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The application of multiwavelet filterbanks to image processing

机译:多小波滤波器组在图像处理中的应用

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Multiwavelets are a new addition to the body of wavelet theory. Realizable as matrix-valued filterbanks leading to wavelet bases, multiwavelets offer simultaneous orthogonality, symmetry, and short support, which is not possible with scalar two-channel wavelet systems. After reviewing this theory, we examine the use of multiwavelets in a filterbank setting for discrete-time signal and image processing. Multiwavelets differ from scalar wavelet systems in requiring two or more input streams to the multiwavelet filterbank. We describe two methods (repeated row and approximation/deapproximation) for obtaining such a vector input stream from a one-dimensional (1-D) signal. Algorithms for symmetric extension of signals at boundaries are then developed, and naturally integrated with approximation-based preprocessing. We describe an additional algorithm for multiwavelet processing of two-dimensional (2-D) signals, two rows at a time, and develop a new family of multiwavelets (the constrained pairs) that is well-suited to this approach. This suite of novel techniques is then applied to two basic signal processing problems, denoising via wavelet-shrinkage, and data compression. After developing the approach via model problems in one dimension, we apply multiwavelet processing to images, frequently obtaining performance superior to the comparable scalar wavelet transform.
机译:多小波是对小波理论的新补充。多小波可实现为导致小波基的矩​​阵值滤波器组,同时提供正交性,对称性和短支持,这是标量两通道小波系统无法实现的。在回顾了这一理论之后,我们研究了在滤波器组设置中多小波对离散时间信号和图像处理的使用。多小波与标量小波系统的不同之处在于,需要两个或更多输入流到多小波滤波器组。我们描述了两种用于从一维(1-D)信号中获得矢量输入流的方法(重复行和逼近/解逼近)。然后开发了边界处信号的对称扩展算法,并自然地与基于近似的预处理集成在一起。我们描述了一种用于二维(2-D)信号的多小波处理的附加算法,一次处理两行,并开发了一种新的多小波族(受约束的对),非常适合这种方法。然后将这套新颖的技术应用于两个基本的信号处理问题,即通过小波收缩和数据压缩进行降噪。在通过一维模型问题开发了方法之后,我们将多小波处理应用于图像,经常获得优于可比标量小波变换的性能。

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