1st tomographic image, the u obtained by iteration1For the first intermediate result.
Further, in the step S23, the initial value of third time iterative calculation is set especially by following formula：
In formula,For third time iterative calculation initial value,For u1By bilinear interpolation as a result, u1Among second
As a result, β0For weight coefficient, L0For the 0th layer of edge image of laplacian pyramid；
It is as follows that third time iterates to calculate iterative formula used：
In formula, J () is full variational regularization denoising object function, and t is current iteration round, and d is decline step-length,For introduce after small constant α it is complete become subitem, o' is the addition Item for preventing denominator zero passage, and A is unit matrix, I0For
0th tomographic image of gaussian pyramid, the u obtained by iteration0For denoising image.
Further, in the iterative formula：
In formula,It itemizes for complete become after the small constant α of introducing, u refers to u2、u1Or u0, uxAnd uyFor the first derivative of u,
uxx、uyyAnd uxySecond dervative for u.
Further, in the iterative formula：
The second technical solution for being taken of the present invention is：
A kind of multiresolution quick denoising device under mixed noise model, including：
Memory, for storing at least one program；
Processor, for loading at least one program to perform a kind of mixed noise model described in the first technical solution
Under multiresolution rapid denoising method.
The beneficial effects of the invention are as follows：The present invention passes through combination gaussian pyramid and the successive ignition of laplacian pyramid
It calculating, iterative calculation every time can correspond to different image resolution ratios to solve full variational regularization denoising object function respectively, and
And the initial value iterated to calculate every time can either ensure from the result and laplacian pyramid of last iterative calculation
It makes an uproar effect, obtains the denoising image of high quality, and reduce the calculation amount solved, improve solving speed, optimize computational efficiency.
Description of the drawings
Fig. 1 is the flow chart of the method for the present invention；
Fig. 2 is the noisy image in embodiment 2；
Fig. 3 is the denoising effect figure that gradient descent method is directly used in embodiment 2；
Fig. 4 is the denoising effect figure that the method for the present invention is used in embodiment 2；
Fig. 5 is the performance comparison figure for using gradient descent method in embodiment 2 using the method for the present invention and directly；
Fig. 6 is the structure diagram of apparatus of the present invention.
Specific embodiment
Embodiment 1
Multiresolution rapid denoising method under a kind of mixed noise model of the present invention, as shown in Figure 1, including：
S1. after obtaining noisy image, multilayer gaussian pyramid corresponding with noisy image and multilayer Laplce gold are established
Word tower；
S2. using gradient descent method, successive ignition calculating is carried out successively and solves full variational regularization denoising target letter respectively
Number, so as to obtain denoising image in last time iterative calculation；The input picture iterated to calculate each time is respectively from Gauss gold
The tomographic image chosen in word tower；The initial value of iterative calculation is the tomographic image chosen from gaussian pyramid for the first time, remaining
The initial value iterated to calculate each time is calculated according to the iteration result and laplacian pyramid of last time iterative calculation.
Full variational regularization denoising object function is a function for including noisy image f and denoising image u：
Noisy image and denoising image can be flat images, thus it includes image information all have with plane coordinates
Close, that is, noisy image f and denoising image u may be expressed as plane of delineation coordinate (x, y) function f (x, y) and u (x,
Y), f and f (x, y), u and u (x, y) are not differentiated between in the present patent application.
The method of the present invention be based in single iteration solve calculation amount it is directly proportional to the image resolution ratio size for treating denoising this
One experimental phenomena.Full change is solved with reference to the iterative calculation of multiple gradient descent method by gaussian pyramid and laplacian pyramid
Divide regularization denoising object function, multiresolution is introduced into the denoising method for mixed noise model.
Multilayer is respectively provided with based on the gaussian pyramid that noisy image is established and laplacian pyramid, each layer corresponds to respectively
Image information of the noisy image under different resolution, it is preferable that three layers can be respectively provided with.Each tomographic image in gaussian pyramid
Resolution ratio reduce successively, such as the 0th layer of resolution ratio highest, the 1st layer of resolution ratio are taken second place, and the 2nd layer of resolution ratio is minimum.La Pu
Lars pyramid can be calculated according to gaussian pyramid, and the marginal information of noisy image is included in laplacian pyramid.It is each
Secondary iterative calculation all utilizes gradient descent method, total degree and the gaussian pyramid and total layer of laplacian pyramid of iterative calculation
Number corresponds to, such as in the case where gaussian pyramid and laplacian pyramid are three layers, is iterated to calculate three times altogether,
It iterates to calculate each time all respectively for layer different in gaussian pyramid and/or laplacian pyramid.First for Gauss gold
The layer that word tower and/or laplacian pyramid correspond to low resolution is iterated solution, since low resolution brings low calculating
Amount, therefore iterative solution process can be carried out quickly, avoided and just carried out for high-resolution inefficient iterative solution in starting.
