Approximation and Compression With Sparse Orthonormal Transforms

@article{Sezer2015ApproximationAC,
  title={Approximation and Compression With Sparse Orthonormal Transforms},
  author={Osman Gokhan Sezer and Onur G. Guleryuz and Y{\"u}cel Altunbasak},
  journal={IEEE Transactions on Image Processing},
  year={2015},
  volume={24},
  pages={2328-2343}
}
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… 

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References

SHOWING 1-10 OF 63 REFERENCES

Sparse orthonormal transforms for image compression

TLDR
A block-based transform optimization and associated image compression technique that exploits regularity along directional image singularities and an EZW/SPIHT like entropy coder is used to encode the transform coefficients to show that the designs have competitive rate-distortion performance.

On the importance of combining wavelet-based nonlinear approximation with coding strategies

TLDR
This paper provides a mathematical analysis of transform compression in its relationship to linear and nonlinear approximation theory, and forms a family of functions/stochastic processes for which they provide efficient descriptions in a rate-distortion sense.

Robust Learning of 2-D Separable Transforms for Next-Generation Video Coding

With the simplicity of its application together with compression efficiency, the Discrete Cosine Transform(DCT) plays a vital role in the development of video compression standards. For

Rate Distortion Behavior of Sparse Sources

TLDR
Binding techniques are applied to two source models: Gaussian mixtures and power laws matching the approximately scale-invariant decay of wavelet coefficients, which allow to bound high-rate compression performance of a scalar mixture compared to a corresponding unmixed transform coding system.

K-SVD : An Algorithm for Designing of Overcomplete Dictionaries for Sparse Representation

TLDR
A novel algorithm for adapting dictionaries in order to achieve sparse signal representations, K-SVD, an iterative method that alternates between sparse coding of the examples based on the current dictionary, and a process of updating the dictionary atoms to better fit the data.

$rm K$-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation

TLDR
A novel algorithm for adapting dictionaries in order to achieve sparse signal representations, the K-SVD algorithm, an iterative method that alternates between sparse coding of the examples based on the current dictionary and a process of updating the dictionary atoms to better fit the data.

Wavelet-domain approximation and compression of piecewise smooth images

TLDR
This paper develops a prototype image coder that has near-optimal asymptotic R-D performance D(R)/spl lsim/(logR)/sup 2//R/sup 2/ for piecewise smooth C/Sup 2//C/ Sup 2/ images.

Matching pursuit video coding .I. Dictionary approximation

TLDR
This work introduces for the first time a design methodology which incorporates both coding efficiency and complexity in a systematic way and shows that complexity reduction factors of up to 1000 are achievable with negligible coding efficiency losses.

Stable recovery of sparse overcomplete representations in the presence of noise

TLDR
This paper establishes the possibility of stable recovery under a combination of sufficient sparsity and favorable structure of the overcomplete system and shows that similar stability is also available using the basis and the matching pursuit algorithms.

Learning unions of orthonormal bases with thresholded singular value decomposition

TLDR
It is shown that it is possible to design an iterative learning algorithm that produces a dictionary with the required structure, and how well the learning algorithm recovers dictionaries that may or may not have the necessary structure is assessed.
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