CN103530857A - Multi-scale based Kalman filtering image denoising method - Google Patents
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Abstract
The invention discloses a multi-scale based Kalman filtering image denoising method. The method comprises the following steps: step one, wavelet decomposition: an image is subjected to wavelet transform and is decomposed into multiple layers, wherein each layer comprises an LL part, an HL part, an LH part and an HH part, the LL part belongs to the low-frequency part, and the HL part, the LH part and the HH part belong to high-frequency part; step two, computation and prediction: final estimated wavelet coefficients of the HL part, the LH part and the HH part of a previous layer are used for updating initial estimated wavelet coefficient of the HL part, the LH part and the HH part of a next layer respectively, and the corresponding parts of the front layer and the next layer are processed as shown in the specification; and step three, inverse transformation: multiple layers after the wavelet coefficients are updated are subjected to wavelet inverse transformation to obtain an image after denosing.
Description
[ technical field ] A method for producing a semiconductor device
The invention relates to the field of image processing, in particular to a multi-scale-based Kalman filtering image denoising method.
[ background of the invention ]
Digital images are contaminated by noise during acquisition, conversion and transmission. Image restoration (restoration) is one of the main contents of computer image processing, and aims to eliminate or reduce image quality degradation, i.e., degradation, caused during image acquisition and transmission, and restore the original image.
The traditional denoising methods can be roughly divided into two types, one is a space domain-based method, and the other is a transform domain-based method. The space domain denoising method includes gaussian filtering, median filtering, bilateral filtering and the like. The spatial domain method is to directly process the gray scale of the image. The transform domain method is to transform the image, such as fourier transform, wavelet transform, curvelet transform, contourlet transform, etc.
Wavelet transformation is a relatively typical denoising algorithm in a transform domain, and is mainly used for directly performing threshold processing on transformed coefficients. However, the processing often does not consider the correlation of coefficients between different scales, and the correlation can be utilized to improve the Kalman prediction effect.
Kalman filtering is an optimized autoregressive data processing algorithm, and the most prominent advantage is that the problem can be rapidly processed in real time. The method is widely applied to robot navigation, control, sensor data fusion, radar systems in the military field, missile tracking and the like. More recently, computer image processing such as image denoising, image restoration, face recognition, image segmentation, image edge detection, and the like has been applied. When the traditional kalman filtering is used for image processing, only one image is processed in a single scale, and although the prediction and the update are performed by utilizing the correlation between the images, the prediction and the update are complex and the effect is not ideal.
[ summary of the invention ]
The prior Kalman filtering processes the image, and does not consider more the correlation between low frequency and high frequency in the image. And the dependency of the kalman filtering on the initial estimation is strong, a good initial value can obtain a good prediction effect, otherwise, the prediction effect is not good.
In order to overcome the defects of the prior art, the invention provides a Kalman filtering image denoising method based on multiple scales so as to obtain a better denoising effect on the basis of not increasing the calculation complexity.
A Kalman filtering image denoising method based on multiple scales comprises the following steps:
a wavelet decomposition step of wavelet transforming an image, the image being decomposed into a plurality of layers, each layer including four parts: an LL portion, an HL portion, an LH portion and an HH portion, wherein the LL portion belongs to the low frequency portion and the HL portion, the LH portion and the HH portion belong to the high frequency portion;
a calculation prediction step of updating initial estimation wavelet sub-coefficients of the HL portion, the LH portion, and the HH portion of the next layer with final estimation wavelet sub-coefficients of the HL portion, the LH portion, and the HH portion of the previous layer, respectively, for corresponding portions of the previous and next layers:
wherein,represents the jth final estimated wavelet sub-coefficient of the kth part of the (i + 1) th layer,
is the estimation of the coefficients of the motion vector,
representing initial estimation wavelet sub-coefficients of a kth part of an ith layer, wherein three different values of k respectively correspond to an HL part, an LH part and an HH part;
and an inverse transformation step, namely performing inverse wavelet transformation by using the plurality of layers with updated wavelet sub-coefficients to obtain a denoised image.
