Modern scientific instruments produce vast amounts of data, which can overwhelm the processing ability of computer systems. Lossy compression of data is an intriguing solution, but comes with its own drawbacks, such as potential signal loss, and the need for careful optimization of the compression ratio. In this work, we focus on a setting where this problem is especially acute: compressive sensing frameworks for interferometry and medical imaging. We ask the following question: can the precision of the data representation be lowered for all inputs, with recovery guarantees and practical performance? Our first contribution is a theoretical analysis of the normalized Iterative Hard Thresholding (IHT) algorithm when all input data, meaning both the measurement matrix and the observation vector are quantized aggressively. We present a variant of low precision normalized IHT that, under mild conditions, can still provide recovery guarantees. The second contribution is the application of our quantization framework to radio astronomy and magnetic resonance imaging. We show that lowering the precision of the data can significantly accelerate image recovery. We evaluate our approach on telescope data and samples of brain images using CPU and FPGA implementations achieving up to a 9x speed-up with negligible loss of recovery quality.

中文翻译：

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使用具有低精度数据表示的迭代硬阈值进行压缩感知：理论与应用

现代科学仪器会产生大量数据，这些数据可能会压倒计算机系统的处理能力。数据的有损压缩是一种有趣的解决方案，但也有其自身的缺点，例如潜在的信号损失，以及需要仔细优化压缩比。在这项工作中，我们专注于这个问题特别严重的环境：用于干涉测量和医学成像的压缩传感框架。我们提出以下问题：是否可以降低所有输入的数据表示的精度，同时保证恢复和实际性能？我们的第一个贡献是对所有输入数据（即测量矩阵和观测向量都被积极量化）时归一化迭代硬阈值 (IHT) 算法的理论分析。我们提出了一种低精度归一化 IHT 的变体，它在温和的条件下仍然可以提供恢复保证。第二个贡献是我们的量化框架在射电天文学和磁共振成像中的应用。我们表明，降低数据的精度可以显着加速图像恢复。我们使用 CPU 和 FPGA 实现在望远镜数据和大脑图像样本上评估我们的方法，实现了高达 9 倍的加速，而恢复质量的损失可以忽略不计。