This paper presents a multiple description image coding scheme that facilitates the transmission of digital imagery over multiple noisy channels. The proposed scheme divides the image into smaller parts that are transmitted over the individual channels of an inverse multiplexing system. The division or splitting is done in such a fashion that it facilitates the interpolation of lost coefficients in the case of one or more channel failures. To combat the effects of channel noise, a novel joint source-channel coding scheme is employed, which uses punctured convolutional channel codes and trellis-coded quantization. At the receiver, the image is reconstructed by proper assembly of the data received from each channel. In case of channel failure, the missing coefficients are estimated from the available data with the use of a novel post processing scheme. For operation over four noisy channels with various bit error probabilities, we investigate the quantitative and subjective performance with and without channel failures.