Image compression based on a multipoint Taylor series representation

An image compression/decompression method is proposed, based on a new interpolation formula of Hermite-Birkhoff type. It is based on a function representation that uses a truncated multipoint Taylor (MT) series. Given a regularly tabulated image, first spatial derivatives (up to a chosen order) are computed by a FFT algorithm. Secondly a knot placing strategy selects sample point positions. The image values and spatial derivatives at these sample points are stored as the compressed data. Decompression is achieved by applying the MT interpolant to the compressed data. The quality of compression is user controlled by specifying the maximum order of spatial derivatives and the number of knots to be used. The method is found to be superior to JPEG in both reduction factor and quality, when reasonable smooth data is to be compressed with high accuracy. In this case, data reduction ratios in the range 10-100 can be obtained with a root mean square reconstruction error of the order of 1-2%. For compression of real-life color images it is inferior to JPEG and yields reduction ratios of about 4, at the threshold of notable picture degradation to the eye. A number of compression/decompression examples are shown.