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Data-Driven Forward-Backward Pursuit for Sparse Signal Reconstruction

机译：数据驱动的前向后追求的稀疏信号重构

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摘要

In recent years, compressed sensing has received considerable attention from the signal processing community because of its ability to represent sparse signals with a number of samples much less than that is required by the Nyquist sampling theorem. -minimization is a powerful tool for sparse signal reconstruction from few measured samples, but its computational complexity is a burden for real applications. Recently, a number of greedy algorithms based on orthogonal matching pursuit (OMP) have been proposed, and they have near -minimization performance with much less processing time. In this work, a new OMP-type two-stage sparse signal reconstruction algorithm, namely data-driven forward-backward pursuit (DD-FBP), is proposed. It is based on a former work called forward-backward pursuit (FBP). DD-FBP iteratively expands and shrinks the estimated support set, and these constitute the forward and backward stages. In DD-FBP, unlike FBP, the forward and backward step sizes are not constants, but they are dependent on the correlation and projection values, respectively, which are calculated in each iteration. The recovery performance by using noiseless and noisy sparse signal ensembles, as well as a natural sparse image, indicates that DD-FBP surpasses the other methods in terms of success rate and processing time.
机译：近年来，压缩感测由于其能够以比Nyquist采样定理所要求的数量少得多的样本表示稀疏信号的能力而受到信号处理界的广泛关注。 -minimization是从少量测量样本中重建稀疏信号的强大工具，但其计算复杂性是实际应用的负担。最近，已经提出了许多基于正交匹配追踪（OMP）的贪婪算法，它们具有接近最小化的性能，并且处理时间更少。在这项工作中，提出了一种新的OMP型两阶段稀疏信号重构算法，即数据驱动的前后跟踪（DD-FBP）。它基于以前的工作称为前向后向追踪（FBP）。 DD-FBP迭代地扩展和收缩估计的支持集，这些构成了前进和后退阶段。在DD-FBP中，与FBP不同，前进和后退步长不是常数，而是分别取决于在每次迭代中计算的相关值和投影值。通过使用无噪声和有噪声的稀疏信号集合的恢复性能以及自然的稀疏图像，表明DD-FBP在成功率和处理时间方面超过了其他方法。

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