Single-Image Super-Resolution Based On Local Biquadratic Spline And Adaptive Optimization In Transform Domain

Image resolution represents the richness of detailed information contained in an image.High-resolution images often have finer quality,and greater reliability than low-resolution images.However,in practical applications,high-resolution images with smooth edges and clear textures cannot be obtained directly due to the limitations of imaging equipment,transmission media,noise and other factors.The method of improving the image resolution by improving the hardware of imaging system is difficult in technology and high in manufacturing cost.Therefore,starting from algorithms and software,research on image super-resolution reconstruction technology has practical application needs and academic value.At present,interpolation-based methods and iterative back-projection methods are commonly used.The interpolation-based method is simple and fast,but the images generated by classic interpolation algorithms are often too smooth.At the same time,the iterative back-projection method can make up for the high-frequency information of the original high-resolution image,but it has a limited effect on improving the image quality.Based on the analysis and research of the above problems,this paper proposes a new single-image super-resolution method based on local biquadratic spline and adaptive optimization in transform domain.The local biquadratic spline with edge constraints can generate high-precision enlarged images,but the enlarged images,especially at the edge regions,inevitably have interpolation errors.The adaptive optimization in transform domain can compensate the distortion of interpolation image in texture and edge regions.The internal structure of the image is complex,and the differences between adjacent pixel values are often very large.Using surface patches to interpolate image blocks will avoid large surface swing.Because of the better shape preserving property of quadratic splines,the biquadratic spline surface is constructed on each image block,which makes the interpolation surface of the image block more flexible.After the boundary conditions are given,the biquadratic spline surface is unique.Therefore,the boundary condition has a great influence on the shape of the spline surface.Therefore,the key to constructing a local biquadratic spline surface is to calculate the boundary conditions.In this paper,the edge information is used as a constraint to calculate the boundary conditions,which reduces the aliasing and mosaic effects at the edge areas.For the errors generated by image block fitting of biquadratic spline surfaces,a new adaptive optimization model in transform domain is proposed in this paper to reduce the errors iteratively.In each iteration,first use SVD to transform the similar block matrix of the image into the transform domain.Calculate the contraction coefficients based on the non-local self-similarity,and the singular values are contracted adaptively to reduce the error caused by the interpolation surface.Then,the high-frequency information lost in the interpolation process is compensated by back projection,and the minimum error between the iterative convergence result and the input image is taken as the objective function of back projection.Compared with the traditional iterative back-projection framework,introducing the adaptive optimization in transform domain into the framework further improves the magnification accuracy of the image.The effectiveness of the proposed algorithm is verified by experiments.Firstly,the performance of the proposed local biquadratic spline interpolation with edge constraints is tested,and the experimental results show that it can effectively reduce the fuzzy effect of images.Secondly,the proposed adaptive optimization in transform domain is compared with the non-local mean filtering.The former can reduce interpolation errors more effectively and achieve sharper edges.Finally,the overall performance of the proposed algorithm is analyzed in this paper.Set5,Set14,BSD100 and Urban 100 are used as the test image set,and the experimental comparison results with different types of methods show that the new method has better performance in both visual effect and quantitative measurement.At different magnification scales,the algorithm in this paper can achieve sharper edges and more accurate details.It provides a new idea for image super-resolution based on interpolation and image self-similarity.