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Due to the limitations of hardware technology and launching cost, there is a tradeoff between the spatial resolution and temporal resolution of satellite images. In order to access to the data with both high spatial and high temporal resolution, spatio-temporal fusion (STF) of remotely sensed images came into being. In recent years, convolutional neural networks (CNNs) have been successfully adopted in this field and some efficient STF methods based on CNNs were developed. However, these methods require a significant number of training image pairs, where each pair generally consists of a high spatial resolution image and a low spatial resolution image. Such a requirement limits the applicability of STF methods to real scenarios, as in many cases there is no wide availability of image pairs for training. To overcome this important limitation, in this paper we introduce a single image pair-based method (based on CNNs) for STF of remotely sensed images. Our method, called SS-CNN, uses the spatial information provided by the average image (obtained across the available spectral bands) of the high spatial resolution image to perform CNN-based super-resolution mapping (SRM) between the low and high spatial resolution images. Three experiments, including two simulated and one real ones, were used to evaluate the STF accuracy of SS-CNN. The obtained experimental results clearly demonstrate the effectiveness of our newly proposed method.