[Digital Image Processing] image restoration-Inverse Filtering

Source: Internet
Author: User
1. The aging of the problematic point image of Inverse Filtering can be considered as one of the following processes. One is the impact of degradation functions (resulting in blurred images, fading, etc.), and the other is the impact of additive noise.
Expressed
In the first few blog posts, we mainly introduce the removal of additive noise. This blog post mainly introduces the Inverse Filtering of images, that is, the removal of degradation functions. However, it is inconvenient to process the inverse filter in the spatial domain. In simple consideration, the inverse operation of addition is subtraction, the division of the Inverse Operation of multiplication, And the inverse operation of differentiation is integral (strictly speaking, indefinite integral ). Then we can get a simple conclusion. To get out of convolution, we must use the convolution inverse operation. The convolution inverse operation is --------- anti-convolution. The amount seems to be a proper name. We have established an intuitive understanding of convolution, and obtained the product of signal inversion and filter coefficients. So what kind of operation is anti-convolution? Or, specifically, what is the form of anti-convolution spatial operations? This is actually redundant, or not complicated. In the previous blog post ([Digital Image Processing] frequency domain filtering (1) -- basis and low-pass filter), we have come to an important conclusion. Convolution in the spatial domain is actually the product of the frequency domain. Therefore, it is very simple to consider this. The inverse filtering operation in the frequency domain is actually a division operation. We can obtain the aging model in the next frequency domain through Fourier transformation.
Without convolution, such an expression is a very simple arithmetic operation. The so-called convolution or inverse filtering is the process of removing degradation functions. In this case, the Division can be done directly, as shown below.
According to the textbook, this expression is interesting (where is it interesting ?). First, you must know the exact degradation function. Secondly, if the degraded function contains a value of 0 or a minimum, the noise will be greatly increased. In conclusion, there are two problems with Inverse Filtering: 1. Estimation of degradation functions. 2. Try to prevent noise from affecting image quality. 2. Models of two degraded functions 2.1 Atmospheric Turbulence Model
This model is very simple, similar to Gaussian LPF. As the value increases, the image is blurred. The following is the result of the model execution.
It can be seen from the expression that this model does not have a 0 value. However, this model is very similar to a low-pass filter, and the value of the impedance band is extremely small. This may cause direct inverse filtering of the image to fail. Let's talk about this later. 2.2 The motion blur model actually has a filter with the same name in Photoshop. I will not do the detailed push. The expression of this model is as follows.
Here are several parameters to describe. It indicates the exposure time. The sum here indicates the amount of horizontal movement and the amount of vertical movement. It is worth mentioning that do not forget the following important limits.
Note: the size of the image after motion blur changes. If the image is captured based on the source image, the image composition will be lost. The Restoration effect is not very good, I do not know whether the cause of poor performance is due to missing components or noise interference. Therefore, here I extend the image size appropriately to retain all the components of the image. The execution results of this model are as follows.

3. Inverse Filtering of images 3.1 The experiment steps are similar to the image used in the experiment. First, the degraded function is used to process the image, and then appropriate supplementary noise is added. This image is used for inverse filtering experiments. The following is an image for the experiment. Gaussian noise is used for the image. The mean value is 0 and the variance is 0.08. Degradation functions are based on two types of previously described atmospheric turbulence models, one being motion blur.
3.2 Direct Inverse Filtering: Direct Inverse Filtering is a method that directly performs Inverse Filtering regardless of the noise.
For atmospheric turbulence models, direct inverse filtering will produce unsatisfactory results. The following is the experimental result of direct inverse filtering.
The experiment results have no value at all. Observe the spectrum. The four corners of the spectrum are very bright, and the DC components with the brightest original spectrum cannot be seen. So here is a restriction. That is, only the portion close to the DC component is processed, and others are not processed. The processing result goes through a 10th-order barworth low-pass filter. The following result is displayed.
In this case, you only need to adjust the restriction radius to get a better result than before. Of course, this is a little powerless in the face of blurred motion pictures. I will not post the results.
The derivation of the 3.3-question-and-answer-question filter is actually a very complicated process. Here we will not deduce it. Let's look at the results and draw some useful conclusions. The observed formula has the following two conclusions for suitable constants. 1. For a small point of the degraded function, the constant value is relatively large, and its reciprocal is not too large. 2. For a small point of the degraded function, the constant value is relatively small, and its reciprocal remains unchanged.
The following experimental results of the Viner filter:


3.4 constrain the least square filter. In fact, this method is a good idea. We use the image energy as a measure to evaluate the smoothness of the image and try to smooth it as much as possible. When the noise energy is set to a fixed value, the Laplace undetermined coefficient method is used to iterate and then unlock it. This method has many variants, including the famous TV (total variation, full variational) model. I will talk about it later. Here, the purpose of this method is to reduce the impact of noise on inverse filtering. The expression is as follows.
This filter can eliminate serious noise and restore images. Increase the variance of the noise of the experiment image to 0.2 and filter the image. The following result is displayed.

4. Experiment code


Published in blog: http://blog.csdn.net/thnh169/

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[Digital Image Processing] image restoration-Inverse Filtering

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