Color Image Denoising Method Based On Quaternion

Traditional methods to filter the impulse noises in color images usually process color components separately.These methods ignore the strong spectral correlation between color channels and the spectral characteristics of color and may produce perceivable color artifacts and distortions.By utilizing the pure quaternion form,a color pixel with three components can be represented holistically,and a color image can also be represented holistically,thereby handling the coupling between the color channels naturally.Thus,the original texture features,detail features,color features,shape features and spatial relationship features in an image can be kept as much as possible.The difference between two color pixels include chromaticity difference and luminance difference.Aiming at the problem of how to fuse chromaticity and brightness to measure color distance,this paper proposes a quaternion color distance measurement based on exponential weighted fusion.This method can effectively integrate the chromaticity distance and brightness distance,and then can measure the distance between two color pixels more accurately.Based on the measurement method and the idea of directional samples analysis,an impulse noise detection method based on the minimum absolute mean difference and an impulse noise detection method based on the maximum number of elements of peer group are further proposed.Then we combine the two detectors with a two-stage strategy.Finally,a vector median filter based on spatial distance weighting is proposed to recover the impulse noises detected by the combined detector.Experimental results show that the proposed two-stage quaternion vector filtering method can achieve good results in both objective image quality evaluation indices and visual effect.At present,the detection accuracy of most impulse noise detection algorithms is affected by noise density,and with the increase of noise density,this influence will increase sharply.To solve this problem,an impulse noise detector based on mean shift is proposed.The detector can obtain low and stable false detection rate when processing high or low density noise images.The noise ratio obtained by the detector can reflect the noise density of a noisy image to a certain extent,which is helpful for the next step to adopt the selected strategy to effectively recover the noisy pixels.For low-density noise images,vector median filter is usually used to restore the noisy pixels.However,the traditional methods based on vector median filter fail to take into account that not all channels of a noisy color pixels are necessarily contaminated.Aiming at this shortcoming,a vector median filtering method based on channel suppression is proposed.The filtering method only changes the values of the polluted channels,and utilizes a kind of prior knowledge to further modify the results obtained after channel suppression.By this way,the correlation of color channels can be protected as much as possible.Experimental results show that this method not only provides good noise suppression performance but also better preserves thin lines,edges,and image details.Although the quaternion color distance measurement method based on exponential weighted fusion can effectively measure the distance between two color pixels,it separatly processes the following two cases: the case that chromaticity distance is zero and the case that brightness distance is zero.Thus,the final results gainted by the method are not in the same dimension.In order to solve the shortage,the concept of chromaticity plane and hue line are proposed on the basis of the concept of gray line,and then an improved quaternion color distance measurement method based on exponential weighted fusion based on hue distance is proposed.Finally,an impulse noise detection method based on the improved distance formula and the local outlier factor theory is proposed.The experimental results show that this detector can achieve good results in both the missed detection rate and the false detection rate.Different chromaticity difference and brightness difference should have different effects on color distance.Therefore,among the color distance calculation methods based on brightness/chromaticity,the quaternion color distance measurement methods with fixed brightness/chromaticity weights will not always achieve good results.In order to solve this problem,an adaptive weighted quaternion color distance measurement method is proposed.This method can adaptively adjust the influence of chromaticity and brightness on color distance and thus it can measure the distance between two color pixels more effectively.By combining the distance measurement method with the outlier detection method based on statistical model and the coarse-to-fine detection strategy,an impulse noise detection and filtering method is further proposed.Experimental results show that this method can achieve good results in noise suppression,detail and structure preservation,color fidelity and feature reconstruction.