Efficient Estimation of Decaying Sinusoids with Application in NMR Spectroscopy

Abstract

In this thesis, the Wideband Sparse Exponential Mode Analysis (WSEMA) estimator is introduced.
It combines two recently developed techniques, the wideband dictionary and the Sparse Exponential Mode Analysis (SEMA) to make for an efficient estimator. WSEMA estimates the parameters of decaying sinusoids, without a priori-information about the number of modes present in the signal.
WSEMA works with arbitrary sampling schemes and is therefore compatible with sampling scheme optimization ideas presented recently. The suggested estimator is evaluated using both simulated data and real nuclear magnetic resonance (NMR) spectroscopy data. The results in this thesis sug-gests that WSEMA can be used to efficiently estimate the frequencies and dampings of multi-modal
signals with minimum variance, although work remains concerning the handling of closely spaced peaks.
Parts of the content in this thesis have been published in the article Computationally Efficient Estimation of Multi-dimensional Damped Modes Using Sparse Wideband Dictionaries, accepted to the 26th European Signal Processing Conference (EUSIPCO 2018).

Popular Abstract

The Wideband Sparse Exponential Mode Analysis (WSEMA) estimator of decaying
sinusoids provides a boost to chemistry research. The novel method allows for fast and accurate determination of the structure of chemical compounds, an integral part in the development of modern medicine.
After finishing the best smoothie you ever bought, what do you do? Of course you ask for the recipe!
The business owner, however, doesn’t want to reveal any secrets. You have to carefully analyse the smoothie. Your taste buds tells you that it contains 95 different ingredients, from agave syrup to zucchini. But what smoothie contains 95 ingredients? Are you perhaps over analysing this? Could
that hint of sandalwood you’re sensing be someone’s cologne, and not an ingredient? You decide on a more restrictive approach, trying to distinguish only the most important components. Now you come to the conclusion that with a banana, some raspberries, a couple of plums, some ice, and a splash of soy milk you should be able to get close enough.
Much like a smoothie can be divided into it’s ingredients, a signal can be divided into sinusoidal Waves of different frequencies. Trying to capture as much as possible of a signal with as few components as possible, to avoid over analysing, is called sparse estimation. Until recently, this has typically been
done by providing a large dictionary of possible frequencies (or ingredients, if you will) to capture the essence of the signal. This will, however, for larger problems, make calculations slow, or even infeasible. Recently introduced so called wideband dictionaries allows us to more efficiently estimate
larger parts of the signal spectrum at once. This way, large portions of the frequencies can quickly by discarded, and the computational energy can be focused on achieving better resolution of the present components. Or, in a derived meaning, determine that there are no chips in the smoothie,
regardless of brand or flavour, and instead focus our energy on differentiating between orange and tangerine.
Decaying sinusoids is a model common in many technical applications. One of them is nuclear magnetic resonance (NMR), an experiment method used to determine the structure of chemical compounds. It is computationally demanding and algorithms needs to be fast and accurate. The here introduced WSEMA estimator makes use of recently developed concepts to provide efficient estimation of decaying sinusoids. It possesses a very desirable trait, compared to several previously
existing estimators, namely that it requires no prior information about the number of Components in the signal. This is advantageous since this information typically isn’t available in real-world applications.
Another advantage of WSEMA is that it doesn’t require so called uniform sampling. Having to take sips from your smoothie every twentieth second to be able to determine the ingredients is a pretty inconveniencing requisite. The WSEMA estimator has no such limitations. This is beneficial in smaller problems, but completely essential in larger ones, where uniform sampling is practically
impossible. WSEMA have, with promising results, been evaluated using both simulated data for benchmarking, as well as real world signals to ensure practical relevance.

• author: Jälmby, Martin
• supervisor: Andreas Jakobsson
• organization: Mathematical Statistics
• course: FMS820 20181
• year: 2018
• type: H2 - Master's Degree (Two Years)
• subject: Mathematics and Statistics
• keywords: decaying sinusoids, semi-parametric methods, wideband dictionary, NMR spectroscopy
• language: English
• id: 8943379
• date added to LUP: 2018-05-31 08:01:27
• date last changed: 2018-06-05 13:07:06