基于噪声随机投影的蛋白质结构稀疏近似
Sparse approximations of protein structure from noisy random projections
摘要：
单粒子电子显微镜是一种现代技术，生物学家用来了解蛋白质的结构。它产生的数据由蛋白质结构在随机方向上的噪声随机投影组成，增加了投影角度无法观察的复杂性。为了重建三维模型，需要通过使用未知粒子的ad-hoc起始估计来估计投影方向。在本文中，我们提出了一种方法，不依赖于知识的投影角度，构建一个客观的数据依赖的低分辨率近似的未知结构，可以作为这样的起始估计。该方法假设蛋白质承认一个合适的稀疏表示，并采用离散$L^1$ -正则化（LASSO）以及形状理论的概念，以解决相关的逆问题所涉及的特殊挑战。我们举例说明的方法，通过应用程序的重建的E。大肠杆菌蛋白质组分称为Klenow片段。
英文摘要：
Single-particle electron microscopy is a modern technique that biophysicists employ to learn the structure of proteins. It yields data that consist of noisy random projections of the protein structure in random directions, with the added complication that the projection angles cannot be observed. In order to reconstruct a three-dimensional model, the projection directions need to be estimated by use of an ad-hoc starting estimate of the unknown particle. In this paper we propose a methodology that does not rely on knowledge of the projection angles, to construct an objective data-dependent low-resolution approximation of the unknown structure that can serve as such a starting estimate. The approach assumes that the protein admits a suitable sparse representation, and employs discrete $L^1$-regularization (LASSO) as well as notions from shape theory to tackle the peculiar challenges involved in the associated inverse problem. We illustrate the approach by application to the reconstruction of an E. coli protein component called the Klenow fragment.
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