The　algorithms　for　block　compressed　sensing　based　on　total　variation　and　mixed　variation　(abbreviated　as　BCS-TV　and　BCS-MV)　models　were　proposed　to　improve　the　performance　of　current　reconstruction　algorithms　for　the　block-based　compressed　sensing.　In　the　measuring　phase,　an　image　was　sampled　block-by-block.　In　the　recovering　period,　it　took　the　sparse　regularization　of　the　natural　image　as　a　priori　knowledge,　and　approached　the　target　function　within　the　whole　image　through　the　modified　augmented　Lagrange　method　and　alternating　direction　method　of　multipliers　(ALM-ADMM).　The　method　proposed　achieves　average　PSNR　gain　of　1.5　dB　and　SSIM　gain　of　0.05　at　a　more　stable　running　speed,　over　the　previous　uniformly　block-based　compressed　sensing.　It　is　particularly　suitable　for　the　applications　of　the　multimedia　data　processing　with　fixed　transmission　delay.　©　2016,　Editorial　Board　of　Journal　on　Communications.　All　right　reserved.