# A Geometric Dictionary Learning Based Approach for Fluorescence Spectroscopy Image Fusion
## 2 Geometry Dictionary Construction and Fusion Scheme  
### Dictionary Learning Analysis  
During the sparse representation of the dictionary construction process, the key step is to construct an over-complete dictionary that covers the important information of input image. Since geometry information of image plays an important role in describing an image, an informative dictionary should take the geometric information into consideration. Smooth and non-smooth information as two important types of geometry information can be used to classify source images. A multiple geometry information classification approach was proposed for single image super-resolution reconstruction (SISR) [39]. According to the geometric features, a large number of high-resolution (HR) image patches were randomly extracted and clustered to generate corresponding geometric dictionaries for sparse representations of local patches in low-resolution (LR) images. The geometric features were classified into three types, smooth patch, dominant orientation patch, and stochastic patch. According to the estimated dominant orientation, the dominant orientation patches could be divided into different directional patches. Rather than adaptively selecting one dictionary, the recovered patches were weighted in the learned geometric dictionaries to characterize the local image patterns, by a subsequent patch aggregation to estimate the whole image. To reduce the redundancy in image recovery, the self-similarity constraints were added on HR image patch aggregation. Both LR and HR residual images were estimated from the recovered image and compensated for the subtle details of reconstructed image. In SISR, the source images are classified as smooth, dominant orientation, and stochastic patches. Dominant orientation and stochastic patches are non-smooth patches. Since the detection of orientation in finite dimensional Euclidean spaces corresponded to fitting an axis or a plane by Fourier transformation of an n-dimensional structure, [PERSON] verified dominant orientation and stochastic patches can be separated by orientation estimation in the spatial domain based on the error of the fit [42]. In dictionary learning, the redundancy of trained dictionary is usually not considered. A redundant dictionary not only has high computational complexity, but cannot also obtain the best effect in image representation. Different methods are proposed to reduce the redundancy in learning process to construct the compact dictionary. [PERSON] [43] estimated the maximum a posteriori probability (MAP) by a compact dictionary. An effective image interpolation method by nonlocal autoregressive modeling (NARM) was developed and embedded in SRM by [PERSON] [44] to enhance the effectiveness of SRM in image interpolation by reducing the coherence between the sampling matrix and the sparse representation dictionary and minimizing the nonlocal redundancy. To improve the performance of sparse representation-based image restoration, a non-locally centralized sparse representation (NCSR) model proposed by [PERSON] [45] suppressed the sparse coding noise in image restoration. The sparse representation-based approach linearly combines a few atoms extracted from an over-complete dictionary as an image patch. The promising results have been shown in various image restoration applications [38; 45]. Based on the classification of image patches, this paper proposed sparse representation-based approach that uses PCA algorithm to construct more informative and compact dictionary [38]. The proposed solution cannot be extended to other sparse-representation applications. Most sparse representation methods are based on a large number of sample images. The corresponding learned dictionaries are expected to be applied to different scenic source images. The proposed solution uses sparse feature to do image sparse representation and fusion. Therefore, the learned dictionary of proposed solution does not need to be extended to different source images, and only specializes for experimented source images.