Low-Rate Reduced Complexity Image Compression using Directionlets

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 and contours, that are anisotropic and characterized by geometrical regularity along different directions. In our previous work, we proposed a construction of critically sampled perfect reconstruction anisotropic transform with directional vanishing moments (DVM) imposed in the corresponding basis functions, called directionlets. Here, we show that the computational complexity of our transform is comparable to the complexity of the standard 2-D WT and substantially lower than the complexity of other similar approaches. We also present a zerotree-based image compression algorithm using directionlets that strongly outperforms the corresponding method based on the standard wavelets at low bit rates.

[1]  William A. Pearlman,et al.  A new, fast, and efficient image codec based on set partitioning in hierarchical trees , 1996, IEEE Trans. Circuits Syst. Video Technol..

[2]  Stéphane Mallat,et al.  Sparse geometric image representations with bandelets , 2005, IEEE Transactions on Image Processing.

[3]  Baltasar Beferull-Lozano,et al.  Approximation power of directionlets , 2005, IEEE International Conference on Image Processing 2005.

[4]  Minh N. Do,et al.  Ieee Transactions on Image Processing the Contourlet Transform: an Efficient Directional Multiresolution Image Representation , 2022 .

[5]  Jelena Kovacevic,et al.  Wavelets and Subband Coding , 2013, Prentice Hall Signal Processing Series.

[6]  E. Candès,et al.  Curvelets: A Surprisingly Effective Nonadaptive Representation for Objects with Edges , 2000 .

[7]  Stéphane Mallat,et al.  Discrete bandelets with geometric orthogonal filters , 2005, IEEE International Conference on Image Processing 2005.

[8]  Baltasar Beferull-Lozano,et al.  Directionlets: anisotropic multidirectional representation with separable filtering , 2006, IEEE Transactions on Image Processing.

[9]  S. Mallat A wavelet tour of signal processing , 1998 .

[10]  Michael T. Orchard,et al.  Space-frequency quantization for wavelet image coding , 1997, IEEE Trans. Image Process..

[11]  Justin K. Romberg,et al.  Wavelet-domain approximation and compression of piecewise smooth images , 2006, IEEE Transactions on Image Processing.

[12]  Jerome M. Shapiro,et al.  Embedded image coding using zerotrees of wavelet coefficients , 1993, IEEE Trans. Signal Process..