Recently, the convolutional neural network (CNN) based reconstruction concept has emerged as a promising implementation of compressed sensing tailored for specific fast imaging applications. The reconstruction performance of such data-driven models may depend on the CNN structure which determines the feature extraction process for sparse representation. In this study, a locally and globally concatenated network is proposed and compared with the residual network as well as the traditional L1-wavelet ESPIRiT. Preliminary experiments on a public knee imaging database showed that the proposed approach provided improved fine structure (e.g. vessel wall) restoration and background noise reduction.