The source and channel coding functions of a communication system are usually designed independently of one another. This is justified by Shannon's separation principle (1948), which indicates that no performance loss is suffered if the two functions are thus partitioned. However, Shannon's theorem is an asymptotic result that permits unlimited delay and complexity; given a constraint on complexity/delay, joint source-channel coding may outperform separately designed pairs. In this work, we consider the problem of reliable communication of compressed still grey-level images over very noisy channels. An unequal error protection (UEP) joint source-channel coding scheme is proposed for transmitting discrete-cosine transform (DCT) encoded images over an additive white Gaussian noise (AWGN) channel used in conjunction with coherent M-ary phase shift keying (MPSK) modulation. More specifically, it consists of a sequence maximum a posteriori (MAP) detection scheme that exploits both the channel soft decision information and the statistical image characteristics.