CN112819701B - Image denoising method and system and electronic equipment - Google Patents
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Abstract
The application relates to an image denoising method, an image denoising system and electronic equipment. The method comprises the following steps: a, step a: calculating the local gradient of the image to be denoised by adopting a preferred interpolation template mode, and calculating the amplitude of the local gradient; step b: constructing a time modulation function T according to the local gradient amplitude; step c: and introducing the time modulation function T into a P-M diffusion equation in the time step of each step, and solving the P-M diffusion equation in a single step iteration manner to obtain a denoised image. According to the method, the diffusion time is dynamically and differentially modulated, the image denoising enhancement with high time resolution is realized, the retention capacity of a diffusion denoising algorithm to texture details and the removal capacity of high-frequency noise are improved, the denoising capacity of other nonlinear denoising operators can be improved by combining the algorithm, and the signal-to-noise ratio after denoising is further improved.
Description
Technical Field
The present application relates to the field of image processing technologies, and in particular, to an image denoising method, system and electronic device.
Background
The diffusion denoising algorithm is always an important image denoising enhancement algorithm, the solution of a linear diffusion equation with an initial value problem is represented by convolution filtering of an initial value function and a Gaussian function, the nonlinear diffusion equation is mainly represented by a P-M diffusion equation, and texture details can be better kept while denoising is carried out after a nonlinear direction diffusion function is introduced. Denoising algorithms based on diffusion equations are valued by various scholars for many years, and variant algorithms of the denoising algorithms are emerging continuously.
However, in addition to various variant algorithms of spatial nonlinear filtering, scholars are aware of the importance of local diffusion time more and more, and therefore, how to adjust diffusion time step by step in the process of solving a nonlinear diffusion equation to achieve different local diffusion time in space becomes a problem to be solved urgently.
Disclosure of Invention
The application provides an image denoising method, an image denoising system and electronic equipment, and aims to solve at least one of the technical problems in the prior art to a certain extent.
In order to solve the above problems, the present application provides the following technical solutions:
an image denoising method comprises the following steps:
step a: calculating the local gradient of the image to be denoised by adopting a preferred interpolation template mode, and calculating the amplitude of the local gradient;
step b: constructing a time modulation function T according to the local gradient amplitude;
step c: and introducing the time modulation function T into a P-M diffusion equation in the time step of each step, and solving the P-M diffusion equation in a single step iteration manner to obtain a denoised image.
The technical scheme adopted by the embodiment of the application further comprises the following steps: step a also includes: setting time step length, gradient threshold value and initial value of iteration variable.
The technical scheme adopted by the embodiment of the application further comprises the following steps: in the step a, the calculating the local gradient of the image to be denoised in a preferred interpolation template mode specifically includes:
the square of the gradient along the x direction is calculated as:
in the above-mentioned formula,
the square of the gradient along the y direction is calculated as:
in the above-mentioned formula,
the technical scheme adopted by the embodiment of the application further comprises the following steps: in step b, the expression of the time modulation function T is:
in the formula, u represents an image gray value variable, and g represents an arbitrary nonlinear denoising operator.
The technical scheme adopted by the embodiment of the application further comprises the following steps: after the step c, the method also comprises the following steps: judging whether the denoised image meets the output requirement, if not, resetting the time step length, and re-executing the step a; and if the output requirement is met, outputting the denoised image.
Another technical scheme adopted by the embodiment of the application is as follows: an image denoising system, comprising:
a gradient calculation module: the method is used for calculating the local gradient of the image to be denoised in a mode of adopting an optimal interpolation template, and calculating the amplitude of the local gradient;
a time modulation function calculation module: for constructing a temporal modulation function T from the local gradient amplitudes;
a diffusion denoising module: and the time modulation function T is introduced into a P-M diffusion equation in the time step of each step, and the P-M diffusion equation is solved in a single step iteration manner to obtain a denoised image.
The technical scheme adopted by the embodiment of the application further comprises a parameter setting module, wherein the parameter setting module is used for setting the time step length, the gradient threshold value and the initial value of the iteration variable.
