Fusing Images Using Joint Sparse Representation

Image fusion is to integrate multi-source image information on multiple sensorson different time or at the same time to obtain the same scene, in order to obtain moreaccurate, comprehensive, reliable scene description. As to facilitate visual perceptionor further image information processing. Compared to the source image before imagefusion, the fused image has higher accuracy and reliability and more abundantinformation. Efficient image fusion algorithm can improve the utilization ratio of theimage, the fusion result can be accurate and complete description of the target. It isconducive to medical imaging and diagnostic, geographic information systems,computer vision, weather forecast, and the application of military target recognition,etc.Donoho and Candes put forward the Compressed Sensing theory is a new theoryof sampling. Sampling and signal compression are completed at the same time,greatly reduces the amount of sampling data, and reduce the pressure of storage andtransmission. In recent years, with the progress of the Compressed Sensing theory, theCompressed Sensing theory is introduced into the image fusion caused wide attentionof scholars both at home and abroad. Its basic principle is: by using the theory ofcompressed sensing theory of sparse representation, solving all of the source image ina over-completed dictionary under the sparse coefficient, the use some fusion rules tofuse the sparse coefficient, the after the over-completed dictionary and the fusedsparse coefficient multiplication, the fused image is obtained. Compared with thetraditional airspace transform frequency domain fusion method, sparse representationmethod is sparser and has characteristic properties. At present there are two majorkinds of algorithm for solving sparse coefficient, greedy algorithm and the convexoptimization algorithm. Greedy algorithm includes Matching Pursuit algorithm (MP)and Orthogonal Matching Pursuit algorithm (OMP). Convex optimization algorithms include Basis Pursuit (BP) algorithm, the Gradient Projection method, etc. The OMPalgorithm is an extension of the MP algorithm, adding the process oforthogonalization.The OMP algorithm has been widely used in the field of image fusion and to getgood fusion effect. Bin Yang and Shutao Li put forward Simultaneous OrthogonalMatching Pursuit (SOMP) ensures the sparse representation in different source imageusing the same atoms in the dictionary with the different coefficient, it is convenienceto the design of fusion rules, finally it got more clearly and rich fusion image than thetraditional method. Yet another type of sparse algorithm, convex optimizationalgorithm because of the complexity of the algorithm is seldom applied to the field ofimage fusion. And actually convex optimization has more sparse characteristics thangreedy algorithm, and it is also more accurate in image reconstruction and has acertain practical value. Joint Sparse Models in the theory of Compressed Sensingwhich put a signal on a fundamental sparse expanded to the concept of a group ofjoint sparse signal is becoming more and more attractive and introduced into theimage fusion, the basic principle of Joint Sparse Models are as follows: in the firstmodel, each signal contains two parts, all signals share a public part and each signalhas a independent part, the public part and the separate part can be sparserepresentation in some basis. Public section reflects the overall environment influenceon signals, separate parts reflect the local environment on the influence of the signals.In the second model (JSM2), each signal only contains one part; they arerepresented in the same sparse basis but with different coefficient. MIMOcommunication and audio signal sequence is JSM2application example.Under the Compressed Sensing theoretical framework, this paper studied usingconvex optimization algorithms based Basis Pursuit (BP) and combined with twoJoint Sparse Models to simulate the source image sparse representation and the fusionimage reconstruction. Specific work is as follows:(1) On the basis of reading a certain number domestic and foreign literature,conclude the background and significance of research of image fusion, several kindsof image fusion technology, image fusion quality evaluation. Introduce the Compressed Sensing theory, sparse representation method, Joint Sparse Models.(2) Put forward the BP-JSM1: Using BP to solve the source images sparserepresentation, represent all the source images into the public part and theindependent part, keep all the public portion of the source image, fuse the separateparts of the source image and get the final fusion result. Put forward the BP-JSM2:Using BP to solve sparse decomposition, compute the image sparse vectordifference’s absolute, choose the minimum of1norm as the sparse representation, usethe maximum absolute values as the final fusion coefficient, and reconstruct the fusedimage.(3) Block the source images in the above two fusion models, using slidingwindow strategy; discuss the influence of window size on fusion results. And discussthe influence of window moving step on the fusion results and fusion time. Determinethe optimal fusion window size and window moving step.(4) Compared the MP algorithm and BP algorithm in the signal reconstructionand image reconstruction, verified the BP algorithm is more accuracy and superiorityin signal reconstruction and image reconstruction. Also verified the BP has thefeasibility of the sparse representation.(5) Experiment the two kinds of models of BP-JSM1and BP-JSM2respectively,including CT and MRI image fusion, multi-focus image fusion, the infrared andvisible image fusion. Combined with the subjective evaluation and objectiveevaluation method comparing with the traditional image fusion methods, verify theeffectiveness of the proposed methods in this paper has significant advantages in thefield of image fusion.(6) Summarize some of the problems existing in the research, and the futureresearch work is prospected.