2D Discrete Mirror Transform for Image Non-Linear Approximation

Alessandro Gnutti, Fabrizio Guerrini, R. Leonardi
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Abstract

In this paper, a new 2D transform named Discrete Mirror Transform (DMT) is presented. The DMT is computed by decomposing a signal into its even and odd parts around an optimal location in a given direction so that the signal energy is maximally split between the two components. After minimizing the information required to regenerate the original signal by removing redundant structures, the process is iterated leading the signal energy to distribute into a continuously smaller set of coefficients. The DMT can be displayed as a binary tree, where each node represents the single (even or odd) signal derived from the decomposition in the previous level. An optimized version of the DMT (ODMT) is also introduced, by exploiting the possibility to choose different directions at which performing the decomposition. Experimental simulations have been carried out in order to test the sparsity properties of the DMT and ODMT when applied on images: referring to both transforms, the results show a superior performance with respect to the popular Discrete Cosine Transform (DCT) and Discrete Wavelet Transform (DWT) in terms of non-linear approximation.
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二维离散镜像变换用于图像非线性逼近
提出了一种新的二维变换——离散镜像变换(DMT)。DMT是通过在给定方向上的最佳位置周围将信号分解为偶数和奇数部分来计算的,以便信号能量在两个分量之间最大限度地分配。通过去除冗余结构,将再生原始信号所需的信息最小化后,迭代该过程,使信号能量分布到一个连续较小的系数集合中。DMT可以显示为二叉树,其中每个节点表示从前一级分解中得到的单个(偶数或奇数)信号。通过利用选择执行分解的不同方向的可能性,还介绍了DMT (ODMT)的优化版本。为了测试DMT和ODMT在图像上应用时的稀疏性,进行了实验模拟:参考这两种变换,结果表明,在非线性近似方面,相对于流行的离散余弦变换(DCT)和离散小波变换(DWT),它们具有优越的性能。
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