# An Integrated Dictionary-Learning Entropy-Based Medical Image Fusion Framework
## 1 Introduction
The transform domain-based methods depend on priori knowledge, but priori knowledge is difficult to obtain. The current solutions more or less have some drawbacks in image fusion, such blur, noise and so on [23; 24]. Medical diagnosis has high requirements regarding the quality of the fused image. Even a small flaw may cause serious error in medical diagnosis. So it is important to enhance the quality of fused medical images. This paper proposes a novel integrated medical image fusion framework. The framework has two parts to do medical image fusion. The source image is discriminated as low-frequency and high-frequency components, and they are fused separately. Two fused images are merged to obtain the final image. There are many ways to discriminate the source image. Multi-scale transform (MST) is usually used to do the classification. MST can decompose source image, and use the corresponding image fusion algorithm to fuse the decomposed image components. However, the MST computation cost is much higher than other methods. MST takes about 5-10 s to process a 256 \(\times\) 256 image on a 2.3 GHZ CPU machine. However, Gaussian filter only takes less than one second to process the same size image. Gaussian filter can successfully decompose image components into high-low frequency image components. At the same time, the image noises are classified as high-frequency image components in the decomposition. This can help in the image denosing during the sparse-representation based fusion of high-frequency image components. Comparing with Gaussian filter, MST is not able to process the image denoising. Gaussian filter does image decomposition in spatial-domain. The results of Gaussian filter are low-frequency components that are the non-detailed parts of the image. The high-frequency components, which are the detailed parts of the image, are obtained by deducting the low-frequency components from source image. The weighted average method decreases the contrast and sharpness of image details, and blurs edges, but it processes the non-detailed image information well. Sparse representation has high performance in representing the details of image, so it is used in high-frequency components. L2-norm can be independently applied over the data mismatch and the regularization terms. It is robust against the noise and outliers and also has good preserving edges (non-smooth optimization). L2-norm can obtain the high precision of image fusion in low-frequency components. So an L2-norm based weighted average method is implemented to low-frequency components fusion. This method calculates the L2-norm of corresponding high frequency components as weight for weighted average components fusion. The fusion performance in non-detailed information, such as blurring edges, contrast and sharpness can be enhanced. An online dictionary-learning based method is implemented to improve detailed information fusion performance. For ensuring the group sparsity as well as the local structure of atoms in group, the sparse representation method is used to represent the form of clusters and construct a dictionary. According to the current research achievements, dictionary-learning based image fusion approaches with a well-constructed dictionary can have great performance in showing details of source. MST-based dictionary-learning method may cause the spatial inconsistency in some smooth area of the fused image by directly using trained dictionary and \"Max-L1\" fusion scheme [27]. Comparing with other types of images, medical image has its own special features. Usually the margins of medical image are in black and contain limited information. However, those marginal image patches affect the accuracy of dictionary learning. So these image patches are removed and only the remaining informative image patches are used for dictionary learning. The proposed framework has four steps:  
* Step 1 is a denoising process. Each input source image is smoothed by Gaussian filter that is robust to noise.