Corresponding layer transforms into next iteration calculating in the result combination laplacian pyramid that last time iterative calculation obtains
Initial value, since laplacian pyramid includes the marginal information of noisy image, iterative calculation can be effective each time
The marginal information of noisy image is protected on ground, and improves iteration starting point, realizes solution efficiency optimization.
Since the resolution ratio for iterating to calculate targeted layer each time is different, each iterative calculation can be distinguished
It, in this way can be quick to low-resolution image processing using the stop condition of relatively low requirement using different iteration stopping conditions
Intermediate result is obtained, quickly obtains the initial value of successive iterations calculating, the stopping of high requirement is used to high-definition picture processing
Condition, it is ensured that the quality of final process result.
Preferred embodiment is further used as, the number of the iterative calculation is three times, the step S2 is specifically included：
S21. one layer of initial value and input picture respectively as first time iterative calculation is chosen from gaussian pyramid, is utilized
Gradient descent method carries out iterative calculation for the first time and solves full variational regularization denoising object function, so as to obtain being tied among first
Fruit；
S22. according to the first intermediate result and laplacian pyramid, the initial value of second of iterative calculation is calculated, from
One layer of input picture as second of iterative calculation is chosen in gaussian pyramid, using gradient descent method, carries out second repeatedly
Generation, which calculates, solves full variational regularization denoising object function, so as to obtain the second intermediate result；
S23. according to the second intermediate result and laplacian pyramid, the initial value of third time iterative calculation is calculated, from
One layer of input picture as third time iterative calculation is chosen in gaussian pyramid, using gradient descent method, third time is carried out and changes
Generation, which calculates, solves full variational regularization denoising object function, so as to obtain denoising image.
The number of iterative calculation to be advisable three times.In iterating to calculate for the first time, one layer can be chosen from gaussian pyramid
Both the initial value as first time iterative calculation also serves as the input picture iterated to calculate for the first time, and iterative calculation for the first time is realized
Gradient descent method is solved the result obtained by full variational regularization denoising object function using gradient descent method and is just tied for the first centre
Fruit.
During second iterates to calculate, a tomographic image that initial value is chosen by the first intermediate result and from laplacian pyramid
It is calculated together, the input picture of second of iterative calculation is then chosen one layer from gaussian pyramid and obtained.Second of iteration
It calculates and realizes gradient descent method, it is just the to solve result obtained by full variational regularization denoising object function using gradient descent method
Two intermediate results.
During third time iterates to calculate, a tomographic image that initial value is chosen by the second intermediate result and from laplacian pyramid
It is calculated together, the input picture of third time iterative calculation is then chosen one layer from gaussian pyramid and obtained.Third time iteration
It calculates and realizes gradient descent method, the result solved obtained by full variational regularization denoising object function using gradient descent method is institute
The denoising image to be obtained, has been finally completed the denoising to noisy image.
Preferred embodiment is further used as, the method for building up of the gaussian pyramid is：
Using following formula, the gray value of pixel in each tomographic image of gaussian pyramid is calculated according to noisy image, from
And establish gaussian pyramid：
In formula, f (x, y) be noisy image, Ii(x, y) is the i-th tomographic image of gaussian pyramid IiAt middle pixel (x, y)
Gray value, Reduce () represent down-sampled operation, and g is the Gaussian template that a size is k × k, and k is custom parameter, and i is height
The serial number of each layer of this pyramid, m and n are sum of parameters.
In the method for the present invention, each tomographic image of gaussian pyramid is all respectively provided with different gray values, for i-th layer of figure
As IiGrey value profile Ii(x, y), the formula that can be provided by the method for the present invention, calculates according to noisy image f (x, y).
The method of the present invention all defines serial number for each layer of gaussian pyramid, and serial number is since 0.Obtain each tomographic image of gaussian pyramid
Gray value after, actually built standing gaussian pyramid.
In above-mentioned formula, g is the Gaussian template that a size is k × k, and k is custom parameter, with reference to the spy of objects in images
Calculated performance of seeking peace requirement can preferably use 5 × 5 Gaussian template, that is,：
The gaussian pyramid established according to the method described above, bottom are original pending images, and top is low resolution
Approximation.When being moved to gaussian pyramid upper strata, the image resolution ratio of respective layer reduces, and each layer of image size
The a quarter of image for preceding layer.
