A　low-complexity　iterative　hard　thresholding　(IHT)　algorithm-based　detector　is　proposed　for　the　compressed　orthogonal　frequency　division　multiplexing　with　index　modulation　(OFDM-IM)　system.　To　improve　recovery　accuracy　and　reduce　the　number　of　iterations,　detection　is　embedded　into　the　iterations　of　the　IHT　algorithm,　and　the　block　energy　information　is　used　to　identify　subblocks　that　are　more　likely　to　be　error-recovered.　Compared　with　the　existing　methods　for　improving　spectral　efficiency,　the　new　method　does　not　expand　the　detection　search　space　and　not　need　extra　pseudo-inverse　calculations　during　iterations.　Theoretical　and　simulation　results　show　that　the　proposed　scheme　can　considerably　reduce　computational　complexity　while　improving　spectral　efficiency　and　preserving　significant　BER　performance　gain.