Transmission of compressed image data over noisy channels is an important problem and has been investigated in a variety of scenarios. In this paper, we propose a progressive time-varying source-channel coding system for transmitting images over wireless channels. The core result of this paper is a systematic method of instantaneous rate allocation between the progressive source coder and channel coder. We develop closed form expressions for end-to-end distortion, as well as rate allocation, in memoryless channels. We extend the memoryless results to an algorithm for fading channels. Experimental results demonstrate the performance of this method.