Preferred embodiment is further used as, the number of plies of the laplacian pyramid is three layers, the Laplce
Pyramidal method for building up is：
Using following formula, to the multi-layer image of gaussian pyramid respectively into row interpolation, according to interpolation result, Laplce is obtained
Pyramidal each tomographic image, so as to establish laplacian pyramid：
In formula, Ti(x, y) is to the interpolation result of gaussian pyramid i+1 layer, LiFor i-th layer of figure of laplacian pyramid
Picture, Expand () represent image interpolation operation, and i is the serial number of gaussian pyramid and each layer of laplacian pyramid, and m and n are
Sum of parameters.
In the method for the present invention, each layer of laplacian pyramid can be obtained by the image of gaussian pyramid respective layer into row interpolation
It arrives, after obtaining each layer interpolation result of gaussian pyramid, actually built standing laplacian pyramid.The method of the present invention is draws
The pula each layer of this pyramid all defines serial number, and serial number is since 0.
It is further used as preferred embodiment, in the step S21, sets especially by following formula and iterate to calculate for the first time
Initial value：
In formula,For the initial value of first time iterative calculation, I2The 2nd tomographic image for gaussian pyramid；
It is as follows that iterative formula used is iterated to calculate for the first time：
In formula, J () is full variational regularization denoising object function, and t is current iteration round, and d is decline step-length,For introduce after small constant α it is complete become subitem, o' is the addition Item for preventing denominator zero passage, and A is unit matrix, iteration
The u of gained2For the first intermediate result.
2nd tomographic image resolution ratio of gaussian pyramid is minimum, in the above method, has chosen the 2nd layer of figure of gaussian pyramid
As the initial value both as first time iterative calculation also serves as the input picture iterated to calculate for the first time.Regularization parameter λ and decline
Step-length d can in the light of actual conditions be set.In order to avoid the denominator in iterative formula is zero, with ensure the method for the present invention into
Row, can enable o'=10-5。
In first time iterates to calculate, stopping iterated conditional being set asStop iterated conditional into
After vertical, iterative calculation for the first time terminates, obtained u2For the first intermediate result.
It is further used as preferred embodiment, in the step S22, is iterated to calculate for second especially by following formula setting
Initial value：
In formula,The initial value iterated to calculate for second,For u2By bilinear interpolation as a result, u2Among first
As a result, β1For weight coefficient, L1For the 1st layer of edge image of laplacian pyramid；
Second of iterative calculation iterative formula used is as follows：
In formula, J () is full variational regularization denoising object function, and t is current iteration round, and d is decline step-length,For introduce after small constant α it is complete become subitem, o' is the addition Item for preventing denominator zero passage, and A is unit matrix, I1For height
This pyramidal 1st tomographic image, the u obtained by iteration1For the first intermediate result.
u2It handles to obtain by bilinear interpolationAfterwards again with L1The initial value of second of iterative calculation is calculatedIt is preferred that
Ground, weight coefficient can take β1=0.5.
In second iterates to calculate, the 1st tomographic image I of gaussian pyramid is had chosen1As input picture, stop iteration
Condition can be set asAfter stopping iterated conditional and setting up, second of iterative calculation terminates, obtained u1
For the second intermediate result.
It is further used as preferred embodiment, in the step S23, third time is set to iterate to calculate especially by following formula
Initial value：
In formula,For third time iterative calculation initial value,For u1By bilinear interpolation as a result, u1Among second
As a result, β0For weight coefficient, L0For the 0th layer of edge image of laplacian pyramid；
It is as follows that third time iterates to calculate iterative formula used：
In formula, J () is full variational regularization denoising object function, and t is current iteration round, and d is decline step-length,For introduce after small constant α it is complete become subitem, o' is the addition Item for preventing denominator zero passage, and A is unit matrix, I0For
0th tomographic image of gaussian pyramid, the u obtained by iteration0For denoising image.
u1It handles to obtain by bilinear interpolationAfterwards again with L0The initial value of third time iterative calculation is calculatedIt is preferred that
Ground, weight coefficient can take β0=0.5.
In third time iterates to calculate, the 0th tomographic image I of gaussian pyramid is had chosen0As input picture, stop iteration
Condition can be set asAfter stopping iterated conditional and setting up, third time iterative calculation terminates, obtained u0For
Required obtained denoising image, completes the denoising to noisy image.
