Reversible Information of Encrypted Image Based on Feature Difference Detection and Wavelet Transform

Aiming at the shortcomings of the existing lossless digital watermarking algorithm based on frequency domain in reversibility and embedding capacity, this study proposes a lossless digital image watermarking algorithm based on fractional wavelet transform, which is used for large-capacity reversible information hiding of images. First, the image is transformed by LeGall5/3 fractional wavelet, and then, the watermark is embedded in the high-frequency subband by the histogram shift method. In order to obtain maximum embedding capacity and reduce image distortion, the methods of selecting embedding parameters and stopping parameters are proposed, respectively. At the same time, in order to prevent overflow and reduce additional information, a new method of generating position map is proposed. The experimental results show that Lena is the result of multilayer embedding based on the algorithm in this study. In order to better observe the distortion phenomenon and enlarge the image, the Lena test image is the watermark image obtained after two and three layers of embedding, and its embedding capacity can be 2.7 bpp. It is proved that wavelet transform is suitable for encrypted images to implement covert communication.

A note on continuous fractional wavelet transform in ℝn

In this paper, we study the continuous fractional wavelet transform (CFrWT) in [Formula: see text]-dimensional Euclidean space [Formula: see text] with scaling parameter [Formula: see text] such that [Formula: see text]. We obtain inner product relation and reconstruction formula for the CFrWT depending on two wavelets along with the reproducing kernel function, involving two wavelets, for the image space of CFrWT. We obtain Heisenberg’s uncertainty inequality and Local uncertainty inequality for the CFrWT. Finally, we prove the boundedness of CFrWT on the Morrey space [Formula: see text] and estimate [Formula: see text]-distance of the CFrWT of two argument functions with respect to different wavelets.

Forecasting Daily Electricity Price by Hybrid Model of Fractional Wavelet Transform, Feature Selection, Support Vector Machine and Optimization Algorithm

This paper proposes a novel hybrid forecasting model with three main parts to accurately forecast daily electricity prices. In the first part, where data are divided into high- and low-frequency data using the fractional wavelet transform, the best data with the highest relevancy are selected, using a feature selection algorithm. The second part is based on a nonlinear support vector network and auto-regressive integrated moving average (ARIMA) method for better training the previous values of electricity prices. The third part optimally adjusts the proposed support vector machine parameters with an error-base objective function, using the improved grey wolf and particle swarm optimization. The proposed method is applied to forecast electricity markets, and the results obtained are analyzed with the help of the criteria based on the forecast errors. The results demonstrate the high accuracy in the MAPE index of forecasting the electricity price, which is about 91% as compared to other forecasting methods.

On the Multilinear Fractional Transforms

In this paper we first introduce multilinear fractional wavelet transform on Rn×R+n using Schwartz functions, i.e., infinitely differentiable complex-valued functions, rapidly decreasing at infinity. We also give multilinear fractional Fourier transform and prove the Hausdorff–Young inequality and Paley-type inequality. We then study boundedness of the multilinear fractional wavelet transform on Lebesgue spaces and Lorentz spaces.

Certain properties of continuous fractional wavelet transform on Hardy space and Morrey space

In this paper we define a new class of continuous fractional wavelet transform (CFrWT) and study its properties in Hardy space and Morrey space. The theory developed generalize and complement some of already existing results.