Directional Lapped Orthogonal Transform: Theory and Design
Directional Lapped Orthogonal Transform: Theory and Design
复制标题
DOI：
10.1109/tip.2011.2182055
复制
发表时间：
2012-05
影响因子：
10.6
通讯作者：
S. Muramatsu;Dandan Han;Tomoya Kobayashi;H. Kikuchi
中科院分区：
文献类型：
--
作者：
S. Muramatsu;Dandan Han;Tomoya Kobayashi;H. Kikuchi
提出了一种二维不可分线性相位准酉滤波器组的定向设计方法。该方法基于二维可分离DCT块和不可分离支撑扩展过程组成的点阵结构。由于不可分性，基被允许具有严格固定的子采样、重叠、正交、对称、实值和紧支持性质的定向。首先，引入一种新的消失力矩（VM）条件作为合适的方向约束，其中的消失力矩称为趋势VM。这种情况迫使小波滤波器，即高通和带通滤波器，消除趋势面分量。其次，讨论了一般二维准系统的tvm的一些理论性质，并将这些性质应用于晶格参数。为了验证其意义，给出了几个设计实例，数值验证了趋势面湮灭特性，并通过收缩评价了图像的去噪能力。结果表明，我们提出的变换产生了感知上较好的结果。
This paper proposes a directional design method of 2-D nonseparable linear-phase paraunitary filter banks. The proposed method is based on a lattice structure consisting of the 2-D separable DCT block and nonseparable support extension processes. Because of the nonseparability, the bases are allowed to be directional with the critically fixed subsampling, overlapping, orthogonal, symmetric, real-valued, and compact support properties. First, a novel vanishing moment (VM) condition is introduced as a suitable directional constraint, where the moment is referred to as the trend VM. The condition forces wavelet filters, i.e., high-pass and bandpass filters, to annihilate trend-surface components. Second, some theoretical properties of TVMs are discussed for general 2-D paraunitary systems, and then, the properties are applied to the lattice parameters. In order to verify the significance, several design examples are shown, the trend-surface annihilation properties are numerically confirmed, and the denoising capability is evaluated for images through shrinkage. It is shown that our proposed transforms yield perceptually preferable results.