We demonstrate a noniterative adaptive reconstruction technique to significantly improve the imaging performance of sparse terahertz arrays employing single-cycle pulses. Grating lobe artifacts are suppressed by an adaptive weighting factor derived from the temporal coherence of signals from neighboring array elements. Image quality is further improved by a second weighting factor based on the spatial coherence of signals across the entire array. Experiments are performed with a synthetic aperture two-dimensional sparse array of 56x56 elements. Our reconstruction technique suppresses artifacts by 30 dB.