The　Spherical　Measure　Based　Spherical　Image　Representation　(SMSIR)　has　nearly　uniformly　distributed　pixels　in　the　spherical　domain　with　effective　index　schemes.　Based　on　SMSIR,　the　spherical　wavelet　transform　can　be　efficiently　designed,　which　can　capture　the　spherical　geometry　feature　in　a　compact　manner　and　provides　a　powerful　tool　for　spherical　image　compression.　In　this　paper,　we　propose　an　efficient　compression　scheme　for　SMSIR　images　named　Spherical　Set　Partitioning　in　Hierarchical　Trees　(S-SPIHT)　using　the　spherical　wavelet　transform,　which　exploits　the　inherent　similarities　across　the　subbands　in　the　spherical　wavelet　decomposition　of　a　SMSIR　image.　The　proposed　S-SPIHT　can　progressively　transform　spherical　wavelet　coefficients　into　bit-stream,　and　generate　an　embedded　compressed　bit-stream　that　can　be　efficiently　decoded　at　several　spherical　image　quality　levels.　The　most　crucial　part　of　our　proposed　S-SPIHT　is　the　redesign　of　scanning　the　wavelet　coefficients　corresponding　to　different　index　schemes.　We　design　three　scanning　methods,　namely　ordered　root　tree　index　scanning　(ORTIS),　dyadic　index　progressive　scanning(DIPS)　and　dyadic　index　cross　scanning(DICS)to　efficiently　reorganize　the　wavelet　coefficients.　These　methods　can　effectively　exploit　the　self-similarity　between　sub-bands　and　the　fact　that　the　high-frequency　sub-bands　mostly　contain　insignificant　coefficients.　Experimental　results　on　widely-used　datasets　demonstrate　that　our　proposed　S-SPIHT　outperforms　the　straightforward　SPIHT　for　SMSIR　images　in　terms　of　PSNR,　S-PSNR　and　SSIM.　©　2021　ACM.