论文标题
基于量子力学的信号和图像表示：应用
Quantum mechanics-based signal and image representation: application to denoising
论文作者
论文摘要
在信号，图像处理和分析中，将数字信号和图像分解为其他基础或字典是一种非常普遍的方法。这种分解通常是使用固定变换（例如傅立叶或小波）或从示例数据库或信号或图像本身学到的字典获得的。在这项工作中，我们详细研究了一种新的方法，该方法构建了受量子力学工具启发的信号或图像依赖性基础，即通过将信号或图像视为离散化的Schroedinger方程中的潜力。为了说明所提出的分解的潜力，在高斯，泊松和斑点噪声的情况下报道了脱糖性结果，并将基于小波收缩，总变化正则化或斑点稀疏编码的最新算法，非局限性的图像denoising和图形信号处理进行比较。
Decomposition of digital signals and images into other basis or dictionaries than time or space domains is a very common approach in signal and image processing and analysis. Such a decomposition is commonly obtained using fixed transforms (e.g., Fourier or wavelet) or dictionaries learned from example databases or from the signal or image itself. In this work, we investigate in detail a new approach of constructing such a signal or image-dependent bases inspired by quantum mechanics tools, i.e., by considering the signal or image as a potential in the discretized Schroedinger equation. To illustrate the potential of the proposed decomposition, denoising results are reported in the case of Gaussian, Poisson, and speckle noise and compared to the state of the art algorithms based on wavelet shrinkage, total variation regularization or patch-wise sparse coding in learned dictionaries, non-local means image denoising, and graph signal processing.
