# An Integrated Dictionary-Learning Entropy-Based Medical Image Fusion Framework
## 1 Introduction  
High-quality images are often required in application. A high-quality image can help people to increase the accuracy and efficiency of image processing. Image fusion techniques are used to combine multiple images from the same senior modality or different sensor modalities for enhancing visibility. Following the development of cloud computing, cloud environment provides more and more strong computation capacity to process various images [1; 2; 3]. Imaging technologies are widely used in disease diagnosis, analysis and historical documentation. Image fusion has also aroused research interest in the field of medicine. Medical image fusion is used to fuse multiple images from the same imaging modality or combine information from multiple modalities, such as magnetic resonance image (MRI) [4], computed tomography (CT) [5], positron emission tomography (PET) [6], and single photon emission computed tomography (SPECT) [7]. The fused medical image can reflect medical issues through images of human body, organs and cells. The fused image provides a great diversity of features for medical analysis and diagnosis. Although lots of medical image fusion techniques are available, the quality of fused medical image canstill be improved. The unsatisfied fused medical image may affect the interpretation and diagnosis of medical conditions. A large number of image fusion methods have been proposed for image fusion. Spatial-domain fusion and transform-domain fusion are two typical approaches. Spatial-domain based methods directly choose clear pixels, blocks or regions from source images to compose a fused image without doing any transformation. In general, spatial-domain methods may lead to blurring edges, contrast decrease, and reduction of sharpness [8; 9]. Transform-domain based methods decompose source images into coefficients and transform basis first. Then the coefficients are fused by fusion rules. Finally, the fused coefficients and transform basis are inversely transformed to obtain a fused image. It is difficult to select an optimal transform basis without a priori knowledge. Sparse-representation-based methods are introduced to transform-domain fusion methods to recover a visually appealing reconstruction of the original signal. Sparse-representation based methods can adaptively transform input images without priori knowledge by using trained basis. Based on the adaptively learning feature, images and signals can be described and reconstructed efficiently. Sparse-representation is widely applied to image denoising [10], image deblurring [11], image inpainting [12], super-resolution [13], and image fusion [14; 15]. The following three classical sparse-representation based methods improve the learning efficiency of original sparse coding problems. The K-means generalized singular value decomposition (K-SVD) algorithm, as a representative dictionary learning method, focuses on efficiently learning an over-complete dictionary to maximize the image reconstruction power [16; 17]. [PERSON] solved the optimization function to speed up the sparse coding algorithm [18]. Based on stochastic approximations, an online dictionary learning method was proposed by [PERSON] to process the large size dataset efficiently [19; 20; 21]. [PERSON] and [PERSON] [15] first applied the sparse-representation theory to an image fusion field. A joint sparse-representation image fusion method was proposed by [PERSON] and [PERSON] [22]. Although the image fusion method had lower complexity than K-SVD, it still required a substantial amount of computations. [PERSON] and [PERSON] [23] proposed a joint-clustering based dictionary construction method for image fusion that used K-means clustering to group the image patches before dictionary learning. However, it is difficult to get the cluster centers accurately for K-means clustering. The spatial domain-based methods cannot handle the issues of blurring edges, contrast decrease, and reduction of sharpness well.