Preferred embodiment is further used as, in the iterative formula：
In formula,It itemizes for complete become after the small constant α of introducing, u refers to u2、u1Or u0, uxAnd uyFor the first derivative of u,
uxx、uyyAnd uxySecond dervative for u.
The form of the iterative formula iterated to calculate three times in the present embodiment is identical, is directed toWithCalculating, the targeted object of the iterative formula that iterates to calculate three times is u respectively2、u1And u0, therefore can distinguish
U in above-mentioned two formula is substituted for u2、u1Or u0, above-mentioned two formula can be applied in iterative calculation three times, it is quick to calculate
It obtains correspondingWithα is small constant, can its self-defined numerical value, such as α=1 as needed.
Preferred embodiment is further used as, in the iterative formula：
In the case where noisy image is discrete digital image, can above-mentioned public affairs be used according to Second-Order Central Difference method
Formula calculates the first derivative and second dervative of u.
Embodiment 2
In order to illustrate the denoising effect and odds for effectiveness of the method for the present invention, the present embodiment utilizes the method for the present invention, to addition
The Barbara images of Gauss-Poisson mixed noise carry out denoising experiment, and under identical iterations with gradient descent algorithm
It is compared.Experiment parameter setting is as follows：
1. Gaussian noise parameter is μ=0, σ2=90.
2. iteration stopping condition is
3. λ=40, β0=β1=0.5, d=0.002, α=1.
Noisy image is as shown in Figure 2.Simultaneously using the method for the present invention and directly using gradient descent method to noisy image
Carry out denoising.Directly using gradient descent method denoising result as shown in figure 3, using the method for the present invention denoising result such as
Shown in Fig. 4, the denoising effect of the method for the present invention can be kept and level similar in gradient descent method.
Two methods complete the required iterations of denoising process and the time is as shown in table 1, and two methods iteration is opposite
Error e rr is as shown in Figure 5 with the curve comparison that iterations iteration changes.The method of the present invention is shown
Work improves convergence rate, and iterations are greatly reduced, and run time, which only has, directly uses 1/3rd of gradient descent method.
Table 1
| Index | Directly use gradient descent method | The method of the present invention |
| Iterations | 493 | 180 |
| Time (s) | 121.05 | 40.82 |
Embodiment 3
The quick denoising device of multiresolution under a kind of mixed noise model of the present invention, as shown in fig. 6, including：
Memory, for storing at least one program；
Processor, for loading at least one program to perform a kind of mixed noise described in embodiment 1 and embodiment 2
Multiresolution rapid denoising method under model.
Apparatus of the present invention can perform more under a kind of mixed noise model that Example 1 and Example 2 of the present invention is provided
Resolution ratio rapid denoising method, the arbitrary combination implementation steps of executing method embodiment, have the corresponding function of this method and
Advantageous effect.
It is that the preferable of the present invention is implemented to be illustrated, but be not limited to the invention the implementation above
Example, those skilled in the art can also make various equivalent variations under the premise of without prejudice to spirit of the invention or replace
It changes, these equivalent deformations or replacement are all contained in the application claim limited range.
Claims (10)
1. a kind of multiresolution rapid denoising method under mixed noise model, which is characterized in that including：
S1. after obtaining noisy image, multilayer gaussian pyramid corresponding with noisy image and multilayer laplacian pyramid are established；
S2. using gradient descent method, successive ignition calculating is carried out successively and solves full variational regularization denoising object function respectively, from
And obtain denoising image in last time iterative calculation；The input picture iterated to calculate each time is respectively from gaussian pyramid
The tomographic image chosen；The initial value of iterative calculation is the tomographic image chosen from gaussian pyramid for the first time, remaining is each time
The initial value of iterative calculation is calculated according to the iteration result and laplacian pyramid of last time iterative calculation.
2. the multiresolution rapid denoising method under a kind of mixed noise model according to claim 1, which is characterized in that
The number of the iterative calculation is three times, the step S2 is specifically included：
S21. one layer of initial value and input picture respectively as first time iterative calculation is chosen from gaussian pyramid, utilizes gradient
Descent method carries out iterative calculation for the first time and solves full variational regularization denoising object function, so as to obtain the first intermediate result；
S22. according to the first intermediate result and laplacian pyramid, the initial value of second of iterative calculation is calculated, from Gauss
One layer of input picture as second of iterative calculation is chosen in pyramid, using gradient descent method, carries out second of iteration meter
It calculates and solves full variational regularization denoising object function, so as to obtain the second intermediate result；
S23. according to the second intermediate result and laplacian pyramid, the initial value of third time iterative calculation is calculated, from Gauss
One layer of input picture as third time iterative calculation is chosen in pyramid, using gradient descent method, carries out third time iteration meter
It calculates and solves full variational regularization denoising object function, so as to obtain denoising image.
