Data adaptive multi-scale representations for image analysis
Data adaptive multi-scale representations for image analysis
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DOI：
10.1117/12.2529695
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发表时间：
2019-09
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影响因子：
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通讯作者：
Julia A. Dobrosotskaya;Weihong Guo
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文献类型：
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作者：
Julia A. Dobrosotskaya;Weihong Guo
数据自适应紧框架方法已被证明是一个强大的稀疏近似工具，在各种设置。我们介绍了一个模型的数据自适应表示，也提供了一个多尺度的结构。我们的想法是为给定的数据集设计一个多尺度框架表示，具有类似于小波基的缩放特性，但没有必要的自相似结构。自适应性提供了更好的稀疏性，使用Besov样范数结构既诱导稀疏性，又有助于识别重要特征。我们专注于调查的效率加权l1约束的背景下稀疏恢复噪声数据和比较它的加权l0模型旁边。数值实验证实，恢复的帧向量分配较低的权重对应于较大规模和较低的局部变化的图像元素，从而表明在自然图像中的加权稀疏导致自然的尺度分离。
Data adaptive tight frame methods have been proven a powerful sparse approximation tool in a variety of settings. We introduce a model of a data adaptive representation that also provides a multi-scale structure. Our idea is to design a multi-scale frame representation for a given data set, with scaling properties similar to the ones of a wavelet basis, but without the necessary self-similar structure. The adaptivity provides better sparsity properties, using Besov-like norm structure both induces sparsity and helps in identifying important features. We focus on investigating the efficiency of a weighted l1 constraint in the context of sparse recovery from noisy data and compare it to the weighted l0 model alongside. Numerical experiments confirm that the recovered frame vectors assigned lower weights correspond to image elements of larger scale and lower local variation, thus indicating that weighted sparsity in natural images leads to a natural scale separation.