Study On Image Super-Resolution Algorithm Based On Fractional Calculus

As an important technique in the field of image processing,Super-resolution focuses on gaining more information of origin image for the improvement of image value.The main advantage of super-resolution algorithm is it can improve the image degradation problems when image signals are sampled,and it's cheap and suit with most degradation conditions compared with hardware improvement.Thus it plays an important role in fields like engineering,medical science,and many others.Some good algorithms in this field are introduced in this paper,and analysis are made about these algorithms about their advantages and disadvantages,then fractional calculus theory is introduced to improve the traditional Projection onto Convex Sets(POCS)algorithm,and some efforts are made.On the foundation of this algorithm,based on the image structure similarity and filter operation similarity and the association between them,an image super-resolution algorithm based on modified fractional calculus operator is developed,and the preliminary experiments shows good results.In recent years,the application of fractional calculus theory has made great progress,it shows good performance and considerable potential in fields like engineering,control,mathematical modeling,physical modeling,and signal processing.After reviewing and summarizing a large number of image processing algorithms based on fractional calculus,we attempts to use fractional calculus theory in the fields of super-resolution,we combines POCS with fractional calculus to reconstruct the image super-resolution result.Traditional POCS algorithms use priori knowledges as a series of convex sets,then use these sets as limitations to restrict the final result image.We think that the lateral inhibition effect of human eye,which can be best simulated by a fractional calculus operator,can also be used as a convex set.Thus a POCS algorithm based on fractional calculus is proposed and tested by a sets of experiments.The results shows that the combination of fractional calculus and POCS improves the subjective observation effect and objective evaluation indexes effectively.Go a step further,we explore the role of fractional theory in image super-resolution algorithm,and modify the POCS by methods below:1.Contour stencils is used to interpolate the image,which can keep edge information by the self-similarity theory,combined with fractional differential filter,it can obtain a better interpolation result.2.By changing the weight of its center point,the traditional fractional calculus filter is modified to decrease the damage of image edge while doing enhancement,as long as keeping its quality to enhance image.3.A residual image is used to superimpose the reference image,instead of doing POCS iterations,the super-resolution result is generated by one superimposition,which means a decrease in the complexity of algorithm.An image super-resolution algorithm based on modified fractional calculus operator is proposed.A series experiments are carried out for this algorithm and it is found that this algorithm performs well with images of many conditions,and shows better results than common algorithms like BICUBIC,CS,SCN,ScSR and PCA.It is proved of good practical value.