Preferably, wavelet sub-coefficients V for HL, LH and HH portions of the uppermost layer are calculated prior to the predicting stepikThe following modifications were made:
wherein, V'ikMeans the wavelet sub-coefficient, V, of the kth high-frequency part of the ith layer of the uppermost layer after correctionikRefers to the wavelet sub-coefficient of the kth high-frequency part of the ith layer,
refers to the atrophy threshold of the kth high frequency part of the ith layer,
refers to the noise variance, delta, of the kth high-frequency part of the ith layerxIt refers to the standard deviation of the high frequency part,
preferably, in the step of calculating the prediction, the prediction is carried out
After the treatment, the following treatments were performed:
wherein,represents the final estimated wavelet sub-coefficients of the kth part of the ith layer, Z (i, K) and K (i, K) represent the wavelet sub-system observed values and Kalman gains of the kth part of the ith layer respectively, M represents an observation matrix,
wherein K (i, K) = p (i | i +1, K) MT[Mp(i|i+1,k)MT+Q(i)]-1,
P(i|i,k)={I-K(i)M}p(i|i+1,k),
Where P (i | i +1, k) denotes an error covariance prediction matrix from the k-th part of the i + 1-th layer to the k-th part of the i-th layer, and P (i +1| i +1, α)jk) Denotes the i +1 th layerPart k the error covariance matrix of the jth coefficient, P (i | i, k) denotes the error covariance matrix of part k of the ith layer, and Q (i) and R (i) are white noise.
The invention has the beneficial effects that:
on the basis of wavelet decomposition, the method uses the correlation between parent and child in the same direction with different scales, uses the coefficients of the child to predict the coefficients of the parent to obtain initial estimation wavelet coefficients, and uses the observation values of the coefficients of the parent to update the initial estimation wavelet coefficients of the parent to obtain final estimation wavelet coefficients. And repeating the steps for a plurality of times until all scales are processed. The method and the device make better use of the correlation between the low frequency and the high frequency to carry out Kalman prediction and updating, and can obtain better denoising effect on the basis of not increasing the calculation complexity.
[ description of the drawings ]
Fig. 1 is a flow chart of denoising a multi-scale kalman image according to an embodiment of the present invention.
Fig. 2 shows the dimension and direction diagram of the image after wavelet decomposition.
FIG. 3 is a relationship between parents and children utilized in multi-scale card Raman modeling.
[ detailed description ] embodiments
Specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.
(1) The input noisy natural image is subjected to wavelet transform, and the natural image is decomposed into a low-frequency image and a high-frequency image, as shown in fig. 2, the natural image is decomposed into 4 layers (also called scales), each layer including four partial images: an LL portion, an HL portion, an LH portion and an HH portion, wherein the LL portion belongs to the low frequency portion and the HL portion, the LH portion and the HH portion belong to the high frequency portion; wherein, the precision of the 4 th layer is the smallest, i.e. the coarsest, and the precision of the 1 st layer is the largest, i.e. the finest, which are defined herein as the 4 th layer to the 1 st layer from top to bottom.
(2) Correcting the coefficient of the high-frequency image with the highest scale (the uppermost layer) by using a Bayesian Shrink method to obtain a corrected high-frequency image;
the bayesian spring method corrects the high frequency image coefficients,
wherein, V'ikMeans the wavelet sub-coefficient, V, of the kth high-frequency part of the ith layer of the uppermost layer after correctionikRefers to the wavelet sub-coefficient of the kth high-frequency part of the ith layer,
refers to the atrophy threshold of the kth high frequency part of the ith layer,
refers to the noise variance, delta, of the kth high-frequency part of the ith layerxIt refers to the standard deviation of the high frequency part,
(3) and establishing a Kalman state equation and an observation equation for image denoising.
An image can be decomposed into coarse to fine precision. One signal at coarse precision corresponds to 4 signals at next precision, and at mth layer precision, corresponds to 4x-mSignals, as shown in FIGS. 2 and 3, one coefficient (indicated by a triangle) of the HH portion of the 1 st layer corresponds to 16 coefficients (indicated by a triangle) of the HH portion of the 4 th layer。
Analysis of the wavelet tree structure shows that there is a certain correlation between wavelet sub-numbers of the same part (sub-band) between different scales, such as the HH part of the 4 th layer and the HH parts of the 3 rd to 1 st layers. The accuracy of the kalman filter can be improved by using this correlation.
