A hybrid digital-analog wireless image transmission scheme, called SparseCast, is introduced, which provides graceful degradation with channel quality. SparseCast achieves improved end-to-end reconstruction quality while reducing the bandwidth requirement by exploiting frequency domain sparsity through compressed sensing. The proposed algorithm produces a linear relationship between the channel signal-to-noise ratio (CSNR) and peak signal-to-noise ratio (PSNR), without requiring the channel state knowledge at the transmitter. This is particularly attractive when transmitting to multiple receivers or over unknown time-varying channels, as the receiver PSNR depends on the experienced channel quality, and is not bottlenecked by the worst channel. SparseCast is benchmarked against two alternative algorithms: SoftCast and BCS-SPL. Our findings show that the proposed algorithm outperforms SoftCast by approximately 3.5 dB and BCS-SPL by 15.2 dB.