This paper investigates the potential applications of a parametric family of polynomial wavelets that has been recently introduced starting from de la Vall\'ee Poussin (VP) interpolation at Chebyshev nodes. Unlike classical wavelets, which are constructed on the real line, these VP wavelets are defined on a bounded interval, offering the advantage of handling boundaries naturally while maintaining computational efficiency. In fact, the structure of these wavelets enables the use of fast algorithms for decomposition and reconstruction. Furthermore, the flexibility offered by a free parameter allows a better control of localized singularities, such as edges in images. On the basis of previous theoretical foundations, we show the effectiveness of the VP wavelets for basic signal denoising and image compression, emphasizing their potential for more advanced signal and image processing tasks.

翻译：本文研究了一种基于切比雪夫节点 de la Vallée Poussin (VP) 插值最近提出的参数化多项式小波族的潜在应用。与在实轴上构造的经典小波不同，这些 VP 小波定义在有界区间上，其优势在于能够自然地处理边界问题，同时保持计算效率。事实上，这些小波的结构使得能够使用快速算法进行分解与重构。此外，通过一个自由参数提供的灵活性，可以更好地控制局部奇异性，例如图像中的边缘。基于先前的理论基础，我们展示了 VP 小波在基本信号去噪和图像压缩方面的有效性，并强调了其在更高级的信号与图像处理任务中的潜力。