Spectral estimation of irregularly sampled exponentially decaying signals with applications to RF spectroscopy

High resolution sparse estimation of exponentially decaying signals

“…Exponentially decaying sinusoidal signals occur naturally in a wide range of fields, such as, for instance, radio frequency spectroscopy, wireless communications, sonar and radar (see, e.g., [1,2] and the references therein). Commonly, the measurements suffer from various kinds of interference signals or corrupting additive colored noise.…”

“…Given such difficulties, it is often of interest to formulate non-parametric or semi-parametric modeling techniques, imposing only mild assumptions of the a priori knowledge of the signal structure. Popular solutions include the so-called dCapon, dAPES, and dIAA spectral estimators which form a generalized spectral estimate of the signal, constructing their spectral representation over both the frequency and damping dimensions [1,2] (see also [3,4]). Although this form of techniques are robust to the model assumptions, they suffer difficulties in separating closely spaced frequency and damping modes from each other, and typically require notable computational efforts if not implemented carefully [4].…”

“…Such techniques have successfully been applied to line spectral data, and the topic has attracted notable attention in the recent literature (see, e.g., [5][6][7][8][9][10][11]). Although these algorithms appear quite different from each other, they share the property that the considered dictionary grid should be selected sufficiently fine to allow for a sparse signal representation (see also [12,13]), which, if extended to also consider damped modes, necessitates a large dictionary matrix containing elements with a sufficiently fine grid over the range of both the potential frequencies and damping candidates (see, e.g., [2,14,15]); this will be particularly noticeable if treating large data sets, or data sets with multiple measurement dimensions, such as in NMR measurements. In order to mitigate this problem, we here propose a novel dictionary learning approach wherein we iteratively decompose the signal with a fixed small dictionary, adaptively learning the dictionary elements best suited to enhance sparsity.…”

Non-parametric data-dependent estimation of spectroscopic echo-train signals

“…Typical analysis and detection algorithms for ET data requires some initial estimates of the expected echo decay within each echo, here denoted β, as well as the overall echo train decay, dentoted η, capturing the decay over the various echoes [3,4]. Such estimates are typically obtained using parameteric estimators, such as the ET-ESPRIT and ETAML [3,5], or non-parametric data-adaptive estimators, such as the dCapon, dAPES, or dIAA algorithms [6,7]. The former kind of estimators suffer from requiring a priori knowledge of the precise data structure and model orders, including the presence of any possible interference components, which are commonly oc- curing in all forms of NQR measurements (see e.g., [4]).…”

“…The mentioned non-parametric estimators on the other hand are robust to such assumptions, allowing for a spectral estimate enabling the separation of the NQR signal and the interference signals, but are then not able to estimate the finer structure of the ET, but rather just an overall exponential decay. In this paper, we extend on the methods in [6,7], presenting a non-parametric data-dependent estimator of both the β and η decays of each relevant spectral line. In order to reduce the computational complexity of the method, the introduced ETCAPA estimator is formed in two steps, such that an initial estimate of the relevant frequencies using a simple exponential decay is formed by a combination of dCapon and dAPES, from which the (β, η) decays are then found for any frequency component of interest.…”