And resetting the state equation, and establishing a Kalman model by utilizing the same direction correlation of different scales.
And estimating the information of the same part (direction) of the i layer by using the information of the i +1 layer to obtain an initial estimation value, and correcting the initial estimation value by using the observation value of the i scale. Therefore, the correlation between the low frequency and the high frequency of the image is better utilized, and a better prediction effect can be achieved by using Kalman filtering.
To illustrate more specifically how the algorithm predicts on coefficients of different scales, a simplified 3-layer model is used to illustrate the problem, as shown in fig. 2. The coefficients of the same part of the upper and lower layers adjacent to each other are called a child coefficient and a parent coefficient, respectively. The parent coefficient and the sub-coefficient have strong correlation, each parent coefficient corresponds to four sub-coefficients, the parent coefficient is predicted by using the final estimation value of the sub-coefficient to obtain the initial estimation value of the complex coefficient, and the initial estimation value of the complex coefficient is updated by using the observation value of the parent coefficient to obtain the final estimation value of the complex coefficient.
The multi-scale state space model of Kalman filtering is the relation between the parent coefficient and the child coefficient, and the observation model is the relation between the noisy observed value and the estimated value of different scale coefficients.
The multi-scale state space model and observation model equations are as follows:
Z(i,k)=MX(i,k)+ε(i)
where X (i, k) represents the coefficient value at the ith layer position k.
Indicating the interpolation of the coefficients of the i +1 layer.
Represents the prediction from the i +1 th layer coarse resolution to the i-th layer fine resolution. Z (i, k) represents an observed value of a coefficient at k on the scale i. σ (i) and ε (i) are white noise processes with zero mean and variance of Q (i) and R (i), respectively, independent of each other.
Specifically, for the multi-layer image after wavelet decomposition, the prediction equation and the update equation of the kalman filter are respectively as follows:
wherein,
represents the initial estimated wavelet coefficients for the image at layer i position k, which is determined by the final estimated wavelet sub-coefficients at layer i +1 position k
Estimated, M represents an observation matrix, where, when k takes different values, positions k represent an LL portion, an HL portion, an LH portion, and an HH portion, respectively,
the j-th final estimated wavelet sub-coefficient representing the i + 1-th layer position k, j =1,2,3, 4. Z (i, K) and K (i, K) respectively represent wavelet sub-system observations and Kalman gains of the kth part of the ith layer,
the kalman gain can be calculated as follows:
K(i)=P(i|i+1,k)MT[MP(i|i+1,k)MT+Q(i)]-1
the update equation is analyzed as follows:
the error covariance prediction matrix is as follows:
the error covariance update matrix is as follows:
P(i|i,k)={I-K(i)MJp(i|i+1,k)
(4) in summary, the iterative equation combining kalman filtering and multiscale is as follows:
1)
2)K(i,k)=p(i|i+1,k)MT[Mp(i|i+1,k)MT+Q(i)]-1
3)
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5) p (I | I, K) = { I-K (I, K) M } P (I | I +1, K)
At the beginning of the iteration, wavelet sub-numbers are assigned for each portion of layer 4,the result obtained in the step 2) is used for assignment, and the final estimation wavelet coefficient of each part of the 4 th layer is obtained
By equation 3), an initial estimated wavelet coefficient estimation value of the corresponding part of layer 3 can be obtained
And (4) evaluating the error covariance of each part of the 4 th layer to obtain P (4|4, alpha)jk) By the formula 1), an error covariance prediction matrix P (3|4, K) obtained by predicting the layer 3 by the layer 4 corresponding part can be obtained, K (3, K) can be calculated by adding an observation matrix M obtained by observation, and P (3|3, K) can be obtained by the formula 5), and the final estimation wavelet coefficient of the layer 3 corresponding part can be obtained by preparing for calculating P (2|3, K) and according to the observed Z (3, K)
And continuously iterating in sequence to finally obtain the estimated wavelet sub-coefficients of the HL part, the LH part and the HH part of the 1 st layer.
