This paper presents an analysis on and experimental comparison of several typical fast algorithms for discrete wavelet transform (DWT) and their implementation in image compression, particularly the Mallat algorithm, ...This paper presents an analysis on and experimental comparison of several typical fast algorithms for discrete wavelet transform (DWT) and their implementation in image compression, particularly the Mallat algorithm, FFT-based algorithm, Short- length based algorithm and Lifting algorithm. The principles, structures and computational complexity of these algorithms are explored in details respectively. The results of the experiments for comparison are consistent to those simulated by MATLAB. It is found that there are limitations in the implementation of DWT. Some algorithms are workable only for special wavelet transform, lacking in generality. Above all, the speed of wavelet transform, as the governing element to the speed of image processing, is in fact the retarding factor for real-time image processing.展开更多
We propose a novel, lossless compression algorithm, based on the 2D Discrete Fast Fourier Transform, to approximate the Algorithmic (Kolmogorov) Complexity of Elementary Cellular Automata. Fast Fourier transforms are ...We propose a novel, lossless compression algorithm, based on the 2D Discrete Fast Fourier Transform, to approximate the Algorithmic (Kolmogorov) Complexity of Elementary Cellular Automata. Fast Fourier transforms are widely used in image compression but their lossy nature exclude them as viable candidates for Kolmogorov Complexity approximations. For the first time, we present a way to adapt fourier transforms for lossless image compression. The proposed method has a very strong Pearsons correlation to existing complexity metrics and we further establish its consistency as a complexity metric by confirming its measurements never exceed the complexity of nothingness and randomness (representing the lower and upper limits of complexity). Surprisingly, many of the other methods tested fail this simple sanity check. A final symmetry-based test also demonstrates our method’s superiority over existing lossless compression metrics. All complexity metrics tested, as well as the code used to generate and augment the original dataset, can be found in our github repository: ECA complexity metrics<sup>1</sup>.展开更多
An efficient algorithm for determining the linear complexity and the minimal polynomial of a binary sequence with period 2npm is proposed and proved, where 2 is a primitive root modulo p2. The new algorithm generalize...An efficient algorithm for determining the linear complexity and the minimal polynomial of a binary sequence with period 2npm is proposed and proved, where 2 is a primitive root modulo p2. The new algorithm generalizes the algorithm for computing the linear complexity of a binary sequence with period 2' and the algorithm for computing the linear complexity of a binary sequence with period pn, where 2 is a primitive root modulo p2.展开更多
基金the Natural Science Foundation of China (No.60472037).
文摘This paper presents an analysis on and experimental comparison of several typical fast algorithms for discrete wavelet transform (DWT) and their implementation in image compression, particularly the Mallat algorithm, FFT-based algorithm, Short- length based algorithm and Lifting algorithm. The principles, structures and computational complexity of these algorithms are explored in details respectively. The results of the experiments for comparison are consistent to those simulated by MATLAB. It is found that there are limitations in the implementation of DWT. Some algorithms are workable only for special wavelet transform, lacking in generality. Above all, the speed of wavelet transform, as the governing element to the speed of image processing, is in fact the retarding factor for real-time image processing.
文摘We propose a novel, lossless compression algorithm, based on the 2D Discrete Fast Fourier Transform, to approximate the Algorithmic (Kolmogorov) Complexity of Elementary Cellular Automata. Fast Fourier transforms are widely used in image compression but their lossy nature exclude them as viable candidates for Kolmogorov Complexity approximations. For the first time, we present a way to adapt fourier transforms for lossless image compression. The proposed method has a very strong Pearsons correlation to existing complexity metrics and we further establish its consistency as a complexity metric by confirming its measurements never exceed the complexity of nothingness and randomness (representing the lower and upper limits of complexity). Surprisingly, many of the other methods tested fail this simple sanity check. A final symmetry-based test also demonstrates our method’s superiority over existing lossless compression metrics. All complexity metrics tested, as well as the code used to generate and augment the original dataset, can be found in our github repository: ECA complexity metrics<sup>1</sup>.
基金This work was supported in part by the National Natural Science Foundation of China ( Grant No.60073051) the Natural Science Foundation of Education Council of Anhui Province.
文摘An efficient algorithm for determining the linear complexity and the minimal polynomial of a binary sequence with period 2npm is proposed and proved, where 2 is a primitive root modulo p2. The new algorithm generalizes the algorithm for computing the linear complexity of a binary sequence with period 2' and the algorithm for computing the linear complexity of a binary sequence with period pn, where 2 is a primitive root modulo p2.
