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This paper proposes a novel single-image super-resolution method based on local biquadratic spline with edge constraints and adaptive optimization in transform domain. The complex internal structure of the image makes the values of adjacent pixels often differ greatly. Using surface patches to interpolate image blocks can avoid large surface oscillation. Because the quadratic spline has better shape-preserving property, we construct the biquadratic spline surface on each image block to make the interpolation more flexible. The boundary conditions have great influence on the shape of local biquadratic spline surfaces and are the keys to constructing surfaces. Using edge information as a constraint to calculate them can reduce jagged and mosaic effects. To decrease the errors caused by surface fitting, we propose a new adaptive optimization model in transform domain. Compared with the traditional iterative back-projection, this model further improves the magnification accuracy by introducing SVD-based adaptive optimization. In the optimization, we convert similar block matrices to the transform domain by SVD. Then the contraction coefficients are calculated according to the non-local self-similarity, and the singular values are contracted. Experimental comparison with the other state-of-the-art methods shows that the proposed method has better performance in both visual effect and quantitative measurement. [ABSTRACT FROM AUTHOR]

• This paper proposes a new feature constrained polynomial interpolation, which not only considers the positional relationship between pixels, but also considers the edge information of the image. By incorporating the anisotropy of the image into the polynomial parameter solution, the polynomial we obtained can effectively preser ve the structure of the image. • We propose a new method for filtering in image structure residuals, which simultaneously utilizes the non local self similarity of the image and the sparsity of the global structure of the image. By decomposing the image into smooth components and structural residual components, we can effectively filter out the noise in the image without destroying the smooth components of the image. • We propose a new single image super resolution model that simultaneously utilizes non local self si milarity, cross resolution similarity, and global structural sparsity. The optimization steps can be selected independently according to the accuracy requirements, and it can also be combined with other image super resolution algorithms. Due to the important application value of image super-resolution, many image super-resolution algorithms have been proposed in recent years. However, many single-image super-resolution algorithms usually have their own limitations and cannot achieve ideal results. To this end, this paper proposes a new single-image super-resolution method that uses non-local self-similarity, cross-resolution similarity, and global structure sparsity without relying on external instances. First, we obtain the initial high-resolution image through feature-constrained polynomial interpolation. Then, we use a database built by the input image to perform cross-resolution learning to predict the missing high-frequency information in the image. Finally, we use the residual filtering proposed in this paper to remove the noise introduced during interpolation and cross-resolution learning. Our method can be combined with other image super-resolution algorithms. Through extensive comparison experiments to verify, our method achieves higher numerical accuracy and pleasing visual effects. [ABSTRACT FROM AUTHOR]