Image restoration and reconstruction

First of all, we must pay attention to the processing conditions that are limited here.

On Image Degradation/Restoration Model

Degraded images are formed by degradation of the imaging system and additional noise.

1. Consider only noise-induced degradation

Noise model includes two kinds: spatial irrelevant and correlative. In addition to spatial periodic noise, all the noise discussed here are spatial irrelevant, such as Gauss, Ireland, Rayleigh, exponential distribution, uniform distribution, impulse (salt and pepper) noise and so on.

For the degradation caused by noise only, noise parameters should be estimated first, then noise model should be estimated, and then noise filtering should be done. Spatial filtering method can be chosen here. There is no difference between image enhancement and restoration. The effect characteristics of several types of filters are as follows:

1. Mean filter

Mean filtering is used when only additive noise exists in the image.

Arithmetic mean filter, blurred image, the worst restoration effect

Geometric mean filtering has the same smoothness as arithmetic mean filtering, but less details are lost.

The above two methods are suitable for dealing with Gauss or uniform noise distribution.

Harmonic mean filter is suitable for processing Gauss and uniformly distributed noise. It has good effect in white point (salt noise) and is not suitable for pepper noise.

Inverse harmonic mean filter can not eliminate salt and pepper noise at the same time by processing salt and pepper noise according to order. The order is 0, it becomes the arithmetic mean, it is - 1, it becomes the harmonic mean filter. If Q chooses improperly, it will have serious consequences.

2. Sequential Statistical Filtering

median filtering

Features: 1) Under the same size, the ambiguity caused by the mean filter is less than that caused by the average filter.

2) It is very effective for unipolar or bipolar pulse (salt and pepper) noise. As long as the spatial density of impulse noise is small, the experience is (less than 0.2).

3) Suitable for dealing with salt and pepper noise. By using small templates for many times, good denoising effect can be obtained, but the image will be blurred by using median filter for many times.

Maximum filtering

Features: 1) Sensitive to bright spots in images;

2) Maximum filter has a good effect on eliminating "pepper" noise.

3) Maximum filter can remove "pepper" noise, but remove some black pixels from the edge of black objects.

Minimum filter

1) It is sensitive to the dark spots in the image.

2) Minimum filter has good effect on eliminating salt noise.

3) Minimum filter can remove salt noise, but remove some white pixels from the edge of bright objects.

Midpoint filtering,

This filter combines sequential statistics and averaging (uniform), and has the best effect on Gauss and uniform random distribution noise.

Modified alpha mean filtering

When the filter is not degenerated into arithmetic mean and median filters, it is very suitable for the case of mixed Gauss and salt and pepper noise.

3. Adaptive filtering

The adaptive filter is superior to all the filters discussed above.

Adaptive local noise cancellation filtering requires estimation of noise variance. However, attention should be paid to the problem of processing when the ratio of noise variance and image variance exceeds 1. One is that the ratio of noise variance to image variance exceeds 1. This will lead to the nonlinearity of filtering, but it can prevent negative values. The other is that negative values are allowed to occur, but the final gray values need to be re-calibrated, but the result is the loss of dynamic range.

Compared with traditional median filtering, adaptive median filtering has more processing space. In addition, it can smooth the non-impulse noise while trying to retain details and reduce the refinement of image boundary and the distortion of coarse language.

4. Frequency domain filtering

Band-stop, band-pass and notch have been mentioned before, not to mention. Only the best notch filter is added here.

Usually the jamming mode is not clearly defined. When several kinds of jamming exist at the same time, and the jamming component is not a single frequency pulse, the former method is not applicable. Here, the local variance of the restoration estimates is minimized.

Firstly, the main frequency components of noise are extracted to obtain the noise function, then the weighting function (or modulation function) is selected again, and then the variance of the estimated value in each specified field is minimized by some meaningful method.

2. Noise and imaging system degradation coexist

1. First of all, linear, position-invariant degradation

Linearity, the response of the sum of input is equal to the sum of input response, and the position is unchanged, which means that the response is only related to the input value and independent of the position.

Therefore, in the case of additive noise, random noise and position-independent, it is concluded that the linear space invariant degradation system with additive noise can be expressed as the convolution of degradation function and image, plus noise.

Many types of degradation can be approximated as a linear and position-invariant process. Many linear tools can be used to solve image restoration problems. Although location-related non-linear techniques are more common, they will bring difficulties without known solutions or when solving computational problems. Recovery technology of variable system. Therefore, image deconvolution is usually used to represent linear image restoration, and the filter used for restoration processing is usually called deconvolution filter.

2. Estimate the degenerate function.

Observation and estimation, select a strong signal region, where the noise interference can be ignored. Next, the region is processed to obtain the results as unambiguous as possible. The ratio of DFT can be approximated as a degenerate function.

Experiments estimate that devices similar to those used to acquire degraded images are simulated using impulse imaging.

Modeling estimation, mathematical modeling, such as atmospheric turbulence, degeneration function model of uniformly moving objects, etc.

3. Image restoration

After ignoring the noise, the DFT of the degraded model, where H is known, is restored by IDFT (F), which is called inverse filtering. In practice, H is zero or

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