Stepien et al. [6] utilized the lifting Pacritinib phase 3 wavelet Inhibitors,Modulators,Libraries to decompose experimental signals containing noise and performed soft-threshold denoising, with the standard peak signal-to-noise ratio as performance indicator to test the denoising effect. Li et al. [7] obtained a way to select optimal operators under two constraint conditions and the principles of both maximization of wavelet coefficients’ kurtosis and minimization of reconstruction error, then followed by the improved intra- and intra-scale dependency denoising algorithm to complete bearing fault diagnosis. Bao et al. [8] proposed an anti-aliasing redundant lifting transform to identify the states of both ball bearings and value trains under different working conditions in a gasoline engine. Lee et al.
[9] presented a method for short-term load forecasting based on a lifting scheme and autoregressive integrated moving average models, which consists of three steps: original load series decomposed by the lifting scheme, sub-series forecasted with ARIMA models and forecasting result reconstruction. Amiri et al. [10] discussed an adaptive lifting algorithm. With the dual Inhibitors,Modulators,Libraries lifting step and the aim to remove the corresponding coefficients in the high-pass component, a linear system of equations was deduced and also solved by the Gaussian elimination algorithm, and this method was then used to detect the interesting components in 2D images. Quellec et al. [11] introduced the nonseparable lifting scheme framework to adaptively design a multidimensional wavelet filter bank.
For the existing Neville filter based on prediction and updating, the additional design degrees of freedom are used to modify a wavelet which was then adapted to specific problems. Based on the adaptive directional wavelet lifting theories, Wang et al. [12] proposed a robust methodology involving image pixel classification, Inhibitors,Modulators,Libraries robust orientation estimation and optimal transform strategy for improvement, which was later used to denoise a set of standard 8-bit grey-scale images and achieved better PSNR and visual effects. From the above review it can be seen that much attention has been paid to the theoretical and application research of lifting schemes. However, the existing research is mainly focused on symmetrical wavelets constructed with interpolation algorithms.
Though the linear phase of filters can be ensured by the symmetry of wavelets to avoid or minimize the phase distortion during signal processing, there is still a problem: how to flexibly and easily construct wavelets with a lifting algorithm Inhibitors,Modulators,Libraries to implement the idea of obtaining Anacetrapib wavelets with desired characteristics through the design of the Vandetanib solubility lifting operator, while also realizing effective feature extraction of various complicated practical signals, which has been a major difficulty to be resolved.