# A Geometric Dictionary Learning Based Approach for Fluorescence Spectroscopy Image Fusion
## 1 Introduction  
Following the development of cloud computing, cloud environment provides more and more strong computation capacity to process various images [1; 2; 3]. Due to the limited depth-of-focus of optical lenses in imaging sensors, one-time focus cannot guarantee to obtain all focused image in the whole scene [4]. In another word, it is difficult to obtain an image that contains all relevant objects in focus. In microscope, only the objects at a certain distance away from the lens can be captured in focus and sharply, and other objects are out of focus and blurred. A fuzzy multi-sensor data fusion Kalman filter model was proposed by [PERSON] to reduce failure risk in an integrated vehicle health maintenance system (IVHMS) [5]. In fluorescence spectroscopy, one scene at least contains several objects. For ensuring the accuracy and efficiency of fluorescence image processing, it usually captures multiple images of the same scene to guarantee all objects are in focus. However, it costs too much on viewing and analyzing a series of images separately. Multi-focus image fusion is an effective technique to resolve this problem by combining complementary information from multiple images ofthe same scene into a sharp and accurate one [6; 7]. The integrated image can precisely describe the corresponding scene, which is beneficial for further analysis and understanding. As one of the most widely recognized image fusion technologies, a large number of multi-focus image fusion methods have been proposed. According to fusion domain, these methods could be categorized into two main categories: spatial-domain-based methods and transform-domain-based methods [8]. Spatial-domain-based methods directly choose clear pixels, blocks, or regions from source images to compose a fused image [9; 10]. Some simple methods, such as averaging or max pixel schemes, are performed on single pixel to generate a fused image. However, these methods may reduce the contrast and edge intensity of fused result. In order to improve the performance of fused image, some advanced schemes, such as block-based and region-based algorithms, were proposed. [PERSON] et al. proposed a scheme by dividing images into blocks and chose the focused one by comparing spatial frequencies (SF) first; then the fused results were produced by consistency verification [11]. Although block-based methods improve the contrast and sharpness of integrated image, they may cause block effect in integrated image [12]. Different from spatial-domain fusion methods, transform-domain methods transform source images into a few corresponding coefficients and transform bases first [13]. Then the coefficients are fused and inverted to an integrated image. Multi-scale transform (MST) and wavelet based algorithms are the most conventional transform approaches applied to transform-domain-based image fusion [14; 15]. Wavelet transform [16; 17], shearlet [18; 19], curvelet [20], dual tree complex wavelet transform [21; 22], nonsubsampled controulet transform (NST) [23] are usually used in MST-based methods. MST decomposition methods have attracted great attention in image processing field and achieved great performance in image fusion fields. However, MST-based methods are difficult to select an optimal transform basis without priori knowledge [24; 25]. As each MST method has its own limitations, one MST method is difficult to fit all kinds of images [14]. In recent years, sparse-representation-based methods, as the subsets of MST fusion methods, are applied to image fusion. Other than MST methods, sparse-representation-based methods usually use trained bases, which can adaptively change according to input images without priori knowledge [26; 27]. Due to adaptive learning feature, sparse representation is widely applied to image de-noising [28; 29], image deblurring [30; 31], image inpainting [32], image fusion [33], and super-resolution [34]. [PERSON] and [PERSON] [35] took the first step for applying sparse representation theory to image fusion field.