The signal reconstruction problem (SRP) is an important optimization problem where the objective is to identify a solution to an under-determined system of linear equations AX = b that is closest to a given prior. It has a substantial number of applications in diverse areas including network traffic engineering, medical image reconstruction, acoustics, astronomy and many more. Most common approaches for solving SRP do not scale to large problem sizes. In this paper, we propose a dual formulation of this problem and show how adapting database techniques developed for scalable similarity joins provides a significant speedup when the A matrix is sparse and binary. Extensive experiments on real-world and synthetic data show that our approach produces a significant speedup of up to 20x over competing approaches.

中文翻译：

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适用于广泛应用的高效信号重构

信号重建问题 (SRP) 是一个重要的优化问题，其目标是确定最接近给定先验的未定线性方程组 AX = b 的解。它在网络流量工程、医学图像重建、声学、天文学等不同领域有大量应用。解决 SRP 的最常见方法不能扩展到大型问题。在本文中，我们提出了这个问题的双重表述，并展示了当 A 矩阵是稀疏和二元矩阵时，为可扩展相似性连接开发的适应数据库技术如何提供显着的加速。对真实世界和合成数据的广泛实验表明，我们的方法比竞争方法产生了高达 20 倍的显着加速。