The technical scheme adopted by the embodiment of the application further comprises the following steps: the gradient calculation module calculates the local gradient of the image to be denoised in a mode of optimizing an interpolation template, and specifically comprises the following steps:
the square of the gradient along the x-direction is calculated as:
in the above-mentioned formula,
the square of the gradient along the y direction is calculated as:
in the above-mentioned formula,
the technical scheme adopted by the embodiment of the application further comprises the following steps: the expression of the time modulation function T is:
in the formula, u represents an image gray value variable, and g represents an arbitrary nonlinear denoising operator.
The technical scheme adopted by the embodiment of the application further comprises an image judgment module and an image output module, wherein the image judgment module is used for judging whether the de-noised image meets the output requirement, if not, the time step length is reset, and the step a is executed again; and if the output requirement is met, outputting the denoised image through an image output module.
The embodiment of the application adopts another technical scheme that: an electronic device, comprising:
at least one processor; and
a memory communicatively coupled to the at least one processor; wherein the content of the first and second substances,
the memory stores instructions executable by the one processor to cause the at least one processor to perform the following operations of the image denoising method as described above:
a, step a: calculating the local gradient of the image to be denoised by adopting a preferred interpolation template mode, and calculating the amplitude of the local gradient;
step b: constructing a time modulation function T according to the local gradient amplitude;
step c: and introducing the time modulation function T into a P-M diffusion equation in the time step of each step, and solving the P-M diffusion equation in a single-step iteration manner to obtain a denoised image.
Compared with the prior art, the embodiment of the application has the advantages that: according to the image denoising method, the image denoising system and the electronic equipment, by introducing the local time modulation function, in each diffusion time step, the diffusion time is modulated according to the gradient amplitude, relatively less diffusion time is applied to the region with steep gradient, and normal relatively longer diffusion time is applied to the smooth region, so that the local time resolution and the dynamic differential modulation diffusion time of the traditional diffusion denoising method are improved, and the image denoising enhancement with high time resolution is realized. The method and the device improve the retention capacity of the diffusion denoising algorithm on texture details and the removal capacity of high-frequency noise, and can also improve the denoising capacity of other nonlinear denoising operators and further improve the signal-to-noise ratio after denoising by combining the algorithm.
Drawings
FIG. 1 is a flowchart of an image denoising method according to an embodiment of the present application;
FIG. 2 is a schematic diagram of gradient approximation for texture discontinuities for different differential modes;
FIG. 3 is a schematic structural diagram of an image denoising system according to an embodiment of the present application;
FIG. 4 is a comparison graph of denoising effect for a Cameraman image with a Gaussian noise variance of 900;
FIG. 5 is a schematic diagram of a grayscale amplitude line drawn on line 100 of an image;
fig. 6 is a schematic structural diagram of hardware devices of the image denoising method provided in the embodiment of the present application.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application more apparent, the present application is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the present application and are not intended to limit the present application.
According to the image denoising method provided by the embodiment of the application, by introducing the local time modulation function, in each diffusion time step, the diffusion time is modulated according to the gradient amplitude, relatively less diffusion time is applied to the region with the steep gradient, and normal relatively greater diffusion time is applied to the smooth region, so that the local time resolution of the traditional diffusion denoising method is improved, the diffusion time is dynamically and differentially modulated, and the image denoising enhancement with high time resolution is realized.
Specifically, please refer to fig. 1, which is a flowchart of an image denoising method according to an embodiment of the present application. The image denoising method of the embodiment of the application comprises the following steps:
step 100: inputting an image to be denoised;
in step 100, the image to be denoised includes, but is not limited to, a grayscale image or a dimension in a three-primary color image.
Step 200: setting initial values of parameters such as a time step length, a gradient threshold value, an iteration variable and the like;
in step 200, the application sets an initial time step dt =1.0, a gradient threshold K =1, an initial iteration variable step =1, and specific parameters may be adjusted according to actual operations.
