# Entropy-Based Algorithms for Signal Processing
### Applications  
Image fusion is an efficient technique that can be applied in many fields, such as medicine, remote sensing, and surveillance. In the contribution by [PERSON] et al. [8], \"Entropy-Based Image Fusion with Joint Sparse Representation and Rolling Guidance Filter,\" an image fusion method using multi-scale decomposition and joint sparse representation is introduced. There are five steps in this work. First, joint sparse representation is applied to decompose two source images into a common image and two innovation images. Second, two initial weight maps are generated by filtering the two source images separately. Third, weight maps are obtained by joint bilateral filtering according to the initial weight maps. Fourth, the multi-scale decomposition of the innovation images is performed through the rolling guide filter. Finally, Lastly, the final weight maps are used to generate the fused innovation image. The fused innovation image and the common image are combined to generate the ultimate fused image. The experimental results show that their method's average metrics are: mutual information--5.3377, feature mutual information--0.5600, normalized weighted edge preservation value--0.6978, and nonlinear correlation information entropy--0.8226. Their approach can achieve better performance compared to the state-of-the-art methods in visual perception and objective quantification. In multi-modality image fusion, source image decomposition, such as multi-scale transform, is a necessary step and also widely used. However, when MST is directly applied to decompose source images into high- and low-frequency components, the corresponding decomposed components are not precise enough for the following infrared-visible fusion operations. The contribution by [PERSON] et al. [9], \"A Novel Infrared and Visible Image Information Fusion Method Based on Phase Congruency and Image Entropy,\" proposes a non-subsampled contourlet transform based decomposition method for image fusion, by which source images are decomposed to obtain corresponding high- and low-frequency sub-bands. Unlike MST, the obtained high-frequency sub-bands have different decomposition layers, and each layer contains different information. To get a more informative, a fused high-frequency component, maximum absolute value, and pulse coupled neural network fusion rules are applied to different sub-bands of high-frequency components. Activity measures, such as phase congruency, local measure of sharpness change, and local signal strength, are designed to enhance the detailed features of fused low-frequency components. The fused high- and low-frequency components are integrated to form a fused image. Their experiment results show that the fused images obtained by the proposed method achieve good performance in clarity, contrast, and image information entropy. Image recovery from compressive sensing measurement data, especially noisy data, has always been challenging due to its inherent ill-posed nature. Thus, to seek a domain where a signal can exhibit a high degree of sparsity and to design an effective algorithm has drawn more attention. Among various sparsity-based models, structured or group sparsity often leads to more powerful signal reconstruction techniques. In the contribution by [PERSON] et al. [10], \"An Entropy-Based Algorithm with Nonlocal Residual Learning for Image Compressive Sensing Recovery,\" authors propose a novel entropy-based algorithm for CS recovery to enhance image sparsity through learning the group sparsity of residual. To reduce the residual of similar packed patches, the group sparsity of residual is described by a Laplacian scale mixture model. Therefore, each singular value of the residual of similar packed patches is modeled as a Laplacian distribution with a variable scale parameter, to exploit the benefits of high-order dependency among sparse coefficients. Due to the latent variables, the maximum a posteriori estimation of the sparse coefficients cannot be obtained.