Subspace-sparsifying steerable discrete cosine transform from graph fourier transform

In image compression, block-based transforms tend to be inefficient when blocks contain arbitrarily shaped discontinuities. For this reason, transforms incorporating directional information are an appealing alternative. Starting from the graph Fourier transform, in this paper we present a new transform, called Subspace-Sparsifying Steer-able DCT, that can be obtained by rotating the basis vectors of the 2D DCT using a set of angles that best matches the block to be encoded. In particular, this new transform chooses the set of angles providing the sparsest image representation in the transform domain, yielding a matrix of transform coefficients that is triangular. In this way, it nearly halves the number of coefficients that need to be transmitted, obtaining a significant coding gain in comparison to the classical DCT.

[1]  Feng Wu,et al.  Lifting-Based Directional DCT-Like Transform for Image Coding , 2007, IEEE Transactions on Circuits and Systems for Video Technology.

[2]  Pascal Frossard,et al.  The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains , 2012, IEEE Signal Processing Magazine.

[3]  Bernd Girod,et al.  Direction-adaptive partitioned block transform for image coding , 2008, 2008 15th IEEE International Conference on Image Processing.

[4]  Khalid Sayood,et al.  Introduction to Data Compression , 1996 .

[5]  Sunil K. Narang,et al.  Graph based transforms for depth video coding , 2012, 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[6]  Susanto Rahardja,et al.  Mode-Dependent Transforms for Coding Directional Intra Prediction Residuals , 2012, IEEE Transactions on Circuits and Systems for Video Technology.

[7]  Cha Zhang,et al.  Analyzing the Optimality of Predictive Transform Coding Using Graph-Based Models , 2013, IEEE Signal Processing Letters.

[8]  G. Bjontegaard,et al.  Calculation of Average PSNR Differences between RD-curves , 2001 .

[9]  Christine Guillemot,et al.  Sparse optimization with directional DCT bases for image compression , 2010, 2010 IEEE International Conference on Acoustics, Speech and Signal Processing.

[10]  Bing Zeng,et al.  Directional Discrete Cosine Transforms—A New Framework for Image Coding , 2008, IEEE Transactions on Circuits and Systems for Video Technology.

[11]  Oscar C. Au,et al.  Multiresolution Graph Fourier Transform for Compression of Piecewise Smooth Images , 2015, IEEE Transactions on Image Processing.

[12]  Antonio Ortega,et al.  Intra-Prediction and Generalized Graph Fourier Transform for Image Coding , 2015, IEEE Signal Processing Letters.

[13]  Feng Wu,et al.  Lifting-Based Directional DCT-Like Transform for Image Coding , 2007, IEEE Trans. Circuits Syst. Video Technol..

[14]  Enrico Magli,et al.  Superpixel-driven graph transform for image compression , 2015, 2015 IEEE International Conference on Image Processing (ICIP).

[15]  Onur G. Guleryuz,et al.  Sparse orthonormal transforms for image compression , 2008, 2008 15th IEEE International Conference on Image Processing.

[16]  Jaejoon Lee,et al.  Edge-adaptive transforms for efficient depth map coding , 2010, 28th Picture Coding Symposium.

[17]  Anthony Vetro,et al.  Direction-adaptive transforms for coding prediction residuals , 2010, 2010 IEEE International Conference on Image Processing.

[18]  Enrico Magli,et al.  Predictive graph construction for image compression , 2015, 2015 IEEE International Conference on Image Processing (ICIP).

[19]  Jianqin Zhou,et al.  On discrete cosine transform , 2011, ArXiv.

[20]  R. Merris Laplacian matrices of graphs: a survey , 1994 .

[21]  R. Merris Laplacian graph eigenvectors , 1998 .

[22]  Enrico Magli,et al.  Steerable Discrete Cosine Transform , 2017, IEEE Trans. Image Process..