PS-Wavelet: A Novel Cubic Polishing Spline Wavelet for Image Processing

Image processing, especially industrial image processing, plays an important role in the fourth industrial revolution. Wavelet transform as a powerful image processing algorithm enables local features and provides multiscale analysis. To explore an efficient image processing algorithm, this article proposes a novel cubic polishing spline wavelet (PS-wavelet). First, we propose the two-scaling functions and the multiresolution analysis of the cubic polishing spline and provide corresponding proof. Then, we propose the expression of the PS-wavelet, along with the corresponding coefficients of the decomposition and reconstruction filters. These filters play a crucial role in efficient decomposition and reconstruction algorithms. Next, we provide a crucial properties analysis of the PS-wavelet, namely the order of approximation, vanishing moments, and symmetry. Finally, we propose an efficient PS-wavelet algorithm based on the two-channel filters for image decomposition and reconstruction as well as image denoising. To evaluate the performance of PS-wavelet, we conduct several experiments on image decomposition and reconstruction, and image denoising. Experimental results demonstrate that compared with other existing wavelet algorithms, the PS-wavelet has good performance in terms of image quality indicators, and indicates the effectiveness of the PS-wavelet in image reconstruction and image denoising.