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This paper introduces a new fast image encryption scheme based on a chaotic system and cyclic shift in the integer wavelet domain. In order to increase the effectiveness and security of encryption, we propose a new diffusion scheme by using bidirectional diffusion and cyclic shift and apply it to our encryption scheme. First, a two-level integer wavelet transform is used to split the plaintext picture into four low-frequency components. Second, we use random sequences generated by Chen's hyper-chaotic system to scramble four low-frequency components. The initial value is determined by Secure Hash Algorithm 256-bit (SHA256) and user-defined parameters, which increases the plaintext sensitivity. Then, the new diffusion scheme is applied to the matrix containing most of the information and matrices are transformed by a one-level inverse integer wavelet. Finally, to create the ciphertext image, the diffused matrices are subjected to the one-level inverse integer wavelet transform. In the simulation part, we examine the suggested algorithm's encryption impact. The findings demonstrate that the suggested technique has a sufficient key space and can successfully fend off common attacks. [ABSTRACT FROM AUTHOR]

In this paper, we propose a secure image encryption method using compressive sensing (CS) and a two-dimensional linear canonical transform (2D LCT). First, the SHA256 of the source image is used to generate encryption security keys. As a result, the suggested technique is able to resist selected plaintext attacks and is highly sensitive to plain images. CS simultaneously encrypts and compresses a plain image. Using a starting value correlated with the sum of the image pixels, the Mersenne Twister (MT) is used to control a measurement matrix in compressive sensing. Then, the scrambled image is permuted by Lorenz's hyper-chaotic systems and encoded by chaotic and random phase masks in the 2D LCT domain. In this case, chaotic systems increase the output complexity, and the independent parameters of the 2D LCT expand the key space of the suggested technique. Ultimately, diffusion based on addition and modulus operations yields a cipher-text image. Simulations showed that this cryptosystem was able to withstand common attacks and had adequate cryptographic features. [ABSTRACT FROM AUTHOR]

The offset linear canonical transform (OLCT) plays an important role in many fields of optics and signal processing. In this paper, we address the problem of signal filtering and reconstruction in the OLCT domain based on new convolution theorems. Firstly, we propose new convolution and product theorems for the OLCT, which state that a modified ordinary convolution in the time domain is equivalent to simple multiplication operations for the OLCT and the Fourier transform (FT). Moreover, it is expressible by a one dimensional integral and is easy to implement in designing filters. The classical convolution theorem in the FT domain is shown to be a special case of our derived results. Then, a practical multichannel sampling expansion for band-limited signal with the OLCT is introduced. This sampling expansion constructed by the new convolution structure can reduce the effect of spectral leakage and is easy to implement. By designing OLCT filters, we can obtain derivative sampling and second-order derivative interpolation. Furthermore, potential applications of the multichannel sampling are discussed. Last, based on the new convolution structure, we investigate and discuss several applications, including swept-frequency filter analysis, image denosing and image encryption. Some illustrations and simulations are presented to verify the validity and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Fourier transform (FT) plays an important role in many fields of optics and signal processing. As its fundamental topics, various sampling theories have been established, of course, which include multidimensional (MD) sampling in the FT domain. However, given the deficiency of the existing sampling methods associated with arbitrary lattices sampling, we introduce a new simple method to get alias-free sampling matrix. Then under the premise of alias-free sampling, we drive an easy-to-compute reconstruction formula for MD bandlimited signal, which provides us with a simple way to reconstruct original signal from its sampled vision in terms of an arbitrary frequency support and has never been presented before. Consequently, the MD uniform sampling theorem about arbitrary lattices is proposed. Furthermore, in order to get optimal sampling matrix, we improve this sampling method by applying the idea of segmentation to the bandlimited area. Finally, simulations are presented to prove the rationality of the new sampling method. [ABSTRACT FROM AUTHOR]

The linear canonical transform (LCT) has been shown to be a powerful tool for optics and signal processing. This study addresses the problem of filterbank implementation for multichannel sampling in the LCT domain. First, the interpolation and sampling identities in the LCT domain are derived by the properties of LCT. The interpolation identity is the key result of the current study, which establishes the equivalence of two signal processing operations. One of these uses continuous‐time‐domain filters, whereas the other uses discrete processing. Then, applying the interpolation identity, the particularly efficient filterbank implementation for derivative sampling, periodic non‐uniform sampling and multichannel sampling are obtained in the LCT domain. Moreover, the authors present filterbank implementation using polyphase structures in LCT domain. Furthermore, the simulations are carried out to verify the effectiveness of the results and the potential applications of the multichannel sampling are also presented. Finally, combining the sampling and interpolation identity, they explore the relationship between the multichannel sampling and the filterbank in the LCT domain. [ABSTRACT FROM AUTHOR]

The affine Fourier transform (AFT) plays an important role in many fields of optics and signal processing. The Gabor transform (GT) is a kind of linear time–frequency representation (TFR). Compared with many bilinear TFRs, the GT does not have the cross‐term problem. In this study, the authors propose a time–frequency analysis method based on the AFT and GT. First, they obtain an affine relation between the AFT and the modified GT (MGT). Since the MGT is closely related to the AFT, they can use it as an assistant tool for signal processing in the AFT domain. Moreover, many useful relations between the AFT and the MGT are derived, such as recovery relation, projection relation and power integration relation. Then, they demonstrate that the AFT also has the affine relation with other TFRs, such as the Gabor–Wigner transform and the general class of quadratic distribution. Last, using the new time–frequency analysis method associated with the AFT and MGT, they present the filter design for multiple component chirp signal separation. Moreover, the simulation results illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this stydy, the authors present a single image super‐resolution (SISR) reconstruction based on high‐order derivative interpolation (HDI) in the fractional Fourier transform (FRFT) domain. First, the HDI formula is derived using a simple technique, which is based on the relationship between the fractional band‐limited signal and the traditional band‐limited signal. This interpolation formula contains the derivative information of the image and the FRFT domain filter functions (FDFF). Moreover, the advantages of the FDFF are also analysed. Second, the new SISR reconstruction is presented via the HDI. The main advantage is that the presented method involves the derivatives of an image in the resizing process. Moreover, the authors take advantage of the FDFF to resize the image. Furthermore, three evaluation criteria and some simulations are presented to validate the effectiveness of the proposed method. Last, the proposed method is applied to colour image processing. For a colour image case, the RGB colour space is chosen for super‐resolution reconstruction. In addition to peak signal‐to‐noise ratio, the authors have also used the correlation to assess the quality of the reconstruction. Compared with many methods, extensive experimental results validate that the proposed method can obtain the better‐edge characteristic, less blur and less aliasing. [ABSTRACT FROM AUTHOR]