In this paper, a new image synthesis model based on a set of wavelet bases is proposed. In the proposed model, images are approximated by the sum of synthesis functions that are translated to image edge positions. By applying the proposed model to sketch-based image coding, no iterative image recovery procedure is required for image decoding. In the design of the synthesis functions, we define the synthesis functions as a linear combination of wavelet bases. The coefficients for wavelet bases are obtained from an iterative procedure. The vector quantization is applied to the vectors of the coefficients to limit the number of the synthesis functions. We apply the proposed synthesis model to the sketch-based image coding. Image coding experiments by eight synthesis functions and a comparison with the orthogonal transform methods are also given.