The accelerated acquisition of multidimensional NMR spectra using sparse non-uniform sampling (NUS) has been widely adopted in recent years. The key concept in NUS is that a major part of the data is omitted during measurement, and then reconstructed using, for example, compressed sensing (CS) methods. CS requires spectra to be compressible, that is, they should contain relatively few “significant” points. The more compressible the spectrum, the fewer experimental NUS points needed in order for it to be accurately reconstructed. In this paper we show that the CS processing of similar spectra can be enhanced by reconstructing only the differences between them. Accurate reconstruction can be obtained at lower sampling levels as the difference is sparser than the spectrum itself. In many situations this method is superior to “conventional” compressed sensing. We exemplify the concept of “difference CS” with one such case—the study of alpha-synuclein binding to liposomes and its dependence on temperature. To obtain information on temperature-dependent transitions between different states, we need to acquire several dozen spectra at various temperatures, with and without the presence of liposomes. Our detailed investigation reveals that changes in the binding modes of the alpha-synuclein ensemble are not only temperature-dependent but also show non-linear behavior in their transitions. Our proposed CS processing approach dramatically reduces the number of NUS points required and thus significantly shortens the experimental time.

近年来，使用稀疏非均匀采样（NUS）加速采集多维核磁共振谱已被广泛采用。NUS 的关键概念是在测量过程中省略大部分数据，然后使用压缩感知 (CS) 等方法进行重建。CS 要求谱是可压缩的，也就是说，它们应该包含相对较少的“重要”点。频谱的可压缩性越高，准确重建频谱所需的实验 NUS 点就越少。在本文中，我们表明，可以通过仅重建相似光谱之间的差异来增强相似光谱的 CS 处理。由于差异比频谱本身更稀疏，因此可以在较低的采样级别获得准确的重建。在许多情况下，这种方法优于“传统”压缩感知。我们用一个这样的案例来举例说明“差异CS”的概念——研究α-突触核蛋白与脂质体的结合及其对温度的依赖性。为了获得不同状态之间温度依赖性转变的信息，我们需要在有或没有脂质体存在的情况下获得不同温度下的几十个光谱。我们的详细研究表明，α-突触核蛋白整体的结合模式的变化不仅取决于温度，而且在转变中表现出非线性行为。我们提出的 CS 处理方法极大地减少了所需的 NUS 点数，从而显着缩短了实验时间。