A high-resolution technique for multidimensional NMR spectroscopy

Abstract

Abstract-In this paper, a scheme for estimating frequencies and damping factors of multidimensional nuclear magnetic resonance (NMR) data is presented. multidimensional NMR data can be modeled as the sum of several multidimensional damped sinusoids. The estimated frequencies and damping factors of multidimensional NMR data play important roles in determining protein structures. In this paper we present a high-resolution subspace method for estimating the parameters of NMR data. Unlike other methods, this algorithm makes full use of the rank-deficiency and Hankel properties of the prediction matrix composed of NMR data. Hence, it can estimate the signal parameters under low signal-to-noise ratio (SNR) by using a few data points. The effectiveness of the new algorithm is confirmed by computer simulations and it is tested by experimental data.

An Efficient Approach for Two-Dimensional Parameter Estimation of a Single-Tone

“…To facilitate the algorithm development, we express (1) in matrix form as (3) where , , and with , , and . From the regular structure of , it is straightforward to see that the noise-free data matrix can be represented as (4) where (5) and (6) are complex vectors which are characterized by and , and and , respectively. It is also observed that the elements in and satisfy the LP property: (7) and (8) where (9) and (10) On the other hand, can be decomposed using SVD as (11) where is the diagonal matrix of singular values of with while and are orthonormal matrices whose columns are the corresponding left and right singular vectors, respectively.…”

“…The is assumed to be a real zero-mean white Gaussian process with unknown variance . Expressing (37) in matrix form, we find that it can be decomposed as in (4) The former is constructed from and while the latter is a function of . Pre-multiplying both sides of (55) by yields (58)…”

“…Alternatively, subspace-based methodology is another popular choice for the 2-D sinusoidal parameter estimation problem, which includes multiple signal classification (MUSIC) [2], [4], estimation of signal parameters via rotational invariance techniques (ESPRIT) [5], [6], [8], and matrix pencil (MP) [9], [10] algorithms. Comparing with the ML estimator and its approximations, these methods are more computationally attractive at the expense of suboptimality.…”

High-Resolution Subspace-Based Methods: Eigenvalue- or Eigenvector-Based Estimation?

“…Parameter estimation from bidimensional (2-D) and multidimensional (N -D) signals finds many applications in signal processing and communications such as magnetic resonance (NMR) spectroscopy [5], wireless communication channel estimation, antenna array processing, radar and medical imaging [1]. In these applications, signals are modeled by a superposition of damped or undamped N -D complex exponentials.…”

Correlation-based algorithm for multi-dimensional single-tone frequency estimation

“…Apart from the standard one-dimensional signal model [4]- [6], multi-dimensional spectral estimation [7] in fact has many applications such as array processing [8]- [9], nuclear magnetic resonance (NMR) spectroscopy [10], wireless communication channel estimation [11]- [12] as well as detection and localization of multiple targets using multiple-input multiple-output (MIMO) radar [13].…”