Convex accelerated maximum entropy reconstruction

Abstract

Maximum entropy (MaxEnt) spectral reconstruction methods provide a powerful framework for spectral estimation of nonuniformly sampled datasets. Many methods exist within this framework, usually defined based on the magnitude of a Lagrange multiplier in the MaxEnt objective function. An algorithm is presented here that utilizes accelerated first-order convex optimization techniques to rapidly and reliably reconstruct nonuniformly sampled NMR datasets using the principle of maximum entropy. This algorithm – called CAMERA for Convex Accelerated Maximum Entropy Reconstruction Algorithm – is a new approach to spectral reconstruction that exhibits fast, tunable convergence in both constant-aim and constant-lambda modes. A high-performance, open source NMR data processing tool is described that implements CAMERA, and brief comparisons to existing reconstruction methods are made on several example spectra.

Subrandom methods for multidimensional nonuniform sampling

“…Two previously described uniformly collected datasets, a 1 H- 15 N HSQC and an HNCA, were used in the computations [31]. For each one-dimensional schedule, the HSQC dataset was subsampled and reconstructed using 500 iterations of convex accelerated maximum entropy reconstruction (CAMERA) [14] in the MINT regime. For each two-dimensional schedule, the HNCA was also subsampled and reconstructed using the same parameters.…”

“…Consequently, non-Fourier methods of spectrum analysis must be employed to reconstruct the missing time-domain information in NUS datasets. Popular methods include maximum entropy (MaxEnt) estimation or interpolation [5, 12–14], iterative soft thresholding (IST) and its accelerated equivalent NESTA [15, 16], and multidimensional decomposition [17, 18]. Each method approaches the problem of spectrum estimation using a slightly different mathematical model, but all attempt the same result: deconvolution of the sampling schedule’s PSF from the measured data to yield the complete dataset.…”

Interpolating and extrapolating with hmsIST: seeking a tmax for optimal sensitivity, resolution and frequency accuracy

“…Programs written to reconstruct NUS data utilize a number of different algorithms. These algorithms are either based on Claude Shannon’s work (Shannon 1948) on Maximum Entropy reconstruction (MaxEnt) (Balsgart and Vosegaard 2012; Delsuc and Mallavin 1998; Donoho et al 1992; Hoch and Stern 1996; Hyberts et al 2007; Laue et al 1985; Paramasivam et al 2012; Worley 2016), on Jan Högbom’s work (Hogbom 1974) in the CLEAN algorithm (Coggins and Zhou 2008; Kupce and Freeman 2005; Matsuki et al 2009), work by (Candes and Walkin 2008; Donoho 2006; Drori 2007) on Compressed Sensing (Holland et al 2011; Hyberts et al 2012; Kazimierczuk and Orekhov 2011; Stern et al 2007; Sun et al 2015), or, by signal or vector decomposition (Mandelshtam et al 1998; Orekhov et al 2001; Orekhov and Jaravine 2011). Alternatively the NUS obtained spectra may be used with transform only, either by radial transform (Coggins and Zhou 2006; Kim and Szyperski 2003; Kupce and Freeman 2008) or by discrete FT (DFT) (Kazimierczuk et al 2010).…”

Proximity operators for a class of hybrid sparsity + entropy priors application to dosy NMR signal reconstruction

“…The so-called maximum entropy reconstruction approach [4], corresponding to the choice of the Shannon entropy function [5,6] for the penalization term Ψ, has been at the core of several papers dealing with regularized inverse Laplace transform [7,8,9,10,11,12]. A more recent approach consists in adopting for Ψ a criterion enforcing both sparsity and positivity, with the aim to improve the resolution of narrow peaks possibly present in the sought signal [13,14,15,16], but this strategy may be at the price of loosing the smoothness of the solution. Hybrid regularization approaches combining both entropy and sparsity terms in Ψ should thus be envisaged so as to derive a flexible resolution method.…”