A fast algorithm based on the gray code kernel (GCK) for computing the conjugate symmetric sequency-ordered complex Hadamard transform (CS-SCHT) in a sliding window is presented. The proposed algorithm computes the current projection value from the previously computed ones. In order to obtain the peculiar computation order of the projection values, we construct the CS-SCHT matrix tree and also introduce the $\alpha $ -related concept. The properties of the elements of the CS-SCHT matrix are also given for deriving the GCK sliding CS-SCHT algorithm. The proposed algorithm only needs N/2+log $_{2}N-2$ (or log $_{2}N-1$ ) multiplications with $j$ and $4N-2$ (or $2N-1$ ) real additions for complex (or real) input data, which is more efficient than the block-based CS-SCHT and other existing sliding complex transform algorithms, such as the radix-4 sliding CS-SCHT algorithm, sliding FFT algorithm, and sliding DFT algorithm. A comparison of the proposed algorithm with other sliding transforms in terms of computation time is also presented to validate the theoretical results.

Fast Gray Code Kernel Algorithm for the Sliding Conjugate Symmetric Sequency-Ordered Complex Hadamard Transform

The invention discloses an image copy and paste tampering detection method based on two-dimensional sliding window DFT fast calculation. The features of a tampered image are extracted by employing a multipoint sliding window DFT (Discrete Fourier Transform) fast algorithm, tampered pixel positions are detected, and a feature extraction speed and the detection quality are analyzed. By adoption of the method, a detection method combining a multipoint sliding window DFT algorithm with a single-point sliding window DFT algorithm is provided to achieve better balance between the detection speed and the detection quality. Under normal circumstances, in order to ensure the integrity of the image, tampering mainly focuses on local variation, and otherwise tampering traces can be found easily via intuitive vision. When the proportion of the tampered part of the image in the entire image is not large, the calculated amount of the improved detection method provided by the invention has relatively high computational efficiency.

Image tampering detection method based on two-dimensional sliding window DFT fast calculation

Discrete Fourier transform (DFT) is one of the most wildly used tools for signal processing. In this paper, a novel sliding window algorithm is presented for fast computing 2D DFT when sliding window shifts more than one-point. The propose algorithm computing the DFT of the current window using that of the previous window. For fast computation, we take advantage of the recursive process of 2D SDFT and butterfly-based algorithm. So it can be directly applied to 2D signal processing. The theoretical analysis shows that the computational complexity is equal to 2D SDFT when one sample comes into current window. As well, the number of additions and multiplications of our proposed algorithm are less than those of 2D vector radix FFT when sliding window shifts mutiple-point.

A novel sliding window algorithm for 2D discrete Fourier transform

The invention discloses a high-speed algorithm of multi-point sliding two-dimensional sliding window DFT. For a M*M sliding window, when L new points slide into the current window, the DFT of the current window is calculated by utilizing the relationship between the DFTs of the current window and previous L windows. Specifically, the two-dimensional data of the L new points sliding into the current window is converted into two one-dimensional transformations, wherein one of the one-dimensional transformations is calculated by using a butterfly structure and the other one is calculated by using an iterative structure. The algorithm provided by the invention can greatly reduce the calculation amount of the sliding window DFT; when the window size is 16*16 and the sliding point number L=8, the calculation amount of additions is reduced by 61.4% and the calculation amount of multiplications is reduced by 78.4% as the algorithm is compared with the two-dimensional vector radix method. 2-D SDF and MFFT are both implemented with single-point sliding window calculation, and when multiple points slide in, multiple calculations are required, so that the calculation amounts of these methods are greatly higher than that of the algorithm provided in the invention.

Jiasong Wu

Papers

A novel sliding window algorithm for 2D discrete Fourier transform

High-speed algorithm of multi-point sliding two-dimensional sliding window DFT