Step 300: calculating the local gradient of the image to be denoised by adopting a preferred interpolation template mode, constructing an image gradient map, and calculating the amplitude of the local gradient;
in step 300, as shown in FIG. 2, a schematic diagram of gradient approximation for texture discontinuities for different difference modes is shown. When an image gradient map is calculated by the existing central difference, the gradient is smoothed at the texture discontinuity, so that the gradient amplitude cannot be accurately calculated at the gradient discontinuity. Therefore, the local gradient amplitude is calculated by adopting a mode of optimizing an interpolation template, namely, the larger gradient amplitude in the forward difference and the backward difference is taken as the local gradient, and fine gradient depicting of the whole area (including texture discontinuity) is carried out, so that gradient fluctuation at the texture discontinuity is better depicted, and further, time modulation is more accurately realized.
Specifically, the square of the gradient along the x direction is calculated as:
in the formula (1), the first and second groups,
the square of the gradient along the y direction is calculated as:
in the formula (3), the first and second groups,
step 400: constructing a time modulation function T according to the local gradient amplitude;
in step 400, the local gradient amplitude can more accurately divide the discontinuous diffusion time of the texture, a specific expression of a time modulation function is constructed according to the local gradient amplitude, and the calculation of parameters in the expression is given by the full-image statistical property of the image gradient amplitude; specifically, the specific expression of the time modulation function is as follows:
in the formula (5), T * Representing the basic diffusion time guarantee, can be scaled by a statistical image gradient map:
in the formula (7), M and N respectively represent the horizontal and vertical pixel numbers of the input image to be denoised, and S represents that all the pixel numbers satisfy
K is a threshold for distinguishing large gradients.
Step 500: introducing a time modulation function T into a P-M diffusion equation in a time step dt, and solving the diffusion equation in a single-step iteration manner to obtain a denoised image, wherein step = step +1;
in step 500, in order to implement local adjustment of diffusion time in different spaces, in the embodiment of the present application, a time modulation function T is introduced in front of a diffusion term in a conventional diffusion equation to solve the diffusion equation in a time step dt of each step, and the diffusion time of the whole image to be denoised is locally and dynamically adjusted, so that a texture discontinuous region is given with less diffusion time, and a smooth region is given with normal diffusion time, thereby implementing retention of texture features in the denoising process. The specific expression is as follows:
in the formula (8), u represents an image gray value variable, and an image to be denoised containing noise is input initially; g represents an arbitrary nonlinear denoising operator.
Step 600: judging whether the peak signal-to-noise ratio (PSNR) of the denoised image is reduced, if so, executing the step 700; otherwise, re-executing step 300;
in step 600, if the peak signal-to-noise ratio of the denoised image is increased, that is, the denoised image has better peak signal-to-noise ratio output than the previous dt, returning to step 300 to continue iteration; on the contrary, if the peak signal-to-noise ratio of the denoised image is reduced, the best iterative denoised image is obtained according to the time step dt =1.0 set in the step 200.
Step 700: judging whether the obtained denoised image meets the output requirement, if not, executing the step 800; if the output requirement is met, executing step 900;
step 800: reset dt =0.5 × dt, i.e. reduce dt by half, and re-execute step 300;
in step 800, if the peak signal-to-noise ratio cannot meet the output requirement, the fixed time step is modulated back, and finally the closed-loop image denoising effect is output. It will be appreciated that the value of the reset time step dt is not limited to being reduced by half, but may be set according to actual operation.
Step 900: and outputting the denoised image.
Fig. 3 is a schematic structural diagram of an image denoising system according to an embodiment of the present application. The image denoising system comprises an image input module, a parameter setting module, a gradient calculation module, a time modulation function calculation module, a diffusion denoising module, a signal-to-noise ratio judgment module, an image judgment module and an image output module.
An image input module: the image denoising method comprises the steps of inputting an image to be denoised; the image to be denoised includes, but is not limited to, a grayscale image or a certain dimension in a three-primary color image.
A parameter setting module: the initial values of parameters such as time step length, gradient threshold value, iteration variable and the like are set; the method comprises the steps of setting an initial time step dt =1.0, setting a gradient threshold K =1, setting an initial iteration variable step =1, and adjusting specific parameters according to actual operation.