(5) And performing wavelet inverse transformation on the corrected coefficient to obtain a denoised image.
Claims (3)
1. A Kalman filtering image denoising method based on multiple scales is characterized by comprising the following steps:
a wavelet decomposition step of wavelet transforming an image, the image being decomposed into a plurality of layers, each layer including four parts: an LL portion, an HL portion, an LH portion and an HH portion, wherein the LL portion belongs to the low frequency portion and the HL portion, the LH portion and the HH portion belong to the high frequency portion;
a calculation prediction step of updating initial estimation wavelet sub-coefficients of the HL portion, the LH portion, and the HH portion of the next layer with final estimation wavelet sub-coefficients of the HL portion, the LH portion, and the HH portion of the previous layer, respectively, for corresponding portions of the previous and next layers:
wherein,represents the jth final estimated wavelet sub-coefficient of the kth part of the (i + 1) th layer,
is the estimation of the coefficients of the motion vector,representing initial estimation wavelet sub-coefficients of a kth part of an ith layer, wherein three different values of k respectively correspond to an HL part, an LH part and an HH part;
and an inverse transformation step, namely performing inverse wavelet transformation by using the plurality of layers with updated wavelet sub-coefficients to obtain a denoised image.
2. The multi-scale-based Kalman filter image denoising method of claim 1, which is characterized by:
wavelet sub-coefficients V for HL, LH and HH portions of the uppermost layer before the calculating of the prediction stepikThe following modifications were made:
wherein, V'ikMeans the wavelet sub-coefficient, V, of the kth high-frequency part of the ith layer of the uppermost layer after correctionikRefers to the wavelet sub-coefficient of the kth high-frequency part of the ith layer,
refers to the atrophy threshold of the kth high frequency part of the ith layer,refers to the noise variance of the kth high-frequency part of the ith layer,
it refers to the standard deviation of the high frequency part,
3. the multi-scale-based Kalman filter image denoising method of claim 1, which is characterized by:
in the calculation prediction step, the method is carried out
After the treatment, the following treatments were performed:
wherein,represents the final estimated wavelet sub-coefficients of the kth part of the ith layer, Z (i, K) and K (i, K) represent the wavelet sub-system observed values and Kalman gains of the kth part of the ith layer respectively, M represents an observation matrix,
wherein K (i, K) = p (i | i +1, K) MT[Mp(i|i+1,k)MT+Q(i)]-1,
P(i|i,k)={I-K(i)M}p(i|i+1,k),
Where P (i | i ten, k) denotes an error covariance prediction matrix from the kth part of the ith 1 layer to the kth part of the ith layer, and P (i +1| i +1, α)jk) An error covariance matrix representing the jth coefficient of the kth part of the i +1 th layer, P (i | i, k) represents the error covariance matrix of the kth part of the i layer, and Q (i) and R (i) are white noise.
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Cited By (7)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN106507113A (en) * | 2016-11-28 | 2017-03-15 | 河海大学 | A kind of three describe lattice vector quantization prediction wing coding/decoding method |
| CN106507113B (en) * | 2016-11-28 | 2019-03-29 | 河海大学 | One kind three describes lattice vector quantization prediction wing coding/decoding method |
| CN107977944A (en) * | 2017-12-12 | 2018-05-01 | 华南农业大学 | One kind estimation NPP remote sensing image data generation methods |
| CN108830888A (en) * | 2018-05-24 | 2018-11-16 | 中北大学 | Thick matching process based on improved multiple dimensioned covariance matrix Feature Descriptor |
| CN108830888B (en) * | 2018-05-24 | 2021-09-14 | 中北大学 | Coarse matching method based on improved multi-scale covariance matrix characteristic descriptor |
| CN109472834A (en) * | 2018-10-23 | 2019-03-15 | 桂林电子科技大学 | A kind of Kalman filtering phase developing method based on wavelet transformation |
| CN109472834B (en) * | 2018-10-23 | 2023-04-14 | 桂林电子科技大学 | Kalman filtering phase expansion method based on wavelet transformation |
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