The standard separable two-dimensional (2-D) wavelet transform (WT) has recently achieved a great success in image processing because it provides a sparse representation of smooth images. However, it fails to capture efficiently one-dimensional (1-D) discontinuities, like edges or contours [1]. These features, being elongated and characterized by geometrical regularity along different directions, intersect and generate many large magnitude wavelet coefficients.

Since contours are very important elements in visual perception of images, to provide a good visual quality of compressed images, it is fundamental to preserve good reconstruction of these directional features. In our previous work, we proposed a construction of critically sampled perfect reconstruction transforms with directional vanishing moments (DVMs) imposed in the corresponding basis functions along different directions, called directionlets. In this paper, we implement the Directionlets together with the space-frequency quantization (SFQ) image compression method, originally based on the standard 2-D WT and proposed previously in the literature. We show that our new compression method outperforms the standard SFQ in terms of the quality of compressed images, especially in a low-rate compression regime. We also show that our compression method does not increase the order of computational complexity as compared to the standard SFQ algorithm.

Swiss National Science Foundation