A gradient calculation module: the method is used for calculating the local gradient of the image to be denoised by adopting a mode of optimizing an interpolation template, constructing an image gradient map and calculating the local gradient amplitude; the local gradient amplitude is calculated by adopting a mode of optimizing an interpolation template, namely, the larger gradient amplitude in the forward difference and the backward difference is taken as a local gradient, and fine gradient depicting of the whole area (including texture discontinuity) is carried out, so that gradient fluctuation at the texture discontinuity is better depicted, and further, time modulation is more accurately realized.
Specifically, the equation for the square of the gradient along the x-direction is:
in the formula (1), the first and second groups of the compound,
the square of the gradient along the y direction is calculated as:
in the formula (3), the first and second groups of the compound,
a time modulation function calculation module: the time modulation function T is constructed according to the local gradient amplitude; the local gradient amplitude can more accurately divide the discontinuous diffusion time of the texture, a specific expression of a time modulation function is constructed according to the local gradient amplitude, and the calculation of parameters in the expression is given by the full-image statistical property of the image gradient amplitude; specifically, the specific expression of the time modulation function is as follows:
in the formula (5), T * Representing the basic diffusion time guarantee, can be scaled by statistical image gradient maps:
in the formula (7), M and N respectively represent the horizontal and vertical pixel numbers of the input image to be denoised, and S represents that all the pixel numbers satisfy
K is a threshold for distinguishing large gradients.
A diffusion denoising module: the method is used for introducing a time modulation function T into a P-M diffusion equation in a time step dt, solving the diffusion equation through single-step iteration to obtain a denoised image, wherein step = step +1; in order to realize the adjustment of diffusion time of different spatial parts, a time modulation function T is introduced in front of a diffusion term in a traditional diffusion equation in the embodiment of the application, so that the diffusion time of the whole image to be denoised is locally and dynamically adjusted within the time step dt of each step of solving the diffusion equation, a texture discontinuous area is endowed with less diffusion time, and a smooth area is endowed with normal diffusion time, so that the retention of texture characteristics in the denoising process is realized. The specific expression is as follows:
in the formula (8), u represents an image gray value variable, and an image to be denoised containing noise is input initially; g represents an arbitrary nonlinear denoising operator.
A signal-to-noise ratio judgment module: the image processing module is used for judging whether the peak signal-to-noise ratio (PSNR) of the denoised image is reduced or not, and if the peak signal-to-noise ratio (PSNR) of the denoised image is reduced, judging whether the denoised image meets the output requirement or not through the image judging module; otherwise, the local gradient magnitudes are recalculated by the gradient calculation module.
An image judgment module: the local gradient amplitude is recalculated through the gradient calculation module; and if the output requirement is met, outputting the denoised image through an image output module. If the peak signal-to-noise ratio cannot meet the output requirement, the closed-loop image denoising effect is finally output by modulating the fixed time step.
To verify the feasibility and effectiveness of the embodiment of the present application, fig. 4 shows a comparison of denoising effects for a Cameraman image with a gaussian noise variance of 900. Wherein, (a) is original image, (b) is noise image, (c) is traditional P-M denoising, and (d) is P-M denoising introduced by the invention. As can be seen, after the time modulation function T constructed by the method is introduced, the classical P-M algorithm shows great improvement of the denoising effect. Please refer to fig. 5, which is a schematic diagram illustrating the gray scale lines drawn on the 100 th line of the image. The graph in fig. 5 clearly shows that after the time modulation function T is added, denoising shows more obvious retention and enhancement of texture details, and has stronger enhancement of the removing capability for high-frequency noise at a relatively smooth position.
Fig. 6 is a schematic structural diagram of hardware devices of the image denoising method provided in the embodiment of the present application. As shown in fig. 6, the device includes one or more processors and memory. Taking a processor as an example, the apparatus may further include: an input system and an output system.
The processor, memory, input system, and output system may be connected by a bus or other means, as exemplified by the bus connection in fig. 6.
