# Multiple Optimizations-Based ESRFBN Super-Resolution Network Algorithm for MR Images
## 1 Introduction
The method uses a cubic polynomial to approximate the theoretically best interpolation function. IBP [16]: The Iterative Back Projection (IBP) is to adopt an iterative method to reduce the error between the image obtained by the simulated degradation process and the actual low-resolution image gradually, and then the error value between the two is backward projected to update the initial estimate of the high-resolution image and reconstruct the high-resolution image. POCS [5]: The Projection onto Convex Sets Approach (POCS) requires that a set of closed convex constraints be defined in a vector space within which the actual high-resolution image is contained. An estimate of a high-resolution image is defined as a point within the intersection of sets of these constraints. A high-resolution estimation image can be obtained by projecting any initial estimate onto these constrained sets. MAP [6]: The Maximum a Posterior (MAP) method is a probability-based algorithm framework, which is the most widely used method in practical application and scientific research at present, and many specific super-resolution algorithms can be classified into this probabilistic framework. The basic idea of the maximum posterior probability method is derived from conditional probability, which takes the known low-resolution image sequence as the observation result to estimate the unknown high-resolution image. JDL [7]: Compressive Sensing (CS) points out that an image can be accurately reconstructed from a set of sparse representation coefficients on an over-complete dictionary under very harsh conditions. Joint Dictionary Learning (JDL) can strengthen the similarity between the sparse representation of low-resolution and high-resolution image blocks and their corresponding real dictionaries through the joint training of low-resolution and high-resolution image block dictionaries. Therefore, the sparse representation of low-resolution image blocks and the high-resolution super-complete dictionary can work together to reconstruct the high-resolution image blocks, and then the high-resolution image blocks are connected to obtain the final complete high-resolution image. IJDL [17]: Aiming at the problem of dictionary joint cascade training only considers the joint image block pair error and does not consider the individual reconstruction error of the high- and low-resolution dictionary, Improved Joint Dictionary Learning (IJDL), which is a dictionary training method based on independent calculation of high- and low-resolution dictionary reconstruction errors, is proposed. This method optimizes the objective function, and takes the individual reconstruction errors of high- and low-resolution dictionaries into consideration, and discards the traditional cascade calculation method, effectively reducing the reconstruction error and improving the reconstruction accuracy of the image. RDN [11]: The Residual Dense Network (RDN) applies Residual Dense blocks. It can not only read the state of the previous residual dense block through a continuous memory mechanism, but also make full use of all the layers in it through local dense connection, and adaptively retain the accumulated features through Local Feature Fusion (LFF). The global residual learning is used to combine the shallow features with the deep features and make full use of the stratified features of the original low-resolution image. EDSR [18]: Enhanced Deep Residual Networks for Single Image Super-Resolution (EDSR) draws on the residual learning mechanism of the ResNet network. The input is divided into two paths after a layer of convolution. One path goes through the N-layer RDB module for convolution again, and the other leads directly to the intersection for weighted summation, and then the result is output after up-sampling and convolution. SRGAN [12]: SRGAN is a generative adversarial network. It adds a discriminator on the basis of SRResnet. Its function is to add an additional discriminator network and two losses, and to train the two networks in an alternate training way.