Research On Image Super Resolution Algorithm Based On Sparse Representation

With the development of industry and advancement of science and technology,people have designed a lot of image imaging equipment（such as digital camera,mobile phone,and remote sensing image imaging system,etc.）.At the same time,digital images have also become one of the important carriers for humans to transmit and obtain information.In this era of rapid development of information,high-resolution images can not only bring people a better visual enjoyment,but their detailed information also plays an important role in many fields,such as video surveillance,autonomous driving,medical diagnosis,and remote sensing measurement.However,due to the physical limitations of the imaging device itself and the influence of various degradation factors in the transmission,storage,and display of the image,the images we get are often degraded images with lower resolution.In order to obtain high-resolution images with rich information,one of the methods is to improve the imaging equipment directly.Due to the limitation of materials and manufacturing technology,such methods are not only costly but also ineffective.Another type of method is to improve the resolution of degraded images through image processing after imaging.Image super-resolution reconstruction is an effective method to solve the above problem.In recent years,many excellent reconstruction theories have been proposed,which also promote the development of other theories in the field of image processing.Meanwhile,the super-resolution reconstruction technology has also received great attention in the academic circle,and has become one of the hot research topics in the field of image processing.In recent years,the sparse representation theory of signals has received more and more attention,and it has also achieved good results when it is applied to image super-resolution reconstruction.Based on the sparse representation theory,this thesis studies the existing super-resolution reconstruction models for single natural images and hyperspectral remote sensing images,and proposes several improved algorithms.The main innovative researches of this article are as follows:（1）A single image super-resolution method based on adaptive sparse representation and low rank constraint is proposed.This method uses the self similar learning framework to construct the dictionaries and it does not need external training samples.In order to improve the accuracy of the sparse representation coefficients,the adaptive sparse representation which can make the coefficients more accurate is used to automatically trade off between7)7)₁ norm and7)7)₂ norm.In addition,after the sparse representation coefficients are obtained,this method uses low rank to constrain the coefficients of similar blocks,so as to remove the error interference in the coefficients.Finally,the experimental results on 11 test images show that this method is superior to other comparison methods.（2）A single image super-resolution method based on synthetic sparse representation and analytical sparse representation is proposed.In this method,we introduce the less concerned analytical sparse representation into the single image super-resolution model,and replace the synthetic sparse representation in the sparse coding phase of low resolution feature block.The analytic sparse representation does not need to solve the optimization of7)7)₀ or7)7)₁.Therefore,the introduction of analytical sparse representation can reduce the time consumption in reconstruction phase.In addition,in order to improve the convergence,we introduce a linear mapping function to reveal the relationship between high resolution coefficients and low resolution coefficients.Experimental results on several data sets show that the proposed method achieves better performance than other outstanding single image super-resolution methods.（3）A hyperspectral image super-resolution model based on adaptive nonnegative sparse representation is proposed.On the base of nonnegative structure sparse representation model,this method introduces adaptive sparse representation to balance the relationship between sparsity and synergy,and make the sparse representation coefficients more accurate.In addition,we design an alternative optimization algorithm.After updating the sparse representation coefficients each time,they are used to update the spectral dictionary.Compared with the strategy of keeping the pre-trained spectral dictionary unchanged,this method can increase the flexibility of the model.Experimental results on CAVE dataset and three real hyperspectral images show that this method is superior to other advanced methods.（4）A hyperspectral image super-resolution model based on group nonnegative coefficients and low rank is proposed.This method uses super-pixel segmentation which can obtain image blocks with similarity to achieve the local similarity information.This method uses joint sparse regularization and low rank to constrain the sparse coefficients,so as to make the coefficients more accurate.In addition,the information in the low resolution hyperspectral image is introduced into the coefficient matrix solving model.Finally,experimental results on three real hyperspectral images show the advantages of the proposed method.