The memory, which is a non-transitory computer-readable storage medium, may be used to store non-transitory software programs, non-transitory computer-executable programs, and modules. The processor executes various functional applications and data processing of the electronic device, i.e., implements the processing method of the above-described method embodiment, by executing the non-transitory software program, instructions and modules stored in the memory.
The memory may include a storage program area and a storage data area, wherein the storage program area may store an operating system, an application program required for at least one function; the storage data area may store data and the like. Further, the memory may include high speed random access memory, and may also include non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid state storage device. In some embodiments, the memory optionally includes memory located remotely from the processor, and these remote memories may be connected to the processing system over a network. Examples of such networks include, but are not limited to, the internet, intranets, local area networks, mobile communication networks, and combinations thereof.
The input system may receive input numeric or character information and generate a signal input. The output system may include a display device such as a display screen.
The one or more modules stored in the memory, when executed by the one or more processors, perform the following operations of any of the above method embodiments:
step a: calculating the local gradient of the image to be denoised by adopting a mode of optimizing an interpolation template, and calculating the amplitude of the local gradient;
step b: constructing a time modulation function T according to the local gradient amplitude;
step c: and introducing the time modulation function T into a P-M diffusion equation in the time step of each step, and solving the P-M diffusion equation in a single step iteration manner to obtain a denoised image.
The product can execute the method provided by the embodiment of the application, and has the corresponding functional modules and beneficial effects of the execution method. For technical details that are not described in detail in this embodiment, reference may be made to the methods provided in the embodiments of the present application.
Embodiments of the present application provide a non-transitory (non-volatile) computer storage medium having stored thereon computer-executable instructions that may perform the following operations:
step a: calculating the local gradient of the image to be denoised by adopting a mode of optimizing an interpolation template, and calculating the amplitude of the local gradient;
step b: constructing a time modulation function T according to the local gradient amplitude;
step c: and introducing the time modulation function T into a P-M diffusion equation in the time step of each step, and solving the P-M diffusion equation in a single-step iteration manner to obtain a denoised image.
Embodiments of the present application provide a computer program product comprising a computer program stored on a non-transitory computer readable storage medium, the computer program comprising program instructions that, when executed by a computer, cause the computer to perform the following:
step a: calculating the local gradient of the image to be denoised by adopting a mode of optimizing an interpolation template, and calculating the amplitude of the local gradient;
step b: constructing a time modulation function T according to the local gradient amplitude;
step c: and introducing the time modulation function T into a P-M diffusion equation in the time step of each step, and solving the P-M diffusion equation in a single-step iteration manner to obtain a denoised image.
According to the image denoising method, the image denoising system and the electronic equipment, by introducing the local time modulation function, in each diffusion time step, the diffusion time is modulated according to the gradient amplitude, relatively less diffusion time is applied to the region with steep gradient, and normal relatively longer diffusion time is applied to the smooth region, so that the local time resolution and the dynamic differential modulation diffusion time of the traditional diffusion denoising method are improved, and the image denoising enhancement with high time resolution is realized. The method and the device improve the retention capacity of the diffusion denoising algorithm on texture details and the removal capacity of high-frequency noise, and can also improve the denoising capacity of other nonlinear denoising operators and further improve the signal-to-noise ratio after denoising by combining the algorithm.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the application. Thus, the present application is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims (7)
1. An image denoising method is characterized by comprising the following steps:
step a: calculating the local gradient of the image to be denoised by adopting a preferred interpolation template mode, and calculating the amplitude of the local gradient;
step b: constructing a time modulation function T according to the local gradient amplitude;
step c: introducing the time modulation function T into a P-M diffusion equation in the time step of each step, and solving the P-M diffusion equation in a single-step iteration manner to obtain a denoised image;
wherein: in the step a, the calculating the local gradient of the image to be denoised in a preferred interpolation template mode specifically includes:
the square of the gradient along the x-direction is calculated as:
in the above-mentioned formula,
the square of the gradient along the y direction is calculated as:
in the above-mentioned formula,
the step b comprises the following steps: the local gradient amplitude can more accurately divide the discontinuous diffusion time of the texture, a specific expression of a time modulation function is constructed according to the local gradient amplitude, and the calculation of parameters in the expression is given by the full-image statistical property of the image gradient amplitude; the specific expression of the time modulation function is:
in the formula (5), T * Represents the basic diffusion time guarantee, given in scale by the statistical image gradient map:
in the formula (7), M and N respectively represent the horizontal and vertical pixel numbers of the input image to be denoised, and S represents that all the pixel numbers satisfy
K is a threshold value for distinguishing large gradients;
the step c comprises the following steps:
introducing a time modulation function T in front of a diffusion term in a traditional diffusion equation to solve the diffusion equation in a time step dt of each step, and locally and dynamically adjusting the diffusion time of the whole image to be denoised, so that a texture discontinuous region is endowed with less diffusion time, and a smooth region is endowed with normal diffusion time, thereby realizing the retention of texture characteristics in the denoising process, wherein the specific expression is as follows:
in the formula (8), u represents an image gray value variable, and g represents an arbitrary nonlinear denoising operator.