3. the multiresolution rapid denoising method under a kind of mixed noise model according to claim 2, which is characterized in that
The method for building up of the gaussian pyramid is：
Using following formula, the gray value of pixel in each tomographic image of gaussian pyramid is calculated according to noisy image, so as to build
Vertical gaussian pyramid：
In formula, f (x, y) be noisy image, Ii(x, y) is the i-th tomographic image of gaussian pyramid IiGray scale at middle pixel (x, y)
Value, Reduce () represent down-sampled operation, and g is the Gaussian template that a size is k × k, and k is custom parameter, and i is Gauss gold
The serial number of each layer of word tower, m and n are sum of parameters.
4. the multiresolution rapid denoising method under a kind of mixed noise model according to claim 3, which is characterized in that
The number of plies of the laplacian pyramid is three layers, and the method for building up of the laplacian pyramid is：
Using following formula, to the multi-layer image of gaussian pyramid respectively into row interpolation, according to interpolation result, Laplce's gold word is obtained
Each tomographic image of tower, so as to establish laplacian pyramid：
In formula, Ti(x, y) is to the interpolation result of gaussian pyramid i+1 layer, LiFor the i-th tomographic image of laplacian pyramid,
Expand () represents image interpolation operation, and i is the serial number of gaussian pyramid and each layer of laplacian pyramid, m and n to sum
Parameter.
5. the multiresolution rapid denoising method under a kind of mixed noise model according to claim 2, which is characterized in that
In the step S21, the initial value of iterative calculation for the first time is set especially by following formula：
In formula,For the initial value of first time iterative calculation, I2The 2nd tomographic image for gaussian pyramid；
It is as follows that iterative formula used is iterated to calculate for the first time：
In formula, J () is full variational regularization denoising object function, and t is current iteration round, and d is decline step-length,To draw
Enter after small constant α it is complete become subitem, o' is the addition Item for preventing denominator zero passage, and A is unit matrix, the u obtained by iteration2For
First intermediate result.
6. the multiresolution rapid denoising method under a kind of mixed noise model according to claim 2, which is characterized in that
In the step S22, especially by the initial value of following formula second of iterative calculation of setting：
In formula,The initial value iterated to calculate for second,For u2By bilinear interpolation as a result, u2For the first intermediate result,
β1For weight coefficient, L1For the 1st layer of edge image of laplacian pyramid；
Second of iterative calculation iterative formula used is as follows：
In formula, J () is full variational regularization denoising object function, and t is current iteration round, and d is decline step-length,To draw
Enter after small constant α it is complete become subitem, o' is the addition Item for preventing denominator zero passage, and A is unit matrix, I1For gaussian pyramid
The 1st tomographic image, the u obtained by iteration1For the first intermediate result.
7. the multiresolution rapid denoising method under a kind of mixed noise model according to claim 2, which is characterized in that
In the step S23, the initial value of third time iterative calculation is set especially by following formula：
In formula,For third time iterative calculation initial value,For u1By bilinear interpolation as a result, u1For the second intermediate result,
β0For weight coefficient, L0For the 0th layer of edge image of laplacian pyramid；
It is as follows that third time iterates to calculate iterative formula used：
In formula, J () is full variational regularization denoising object function, and t is current iteration round, and d is decline step-length,For
Introduce after small constant α it is complete become subitem, o' is the addition Item for preventing denominator zero passage, and A is unit matrix, I0For Gauss gold word
0th tomographic image of tower, the u obtained by iteration0For denoising image.
8. according to the multiresolution rapid denoising method under a kind of mixed noise model of claim 5-7 any one of them,
It is characterized in that, in the iterative formula：
In formula,It itemizes for complete become after the small constant α of introducing, u refers to u2、u1Or u0, uxAnd uyFor the first derivative of u, uxx、uyy
And uxySecond dervative for u.
9. the multiresolution rapid denoising method under a kind of mixed noise model according to claim 8, which is characterized in that
In the iterative formula：
10. a kind of quick denoising device of multiresolution under mixed noise model, which is characterized in that including：
Memory, for storing at least one program；
Processor, for loading at least one program with a kind of any one of perform claim requirement 1-9 mixed noise moulds
Multiresolution rapid denoising method under type.
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