Paper 108: Image restoration and reconstruction of system learning Digital Image processing

First, you must pay attention to the processing conditions that are limited here.

About image degradation/resiliency models

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

1. Consider only noise-induced degradation

The noise model, which is contained in space unrelated and related two, in addition to the space cycle noise, discussed here are spatially irrelevant noise, such as Gauss, Ireland, Rayleigh, exponential distribution, uniform distribution, pulse (salt and pepper) noise and so on.

For the degradation caused only by noise, the noise parameters are estimated first, then the noise model is estimated and then the noise is filtered out. Here you can choose the spatial filtering method, image enhancement and restoration are not different. The effect characteristics of several types of filters are as follows:

1. Mean Value Filter

Mean filter is used when the image only has additive noise

Arithmetic mean filter, blurred image, worst recovery effect

Geometric mean filtering is similar to arithmetic mean smoothing, but less detail is lost,

Both of the above are suitable for handling Gaussian or uniform noise distributions.

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

Inverse harmonic mean filter, according to order Processing pepper/salt noise, can not simultaneously eliminate salt and pepper noise. The order is 0 and becomes the arithmetic mean, which is 1, and becomes the harmonic mean filter. If q is chosen improperly, it can have serious consequences.

2. Sequential statistical filtering

Median filter

Features:1) Under the same size, less fuzzy than the mean filter;

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

3) suitable for the processing of salt and pepper noise, through the use of small templates, you can get a good denoising effect, but multiple application of median filter , will make the image blurred.

Maximum Value filtering

Features:1) Sensitive to the highlights in the image;

2) The maximum filter has a good effect on "pepper" noise.

3) The maximum filter removes "pepper" noise, but removes some black pixels from the edge of the black object.

Minimum value filtering

1) sensitive to dark spots in the image;

2) The minimum filter has a good effect on "salt" noise.

3) The minimum filter removes "salt" noise , but removes some white pixels from the edge of the bright object.

Midpoint filtering,

This filter combines sequential statistics and averaging (uniformity ), which has the best effect on Gaussian and uniformly randomly distributed noises.

Corrected α-mean-value filter

When the filter is non-regressive into the arithmetic mean and median filter, it is very suitable for mixing gaussian and salt-pepper noise.

3. Adaptive filtering

Adaptive filtering is better than all the filters discussed above.

Adaptive local Noise elimination filtering requires estimating the noise variance. But pay attention to the noise variance and the image variance ratio of more than 1 o'clock processing problem, one is more than 1 limit at 1, which will cause the nonlinearity of the filter, but can prevent negative values, the other is to allow negative values, but finally to re-calibrate the gray value, but the result is a loss of dynamic range.

Adaptive median filtering, compared with the traditional median filter, has a greater probability of processing space, in addition to smoothing non-impulse noise when trying to preserve the details, reduce the image boundary refinement and vulgar language distortion.

4, Frequency domain filter

Band-Stop, band-pass, Notch has been said before, do not repeat. Only the best notch filter is added here.

There is usually no clear definition of the interference mode, there are several disturbances at the same time, and the interference component is not a single-frequency pulse, the previous method is not applicable. Here, the best, minimizing the local variance of the recovery estimate is used.

First, we need to extract the main frequency component of noise, get the noise function, select the weighted function (or the modulation function) again, and then make a meaningful method to minimize the variance of the estimated value at each point in the specified field.

2. Noise and imaging system degradation at the same time 1. First, linear, position-invariant degradation

Linear, the response of the input is equal to the sum of the input response, the position is unchanged, the representation is only related to the input value, regardless of the position.

Therefore, when there is additive noise, and the noise is random, independent of position, it is concluded that for linear space invariant degenerate system with additive noise, it can be expressed as the convolution of degenerate function and image, plus the noise.

Many types of degradation can be approximated to linear, position-invariant processes, which can be used to solve image restoration problems with many linear tools, although the location-related non-linear technology is more common, but it will lead to no known solution difficulties, or solve computational problems is very difficult, here mainly discusses the linear, position-invariant system restoration technology. Therefore, image deconvolution is often used to denote linear image restoration, a filter used for recovery processing, often referred to as a deconvolution filter. 2. Estimate the degenerate function.

Observation estimates, select a strong signal region, where noise interference can be ignored. The area is then processed to get the results as obscure as possible. The ratio of the DfT to the two can be approximated as a degenerate function.

It is estimated that a device similar to that obtained from a degraded image is simulated with impulse imaging.

Modeling estimation, mathematical modeling, such as atmospheric turbulence, uniform motion object degradation function model.

3. Image Restoration

After ignoring the noise, the DfT of the degenerate model, where h is known, then IDFT (F) Gets the reconstructed image, which is inverse filtering. In practice, H is 0 or close to 0 o'clock, and F becomes infinitely large or very large number.

Do not ignore the noise, can not be accurately restored, because the noise of the DFT is unknown, if the degradation is 0 or nearly 0, the noise value is even small, but it is very easy to determine the estimated value of F, because the recovery formula caused by noise recovery is very large.

The solution to a degradation of 0 or nearly 0 is to limit the frequency of filtering so that it approaches the origin. That is, image restoration is performed in a limited area around the origin of H.

This kind of general direct inverse filter, the effect is poor, does not explain how to deal with the noise. The following improved methods are:

Wiener Filter

It considers the statistical characteristics of degenerate function and noise synthetically. That is to find a filter to restore the image and the original image is the least square error. Therefore, the Wiener filter is called the minimum mean square error recovery, also called the Least squares error filter. Note that the Wiener filter assumes that the noise is not correlated with the image, that there is a 0 mean value in the uncontaminated image and the estimated image, and that the estimated gray level is a linear function of the degraded image gray level. If the noise mean value is 0, the Wiener filter becomes the inverse filter. The signal-to-noise ratio is defined based on the power spectrum of the noise and the non-degraded image. However, the power spectrum of the non-degraded image is seldom known, and the constant k is used to estimate it.

So the disadvantage of wiener filtering is that

1. The power spectrum of the non-degraded image and noise must be known;

2. The estimation of the power ratio (signal-to-noise ratio ) constant K is generally not a suitable solution.
   

Therefore, another deconvolution filter is a constrained least-squares filter. It is by the image restoration model, expressed in the form of a matrix, the core is to reduce the noise sensitivity problem, and therefore, based on the best restoration of smoothing measures, such as the sharpness of the Laplace transform. Then, the parameter gamma value is adjusted continuously using the constraint condition. Experience is that for high noise and moderate noise, the least squares are better than wiener, similar to low noise, and the least squares may be better than wiener when manually selecting parameters. parameter values, you can iterate the calculation, but automatically calculate the effect of the parameters than the manual difference. The generalization of the geometric mean filter Wiener filter can be changed to Wiener filter, inverse filter and spectral equalization filter according to the parameter value.

Paper 108: Image restoration and reconstruction of system learning Digital Image processing