Iterative algorithm of discrete Fourier transform for processing randomly sampled NMR data sets

Abstract

Spectra obtained by application of multidimensional Fourier Transformation (MFT) to sparsely sampled nD NMR signals are usually corrupted due to missing data. In the present paper this phenomenon is investigated on simulations and experiments. An effective iterative algorithm for artifact suppression for sparse on-grid NMR data sets is discussed in detail. It includes automated peak recognition based on statistical methods. The results enable one to study NMR spectra of high dynamic range of peak intensities preserving benefits of random sampling, namely the superior resolution in indirectly measured dimensions. Experimental examples include 3D (15)N- and (13)C-edited NOESY-HSQC spectra of human ubiquitin.

Sparse multidimensional iterative lineshape-enhanced (SMILE) reconstruction of both non-uniformly sampled and conventional NMR data

“…Although conceptually the SMILE algorithm is analogous to the SSA method (Stanek and Kozminski 2010; Stanek et al 2012), the actual implementation is quite different and represents a compromise between processing speed and optimal reconstruction. For example, SSA defines a sophisticated multidimensional peak boundary and then performs a least squares nonlinear fitting or, for overlapping peaks, a Hilbert Transform followed by an inverse FT to obtain the corresponding time-domain signal.…”

“…The aim of these, and a host of other algorithms that have been demonstrated for NMR applications, is to minimize either the l 1, l 2 or Gaussian l 0 norm of the frequency domain (Stern et al 2007; Stern and Hoch 2015; Sun et al 2015). Other intuitively appealing methods are based on an iterative algorithm to stepwise remove the point-spread function (PSF) artifacts caused when a regular FT is applied to a matrix where the not-sampled, on-grid data points have simply been replaced by zeros, one effective example being the Signal Separation Algorithm (SSA) (Stanek and Kozminski 2010). Alternatively, removal of PSF artifacts in the frequency domain can be accomplished by iterative algorithms such as FFT-CLEAN (Coggins and Zhou 2008; Werner-Allen et al 2010) and SCRUB (Coggins et al 2012), the latter being particularly effective for highly sparse data.…”

“…A second aim is to provide output data that remain visually as close as possible to the appearance of regular fully sampled FT data, without non-linear treatment of noise. In spirit, SMILE is closest to the SSA algorithm (Stanek and Kozminski 2010), but the actual implementation is rather different in terms of peak detection and reconstruction, and takes advantage of the fact that NMR spectra can be phased to become purely absorptive. Taking advantage of this phase information has been used previously to enhance the results of linear prediction algorithms (Zhu and Bax 1990), and for constructing a “virtual echo” which was shown to benefit a range of sparse data reconstruction methods (Mayzel et al 2014).…”

A comparison of convex and non-convex compressed sensing applied to multidimensional NMR

“…It was proven to be mathematically equivalent to the conjugate gradient search of (4) [27]. Notably, IST is somewhat similar (although not fully equivalent) to artifact cleaning algorithms applied recently in NMR [29][30][31]. An important subgroup of CS algorithms aims at the reduction of sampling requirements imposed by the minimal ' 1 -norm solution of Eqs.…”

The solution structure of the MANEC-type domain from hepatocyte growth factor activator inhibitor-1 reveals an unexpected PAN/apple domain-type fold

“…Chemical shifts of 13 C and 15 N signals were referenced indirectly using the 0.251449530 and 0.101329118 frequency ratios for 13 C/ 1 H and 15 N/ 1 H, respectively [18]. The 2D and conventionallysampled 3D experiments were processed with NMRpipe [16], 3D and 4D NUS experiments were processed by SSA software package available at http://nmr.cent3.uw.edu.pl/software [19][20][21]. Processed spectra were analysed with SPARKY [17].…”