In this paper, a new subband coding system called subband absolute moment block truncation coding (SAMBTC) is introduced to compress monochrome images and color images recorded in YIQ and L*u*v* uniform color spaces. The SAMBTC incorporates full‐band absolute moment block truncation coding (AMBTC) into subbands along with a new subband dynamic bit allocation algorithm which is derived from the Shannon rate‐distortion bound. Simulation results show that the proposed Shannon/bound‐based bit allocation algorithm outperforms the commonly used standard‐deviation‐based bit allocation scheme. Compared with ABMTC, SAMBTC achieves superior imaging without blocking artifacts at low bit rates