2. The image denoising method of claim 1, wherein step a further comprises: setting time step length, gradient threshold value and initial value of iteration variable.
3. The method for denoising an image according to claim 2, further comprising, after step c: judging whether the denoised image meets the output requirement, if not, resetting the time step length and re-executing the step a; and if the output requirement is met, outputting the denoised image.
4. An image denoising system, comprising:
a gradient calculation module: the method is used for calculating the local gradient of the image to be denoised in a mode of adopting an optimal interpolation template, and calculating the amplitude of the local gradient;
a time modulation function calculation module: for constructing a temporal modulation function T from the local gradient amplitudes;
a diffusion denoising module: the time modulation function T is introduced into a P-M diffusion equation in the time step of each step, and the P-M diffusion equation is solved in a single step iteration mode to obtain a denoised image;
the gradient calculation module is specifically configured to:
the square of the gradient along the x direction is calculated as:
in the above-mentioned formula,
the square of the gradient along the y direction is calculated as:
in the above-mentioned formula,
the time modulation function calculation module is specifically configured to:
the local gradient amplitude can more accurately divide the discontinuous diffusion time of the texture, a specific expression of a time modulation function is constructed according to the local gradient amplitude, and the calculation of parameters in the expression is given by the full-image statistical property of the image gradient amplitude; the specific expression of the time modulation function is:
in the formula (5), T * Represents the basic diffusion time guarantee, given in scale by the statistical image gradient map:
in the formula (7), M and N respectively represent the horizontal and vertical pixel numbers of the input image to be denoised, and S represents that all the pixels satisfy
K is a threshold value for distinguishing large gradients;
the diffusion denoising module is specifically configured to:
introducing a time modulation function T in front of a diffusion term in a traditional diffusion equation to solve the diffusion equation in a time step dt of each step, and locally and dynamically adjusting the diffusion time of the whole image to be denoised, so that a texture discontinuous region is endowed with less diffusion time, and a smooth region is endowed with normal diffusion time, thereby realizing the retention of texture characteristics in the denoising process, wherein the specific expression is as follows:
in the formula (8), u represents an image gray value variable, and g represents an arbitrary nonlinear denoising operator.
5. The image denoising system of claim 4, further comprising a parameter setting module, wherein the parameter setting module is configured to set a time step size, a gradient threshold, and an initial value of an iteration variable.
6. The image denoising system of claim 5, further comprising an image judging module and an image output module, wherein the image judging module is configured to judge whether the denoised image meets the output requirement, reset the time step if the denoised image does not meet the output requirement, and re-execute step a; and if the output requirement is met, outputting the denoised image through an image output module.
7. An electronic device, comprising:
at least one processor; and
a memory communicatively coupled to the at least one processor; wherein, the first and the second end of the pipe are connected with each other,
the memory stores instructions executable by the at least one processor to enable the at least one processor to perform the method of denoising an image as described in any one of items 1 to 3 above.
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