Iterative Image Coding with Overcomplete Curvelet Transform

This paper presents a new coding technique based on a overcomplete curvelet transform. Curvelets provide an essentially optimal representation for typical objects which are discontinuities along curves. However curvelets transform has high redundancy, the process of selecting the optimal set of coefficients to code is much more difficult because many different sets of transform coefficients can represent the same decoded image. The transform is optimized through an iterative projection process in the transform domain in order to minimize the quantization error in the image domain. So we select the optimal set of quantized coefficients based on iterative projection of signals between the image domain and transform domain with a non-linear process (a quantizer). The optimal set of quantized coefficients is coded by the simple entropy coder. The compression performance of the coding technique based on a overcomplete curvelet transform is compared with that of Wavelet Transform, both objectively and subjectively, and is found to offer advantages of up to about 0.7 dB for Lena image and to about 1.42 dB for Barbara image in PSNR and significant reduction in visibility of some types of coding artifacts.