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
Fast wavelet transform algorithms for Toeplitz matrices are proposed in this paper. Distinctive from the well known discrete trigonometric transforms, such as the discrete cosine transform （DCT） and the discrete Fou...Fast wavelet transform algorithms for Toeplitz matrices are proposed in this paper. Distinctive from the well known discrete trigonometric transforms, such as the discrete cosine transform （DCT） and the discrete Fourier transform （DFT） for Toeplitz matrices, the new algorithms are achieved by compactly supported wavelet that preserve the character of a Toeplitz matrix after transform, which is quite useful in many applications involving a Toeplitz matrix. Results of numerical experiments show that the proposed method has good compression performance similar to using wavelet in the digital image coding. Since the proposed algorithms turn a dense Toeplitz matrix into a band-limited form, the arithmetic operations required by the new algorithms are O（N） that are reduced greatly compared with O（N log N） by the classical trigonometric transforms.展开更多
A new meaningful image encryption algorithm based on compressive sensing(CS)and integer wavelet transformation(IWT)is proposed in this study.First of all,the initial values of chaotic system are encrypted by RSA algor...A new meaningful image encryption algorithm based on compressive sensing(CS)and integer wavelet transformation(IWT)is proposed in this study.First of all,the initial values of chaotic system are encrypted by RSA algorithm,and then they are open as public keys.To make the chaotic sequence more random,a mathematical model is constructed to improve the random performance.Then,the plain image is compressed and encrypted to obtain the secret image.Secondly,the secret image is inserted with numbers zero to extend its size same to the plain image.After applying IWT to the carrier image and discrete wavelet transformation(DWT)to the inserted image,the secret image is embedded into the carrier image.Finally,a meaningful carrier image embedded with secret plain image can be obtained by inverse IWT.Here,the measurement matrix is built by both chaotic system and Hadamard matrix,which not only retains the characteristics of Hadamard matrix,but also has the property of control and synchronization of chaotic system.Especially,information entropy of the plain image is employed to produce the initial conditions of chaotic system.As a result,the proposed algorithm can resist known-plaintext attack(KPA)and chosen-plaintext attack(CPA).By the help of asymmetric cipher algorithm RSA,no extra transmission is needed in the communication.Experimental simulations show that the normalized correlation(NC)values between the host image and the cipher image are high.That is to say,the proposed encryption algorithm is imperceptible and has good hiding effect.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.
基金Supported by the National Natural Science Foundation under Grants （No.10171109）
文摘Fast wavelet transform algorithms for Toeplitz matrices are proposed in this paper. Distinctive from the well known discrete trigonometric transforms, such as the discrete cosine transform （DCT） and the discrete Fourier transform （DFT） for Toeplitz matrices, the new algorithms are achieved by compactly supported wavelet that preserve the character of a Toeplitz matrix after transform, which is quite useful in many applications involving a Toeplitz matrix. Results of numerical experiments show that the proposed method has good compression performance similar to using wavelet in the digital image coding. Since the proposed algorithms turn a dense Toeplitz matrix into a band-limited form, the arithmetic operations required by the new algorithms are O（N） that are reduced greatly compared with O（N log N） by the classical trigonometric transforms.
基金This work was supported in part by the National Natural Science Foundation of China(Grant Nos.61972103,61772371,62172301)the Natural Science Foundation of Guangdong Province of China(2019A1515011361)+2 种基金the Fundamental Research Funds for the Central Universities of China(22120210545)the Key Scientific Research Project of Education Department of Guangdong Province of China(2020ZDZX3064)the Postgraduate Education Innovation Project of Guangdong Ocean University of China(202143).
文摘A new meaningful image encryption algorithm based on compressive sensing(CS)and integer wavelet transformation(IWT)is proposed in this study.First of all,the initial values of chaotic system are encrypted by RSA algorithm,and then they are open as public keys.To make the chaotic sequence more random,a mathematical model is constructed to improve the random performance.Then,the plain image is compressed and encrypted to obtain the secret image.Secondly,the secret image is inserted with numbers zero to extend its size same to the plain image.After applying IWT to the carrier image and discrete wavelet transformation(DWT)to the inserted image,the secret image is embedded into the carrier image.Finally,a meaningful carrier image embedded with secret plain image can be obtained by inverse IWT.Here,the measurement matrix is built by both chaotic system and Hadamard matrix,which not only retains the characteristics of Hadamard matrix,but also has the property of control and synchronization of chaotic system.Especially,information entropy of the plain image is employed to produce the initial conditions of chaotic system.As a result,the proposed algorithm can resist known-plaintext attack(KPA)and chosen-plaintext attack(CPA).By the help of asymmetric cipher algorithm RSA,no extra transmission is needed in the communication.Experimental simulations show that the normalized correlation(NC)values between the host image and the cipher image are high.That is to say,the proposed encryption algorithm is imperceptible and has good hiding effect.
