Wave atoms and sparsity of oscillatory patterns
Wave atoms and sparsity of oscillatory patterns
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DOI：
10.1016/j.acha.2007.03.003
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发表时间：
2007-11
影响因子：
2.5
通讯作者：
L. Demanet;Lexing Ying
中科院分区：
文献类型：
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作者：
L. Demanet;Lexing Ying
我们引入“波原子”作为服从抛物线缩放波长（直径）2的二维小波包的变体。我们证明，翘曲振荡函数，玩具模型的纹理，有一个显着稀疏的膨胀波原子比其他固定的标准表示，如小波，Gabor原子，或curvelets。我们提出了一种新的算法，一个紧密的框架波原子与冗余2，直接在频率平面上，通过“包裹”技术。我们还提出了在图像处理中的应用程序的基本变换的变种，包括一个正交基，和一个移位不变的紧框架冗余四。地震和指纹图像的稀疏性和去噪实验证明了该工具的潜力。
We introduce “wave atoms” as a variant of 2D wavelet packets obeying the parabolic scaling wavelength∼(diameter)2. We prove that warped oscillatory functions, a toy model for texture, have a significantly sparser expansion in wave atoms than in other fixed standard representations like wavelets, Gabor atoms, or curvelets. We propose a novel algorithm for a tight frame of wave atoms with redundancy two, directly in the frequency plane, by the “wrapping” technique. We also propose variants of the basic transform for applications in image processing, including an orthonormal basis, and a shift-invariant tight frame with redundancy four. Sparsity and denoising experiments on both seismic and fingerprint images demonstrate the potential of the tool introduced.