Discrete cosine transform: algorithms, advantages, applications
Discrete cosine transform: algorithms, advantages, applications
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
Signal Processing with Lapped Transforms
Signal Processing with Lapped Transforms
Lapped Biorthogonal Transforms for Transform Coding with Reduced Blocking and Ringing Artifacts
ICASSP '97 Proceedings of the 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '97)-Volume 3 - Volume 3
IEEE Transactions on Computers
Infinity-norm rotation transforms
IEEE Transactions on Signal Processing
Matrix Factorizations for Parallel Integer Transformation
IEEE Transactions on Signal Processing
Matrix factorizations for reversible integer mapping
IEEE Transactions on Signal Processing
Lapped transform via time-domain pre- and post-filtering
IEEE Transactions on Signal Processing
Image quality assessment: from error visibility to structural similarity
IEEE Transactions on Image Processing
Overview of the H.264/AVC video coding standard
IEEE Transactions on Circuits and Systems for Video Technology
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A recently developed PLUS factorization holds great promise in image coding due to its simplicity and integer reversibility. However, existing PLUS factorizations did not consider stability and optimality. To address these problems, we propose methodologies to design stable and optimal PLUS factorization algorithms. Firstly, we propose three stable PLUS factorization algorithms, prove the stability theorem under no perturbation and analyze stability under perturbation. Furthermore, we obtain a closed-form formula for transform error, and use the formula to design an algorithm for optimal PLUS factorization. Then, we apply the PLUS factorization to image coding. The integer DCTs implemented with the optimal PLUS factorizations found by our algorithms outperform the integer DCT with expansion factors in terms of entropy. The optimal PLUS factorizations are superior to the lifting factorization in JPEG-XR. The experimental results agree with analytical results of PLUS factorization, and show superior performance of our algorithms in image coding.