With traditional beamforming methods, ultrasound B-mode images contain speckle noise caused by the random interference of subresolution scatterers. In this paper, we present a framework for using neural networks to beamform ultrasound channel signals into speckle-reduced B-mode images. We introduce log-domain normalization-independent loss functions that are appropriate for ultrasound imaging. A fully convolutional neural network was trained with the simulated channel signals that were coregistered spatially to ground-truth maps of echogenicity. Networks were designed to accept 16 beamformed subaperture radio frequency (RF) signals. Training performance was compared as a function of training objective, network depth, and network width. The networks were then evaluated on the simulation, phantom, and in vivo data and compared against the existing speckle reduction techniques. The most effective configuration was found to be the deepest (16 layer) and widest (32 filter) networks, trained to minimize a normalization-independent mixture of the l<sub>1</sub> and multiscale structural similarity (MS-SSIM) losses. The neural network significantly outperformed delay-and-sum (DAS) and receive-only spatial compounding in speckle reduction while preserving resolution and exhibited improved detail preservation over a nonlocal means method. This work demonstrates that ultrasound B-mode image reconstruction using machine-learned neural networks is feasible and establishes that networks trained solely in silico can be generalized to real-world imaging in vivo to produce images with significantly reduced speckle.