Atomic　force　microscope　(AFM)　is　a　high-precision　instrument　to　research　surface　topography　of　various　samples.　Nevertheless,　the　standard　AFM　procedure　takes　excessively　long　time　to　acquire　high-resolution　images.　Moreover,　too　much　interaction　between　a　probe　tip　and　a　specimen　potentially　leads　to　tip　abrasion　and　sample　damage.　Compressive　sensing　(CS)　has　been　employed　to　realize　high-speed　AFM　(HS-AFM).　However,　a　considerably　large-sized　image　may　be　hard　to　be　reconstructed　through　the　common　CS　method　with　some　ordinary　algorithms,　due　to　the　high　computational　complexity　and　hardware　costs.　Thus,　block-based　compressive　sensing　(BCS)　is　adopted　as　an　alternative　means.　In　our　work,　three　scanning　patterns　were　utilized　to　generate　undersampled　AFM　images　at　various　sampling　rates　for　five　samples　with　different　surface　appearance.　Each　image　block　was　reconstructed　through　one　of　six　representative　algorithms.　Finally,　an　optimal　measurement　scheme　for　BCS-HS-AFM　was　put　forward　based　on　the　analysis　of　experimental　results,　which　consisted　of　sampling　rate,　scanning　pattern,　block　mode　and　reconstruction　algorithm.　BCS　was　compared　with　other　CS　methods　in　terms　of　the　computational　complexity　and　image　reconstruction　effect　to　reveal　its　superior　performance.　In　brief,　BCS　can　be　applied　to　effectively　realize　the　high-resolution　and　low-damage　HS-AFM　imaging.　©　2019　Elsevier　B.V.