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 as fashion that if facilities the interpolation of lost coefficients in the case of one or more channel failures. At the reciever, 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 probabilites, we investigate the quantitative and subjective performance of the proposed system for the case of multiple channel failures.