For high-frame-rate ultrasound imaging, it remains challenging to implement on compact systems as a sparse imaging configuration with limited array channels. One key issue is that the resulting image quality is known to be mediocre not only because unfocused plane-wave excitations are used but also because grating lobes would emerge in sparse-array configurations. In this article, we present the design and use of a new channel recovery framework to infer full-array plane-wave channel datasets for periodically sparse arrays that operate with as few as one-quarter of the full-array aperture. This framework is based on a branched encoder-decoder convolutional neural network (CNN) architecture, which was trained using full-array plane-wave channel data collected from human carotid arteries (59 864 training acquisitions; 5-MHz imaging frequency; 20-MHz sampling rate; plane-wave steering angles between -15° and 15° in 1° increments). Three branched encoder-decoder CNNs were separately trained to recover missing channels after differing degrees of channelwise downsampling (2, 3, and 4 times). The framework's performance was tested on full-array and downsampled plane-wave channel data acquired from an in vitro point target, human carotid arteries, and human brachioradialis muscle. Results show that when inferred full-array plane-wave channel data were used for beamforming, spatial aliasing artifacts in the B-mode images were suppressed for all degrees of channel downsampling. In addition, the image contrast was enhanced compared with B-mode images obtained from beamforming with downsampled channel data. When the recovery framework was implemented on an RTX-2080 GPU, the three investigated degrees of downsampling all achieved the same inference time of 4 ms. Overall, the proposed framework shows promise in enhancing the quality of high-frame-rate ultrasound images generated using a sparse-array imaging setup.