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This paper proposes a novel image approximation method which represents image signals as a linear combination of multiple 2D functions like the matching pursuit algorithm. The conventional matching pursuit algorithm uses over-complete basis-functions whose sizes and shapes are limited to specific ones available in a predefined dictionary. In order to avoid such limitations, our method employs the 2D Gabor functions whose shapes are controllable by eight kinds of parameters. These parameters are iteratively optimized for the respective functions by the quasi-Newton method so as to minimize the sum of squared approximation errors. Simulation results indicate that the proposed method has a potential to be used as an image coding tool and its rate-distortion performance can be better than the JPEG baseline scheme at very low bit-rates.