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Split Bregman's Optimization Method for Image Construction in Compressive Sensing

机译:压缩感知中图像构造的Split Bregman优化方法

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The theory of compressive sampling (CS) was reintroduced by Candes, Romberg and Tao, and D. Donoho in 2006. Using a priori knowledge that a signal is sparse, it has been mathematically proven that CS can defy Nyquist sampling theorem. Theoretically, reconstruction of a CS image relies on the minimization and optimization techniques to solve this complex almost NP-complete problem. There are many paths to consider when compressing and reconstructing an image but these methods have remained untested and unclear on natural images, such as underwater sonar images. The goal of this research is to perfectly reconstruct the original sonar image from a sparse signal while maintaining pertinent information, such as mine-like object, in Side-scan sonar (SSS) images. Goldstein and Osher have shown how to use an iterative method to reconstruct the original image through a method called Split Bregman's iteration. This method "decouples" the energies using portions of the energy from both the l_1 and l_2 norm. Once the energies are split, Bregman iteration is used to solve the unconstrained optimization problem by recursively solving the problems simultaneously. The faster these two steps or energies can be solved then the faster the overall method becomes. While the majority of CS research is still focused on the medical field, this paper will demonstrate the effectiveness of the Split Bregman's methods on sonar images.
机译:Candes,Romberg和Tao和D.Donoho于2006年重新引入了压缩采样(CS)的理论。使用先验知识即信号稀疏,已在数学上证明了CS可以克服Nyquist采样定理。从理论上讲,CS图像的重建依赖于最小化和优化技术来解决这个复杂的几乎是NP完全的问题。在压缩和重建图像时,有许多路径需要考虑,但是这些方法在自然图像(例如水下声纳图像)上仍未经测试和不清楚。这项研究的目的是从稀疏信号中完美地重建原始声纳图像,同时在侧向扫描声纳(SSS)图像中保持相关信息(如类地物体)。 Goldstein和Osher展示了如何通过称为Split Bregman迭代的方法使用迭代方法重建原始图像。该方法使用来自l_1和l_2范数的能量的一部分来“解耦”能量。一旦能量被分割,Bregman迭代将通过同时递归求解问题来解决无约束优化问题。可以更快地解决这两个步骤或能量,然后整个方法就变得越快。尽管大多数CS研究仍集中在医学领域,但本文将证明Split Bregman方法在声纳图像上的有效性。

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