The fusion of hyperspectral image (HSI) and multispectral image (MSI) is one of the most significant topics in remote sensing image processing. Recently, deep learning (DL) has emerged as an important tool for this task. However, existing DL-based methods have two drawbacks, that is, limited ability for feature extraction and suffering from spectral distortion. To address these issues, this article presents a novel neural network, where sophisticated techniques are employed, including network-in-network convolutional unit, batch normalization, and skip connection. To make full use of the MSI, the proposed model fuses HSI and MSI at different scales. Besides, this article presents a new loss function, called RMSE, angle and Laplacian (RAP) loss (the combination of the relative mean squared error, angle loss, and Laplacian loss), to deal with both spatial and spectral distortions. Experiments conducted on four data sets have verified the rationality of network structure and the proposed loss function and demonstrated that the proposed novel model outperforms state-of-the-art counterparts.

Fuzzy c-means with regularization by K-L information (KLFCM) is an objective function method for clustering, which is regarded as a fuzzy counterpart of Gaussian mixture models (GMMs) with EM algorithm when the regularization parameter lambda equals 2. However, KLFCM method extracts very close or even coincident clusters in many cases because the K-L information term in its objective function is used to minimize the dissimilarity between the membership degrees and the proportions of data belonging to the clusters. To deal with this problem, we propose a new model called fuzzy c-means clustering with conditional probability based K-L information regularization (CKLFCM) which incorporates the conditional probability distributions and the probabilistic dissimilarity functional into the conventional KLFCM algorithm in order to assign appropriate membership degrees to each data point. CKLFCM technique does not suffer from obtaining the unexpected close or coincident clusters. Several experiments are presented to show the effectiveness of the proposed algorithm.