Sparse optimization with directional DCT bases for image compression

Drémeau, Angélique; Herzet, Cédric; Guillemot, Christine; Fuchs, Jean–Jacques

doi:10.1109/icassp.2010.5495421

Cited by 9 publications

(11 citation statements)

References 13 publications

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“…In [9], [35], [36], it has been shown that for DCT transforms there is an approximately linear relationship between the coding bitrate R c and the 0 -norm of c, that is, the number of its non-zero coefficients, i.e. R c = α c 0 (9) where α can be empirically found [35]. Let us now discuss R θ .…”

Section: A Rd Modelmentioning

confidence: 99%

“…To overcome this problem, various approaches and solutions have been developed [5], most of which consist in modifications of the 2D-DCT in order to incorporate directional information [3], [6]- [9]. The Directional DCT (DDCT) presented in [3] is the first attempt in this sense.…”

Section: Introductionmentioning

confidence: 99%

“…In [7], it is suggested to not apply the second-stage DCT, or to apply it only on the DC coefficients generated during the first transform [8]. In [9], DDCT [3] is improved using anisotropic local basis supports, where the optimal basis is selected exploiting the bintree structure of the dictionary. These methods, however, have several issues.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Steerable Discrete Cosine Transform

Fracastoro

Fosson

Magli

2017

IEEE Trans. on Image Process.

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In image compression, classical block-based separable transforms tend to be inefficient when image blocks contain arbitrarily shaped discontinuities. For this reason, transforms incorporating directional information are an appealing alternative. In this paper, we propose a new approach to this problem, namely, a discrete cosine transform (DCT) that can be steered in any chosen direction. Such transform, called steerable DCT (SDCT), allows to rotate in a flexible way pairs of basis vectors, and enables precise matching of directionality in each image block, achieving improved coding efficiency. The optimal rotation angles for SDCT can be represented as solution of a suitable rate-distortion (RD) problem. We propose iterative methods to search such solution, and we develop a fully fledged image encoder to practically compare our techniques with other competing transforms. Analytical and numerical results prove that SDCT outperforms both DCT and state-of-the-art directional transforms.

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Section: A Rd Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Steerable Discrete Cosine Transform

Fracastoro

Fosson

Magli

2017

IEEE Trans. on Image Process.

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“…Model-based work hence focused on the design of anisotropic transforms (multiresolution transforms such as [8], [33], [35], [45] as well as block-based designs [10], [18], [38], [51]) that were geared toward obtaining substantially better performance over directional singularities. On the data-driven side, noting the suboptimality of principal component analysis (PCA) methods and the KLT [13], researchers have concentrated on "independent" component analysis (ICA) and matching pursuit designs among others [20], [32].…”

Section: Introductionmentioning

confidence: 99%

Approximation and Compression With Sparse Orthonormal Transforms

Sezer

Guleryuz

Altunbasak

2015

IEEE Trans. on Image Process.

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We propose a new transform design method that targets the generation of compression-optimized transforms for next-generation multimedia applications. The fundamental idea behind transform compression is to exploit regularity within signals such that redundancy is minimized subject to a fidelity cost. Multimedia signals, in particular images and video, are well known to contain a diverse set of localized structures, leading to many different types of regularity and to nonstationary signal statistics. The proposed method designs sparse orthonormal transforms (SOT) that automatically exploit regularity over different signal structures and provides an adaptation method that determines the best representation over localized regions. Unlike earlier work that is motivated by linear approximation constructs and model-based designs that are limited to specific types of signal regularity, our work uses general nonlinear approximation ideas and a data-driven setup to significantly broaden its reach. We show that our SOT designs provide a safe and principled extension of the Karhunen-Loeve transform (KLT) by reducing to the KLT on Gaussian processes and by automatically exploiting non-Gaussian statistics to significantly improve over the KLT on more general processes. We provide an algebraic optimization framework that generates optimized designs for any desired transform structure (multi-resolution, block, lapped, etc.) with significantly better n-term approximation performance.For each structure, we propose a new prototype codec and test over a database of images. Simulation results show consistent increase in compression and approximation performance compared with conventional methods. Index Termssparse orthonormal transform, sparse lapped transform, sparse multi-resolution transform, transform optimization, image compression, nonlinear approximation 2

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“…In [7], it is suggested to not apply the secondstage DCT, or to apply it only on the DC coefficients generated during the first transform [8]. In [9], DDCT [3] is improved using anisotropic local basis supports, where the optimal basis is selected exploiting the bintree structure of the dictionary. These methods, however, have several issues.…”

Section: Introductionmentioning

confidence: 99%

Steerable Discrete Cosine Transform

Fracastoro

Magli

2015

2015 IEEE 17th International Workshop on Multimedia Signal Processing (MMSP)

View full text Add to dashboard Cite

In image compression, classical block-based separable transforms tend to be inefficient when image blocks contain arbitrarily shaped discontinuities. For this reason, transforms incorporating directional information are an appealing alternative. In this paper, we propose a new approach to this problem, namely a discrete cosine transform (DCT) that can be steered in any chosen direction. Such transform, called steerable DCT (SDCT), allows to rotate in a flexible way pairs of basis vectors, and enables precise matching of directionality in each image block, achieving improved coding efficiency. The optimal rotation angles for SDCT can be represented as solution of a suitable rate-distortion (RD) problem. We propose iterative methods to search such solution, and we develop a fully fledged image encoder to practically compare our techniques with other competing transforms. Analytical and numerical results prove that SDCT outperforms both DCT and state-ofthe-art directional transforms.

show abstract

Sparse optimization with directional DCT bases for image compression

Cited by 9 publications

References 13 publications

Steerable Discrete Cosine Transform

Steerable Discrete Cosine Transform

Approximation and Compression With Sparse Orthonormal Transforms

Steerable Discrete Cosine Transform

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