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Cellular neural networks (CNN) have traditionally been used to perform nonlinear operations on images such as edge detection, hole filling, etc. However, algorithms for image compression using CNN have scarcely been explored. This paper presents new templates and novel algorithms to perform basic operations used for image compression. Thy include wavelet subband decomposition, computation of parameters for bit allocation, quantization and bit extraction. These algorithms are hardware oriented and exploit the massive parallelism provided by the CNN. Compression is an important and widely used operation in image processing. Therefore, the algorithms presented here expand the realm of CNN applications. This feature is especially important for the widespread use of CNN as a multiple purpose image processor.