ROBUST DETECTION OF NUCLEAR QUADRUPOLE RESONANCE SIGNALS IN A NON-SHIELDED ENVIRONMENT Tore Rudberg and Andreas Jakobsson Dept.ofMathematicalStatistics,LundUniversity,Sweden Email: {tore, aj}@maths.lth.se ABSTRACT Nuclear quadrupole resonance (NQR) is a non-invasive radio-frequency technique allowing for a practically unique fingerprint for molecules containing quadrupolar nuclei, makingthetechniqueverypromisingfordetectionpurposes. Ifproperlyexcited,thesenucleiwillemitelectromagneticra- diation,thefrequencyofwhichisgovernedmainlybywhere in the molecule the nuclei are positioned. However, the re- sulting NQR signals are inherently weak and are prone to strong interference signals from the measurement environ- ment, making detection challenging. In this paper, we de- velop a robust and reliable detection algorithm that general- ize earlier techniques and incorporates both efficient inter- ference cancellation and the ability to handle multiple poly- morphs in the sought substance. The usefulness of the al- gorithm is motivated by comparisons using realistic simula- tions. 1. INTRODUCTION Whenexcitingquadrupolarnucleiwithproperlyselectedra- dio frequency (RF) radiation, the resulting quadrupolar res- onance yields a unique signal signature of the excited sub- stance [1]. The technique can be used for detection of var- ious harmful substances, such as explosives and drugs, as wellasfortheauthenticationofmanyformsofpharmaceuti- calsubstances.Theabilitytodetecttheformersubstancesis clearlydesired[2],butalsothelatterapplicationisofsignifi- cantimportance[3]. Counterfeitmedicinesconstitutesadra- matic problem in health care worldwide, and the problems are growing. According to the World Health Organization (WHO), counterfeit drugs constitute up to 25% of the total medicine supply in less developed countries. For instance, severalformsofantimalarialmedicinesarecommonlycoun- terfeited, since these are expensive and the demand is high. InastudyofantimalarialmedicinesfromCameroonin2004, it was shown that 38% of the medicines marked Klorokin, 74% of those marked Kinin, and 12% of those marked An- tifolatescontainednoneoronlytraceamountsoftherespec- tiveactivesubstances[4].Eveninrichcountries,WHOpre- dicts that about 1% of all medicines are counterfeit. Dur- ingrecentyears,aseriesofalgorithmsbasedonapproximate maximumlikelihood(AML)parameterestimationhavebeen proposedforthedetectionofNQRsignals[5–10],exploiting the detailed model for such signals developed in [6]. These techniques have also been extended to allow for multiple and/orpolymorphicsubstances[7,8],aswellasformeasure- mentsmadeinapartly-ornon-shieldedenvironment[9,10]. Theabilitytohandlepolymorphicand/ormultiplesubstances This work was supported in part by the Swedish Research Council Carl Trygger’s foundation, and the Wellcome trust. isofimportanceinthedetectionofseveralformsofhighex- plosives,suchasTNT,thatoccursinbothamonoclinicand anorthorhombiccrystallinestructure,andformanycommon pharmaceutical substances, where often only one of several possiblecrystallinestructuresactsastheactiveingredient.In thiswork,webuildontheseearliercontributions,presenting a merged robust algorithm, termed RESPEQ (Robust Eval- uation using Subspace-based methods of Polymorphic nu- clEar Quadrupole signals), able to handle both polymorphic and/or multiple substances and the presence of very strong corrupting signals. The latter is typical in partly- or non- shielded measurement environments, commonly occurring for the mentioned applications of interest. To allow for ef- ficient interference cancellation, the proposed algorithm as- sumestheavailabilityofaprimarydataset,possiblycontain- ingthesignal-of-interest(SOI),aswellasasecondarySOI- free data set, only containing noise and interference signals. Suchasecondarydatasetcan,forechotrainmeasurements, be obtained in-between the SOI measurements, while wait- ing for the nuclei to dephase to allow for further excitation (seealso[9,10]). 2. DATA MODEL Asdescribedin[8],the m:thechoofanNQRsignalfroma pulsespinlocking(PSL)sequencecanbewellmodeledas y m t P p 1 p y p m t w m t (1) where p y p m t w m t and P are the overall gain, the relative proportion of the p:th polymorph, the signal from the p:thpolymorph,additivenoise,andthenumberofpoly- morphs, respectively. Furthermore, the proportions, p aredefinedsuchthat P p 1 p 1 and[6] y p m t d p k 1 p k e t m p k e p k t t sp i p k T t (2) where, t t 0 t N 1 m 0 M 1 t sp T , d p and are the echo sampling time, the echo number, the time between the (center of the) refocusing pulse and the echo center, the temperature, the number of sinusoidal compo- nents of the p:th polymorph, and the echo spacing, respec- tively. Moreover, p k p k p k and p k T arethe(com- plex)relativeamplitude,theechodampingconstant,theecho traindampingconstant,andtheangularfrequencyofthe k:th spectral line of the p:th polymorph. Typically, t 0 0 due to dead time in the measurement. It is also worth noting 19th European Signal Processing Conference (EUSIPCO 2011) Barcelona, Spain, August 29 - September 2, 2011 © EURASIP, 2011 - ISSN 2076-1465 2079