DESCRIPCIÓN PARAMÉTRICA: Formato ESTÁNDAR.

In this chapter, th e conclusions are draw n for th e work involved in this thesis and possible topics are suggested for fu tu re research.

7.1 Conclusions

In this work, a v ariety of problem s are exam ined:

i. The problem of e stim atin g th e frequency of a sinusoid in noise is sta te d in C hapter 2. A hybrid ph ase-based single frequency estim ator w ith low com putational complexity is proposed, com bining previously proposed SNR threshold reduction approaches with a recent outlier rem oval scheme. T he proposed estim ator achieves a lower m ean square error th a n o th e r available techniques, lowering the SNR threshold a t which the CRLB is closely followed. F urtherm o re, in con trast to m any other techniques, th e performance of th e h ybrid estim a to r is found to be essentially independent of th e tru e frequency. R elated issues such as pow er dam ping and frequency spread are also briefly discussed; ii. D oppler shift e stim a tio n or th e resulting velocity estim ation of a moving targ et is an

im p o rtan t to pic in a w ide variety of fields. In C h ap ter 3, th ree novel velocity estim ators

S e c tio n 7 .1 . C o n c lu s io n s 124

using m ultiple frequency carriers have been developed. E valuation using synthetic d a ta indicates th a t these new estim ators have th e capability to m itigate the poor high velocity perform ance of conventional correlation based techniques and thereby provide usable perform ance beyond th e conventional N yquist velocity limit. Furtherm ore, the CRLB for th e velocity estim atio n is derived to evaluate th e perform ance of the proposed m ethods.

iii. To enable high q u ality u ltra so u n d color flow images, efficient atten u atio n of the clutter signal is one of th e critical factors. T he analysis of existing filters implies th a t the recent introduction of th e E R F /P C A an d possibly the ICA m ethods seem very promising for this purpose. A n efficient approach to recursively form th e clu tter filters using a recent recursive subspace track in g technique is introduced in C h ap ter 5. The proposed m ethod is successfully exam ined w ith realistic carotid flow which is sim ulated w ith the Field II toolbox [Jen96b].

iv. Commonly, n arro w -b an d P W system s estim ate th e blood velocity using an autocorrelation- based estim ato r. In C h a p te r 6, th e hybrid frequency estim ato r proposed in C hapter 2 is exam ined w ith realistic R F d a ta which shows th e achievable perform ance gain of this m etho d as com pared to th e trad itio n al approach.

v. As th e m ultiple-carrier based velocity estim ators proposed in C h ap ter 3 are m otivated in association w ith th e application of blood velocity estim ation, in C hapter 6 the DAVE an d th e NLS estim ato rs are modified (accordingly term ed M-DAVE and M-NLS, respectively) due to th e introd uced clu tter filtering and applied to realistic R F d ata for blood velocity estim atio n . T h e M-DAVE and M-NLS m ethods were found to work well w ith fibre flow, b u t fail w ith parabolic flow. T he m ost likely reason for this failure is due to th e m ism atch betw een th e m ultiple-carrier based sinusoidal d a ta model and th e actu al R F d a ta o b ta in ed from parabolic flow.

S e c tio n 7 .2 . S u g g e s t i o n s fo r F u t u r e R e s e a r c h ₁₂₅

All of the above conclusions illu strate th e usefulness of p aram eter estim ation in solving practical problem s arising in a variety of applications. It also exposes the problem s existing in current research. T herefore, it is believed th a t th e following suggestions provide a pathway for future research.

7.2 S uggestions for F u tu re R esearch

Based on th e w ork an d analysis in th is thesis, four possible topics for futu re research projects are proposed.

Frequency E stim ation o f a G eneral S inu soid al D ata M odel

The problem of a single to n e estim atio n has been well studied in this thesis. However, this study is confined to th e p u re sinusoidal d a ta m odel only, which som ew hat restricts the generality of th is h y b rid estim ato r. As a result, it is n a tu ra l to extend th e hybrid estim ator to be valid for a m ore general sinusoidal d a ta m odel allowing power dam ping and frequency spread.

Estim ation o f 2 -D im e n sio n a l F req u en cies

In C hapter 2, th e h y b rid e stim a to r has been shown to outperform th e exam ined single tone estim ators, ex h ib itin g lower M SE an d SNR threshold as com pared to o ther estim ators. It is believed th a t th e re is m ore to be done in this topic. One thin g to exam ine would be to extend th e single to n e e stim a to r to th e estim ation of 2-dim ensional frequencies.

Order E stim ation o f S u b sp a c e -b a s e d C lu tter Filters

In this thesis, th e c lu tte r rejection problem is studied and an efficient im plem entation of clutter subspace trac k in g tech niqu e for th e subspace-based clu tter filters is successfully in­

S e c tio n 7 .2 . S u g g e s t i o n s fo r F u t u r e R e s e a r c h 126

troduced. However, th e o rder estim ation problem involved in th e clu tter filters has not been investigated yet in th is work. As pointed out in the previous chapters, further research is needed on how th e filter order should be selected appropriately. Thus, to b e tte r implement the introduced efficient subspace tracking technique in clu tter rejection, a critical problem is the corresponding o rd er estim atio n.

Improving th e M u ltip le-carrier B a se d E stim ators

The failure of th e M -DAVE an d th e M-NLS estim ators w ith realistic parabolic flow investi­ gated in C h ap ter 6 im plies th a t th e estim ators are very sensitive to th e d a ta examined and their perform ance will deg rade if th e re is a m ism atch between th e exam ined d a ta and the ideal d a ta m odel from w hich th e estim ato rs are derived. F u rth er research will be needed on how to improve th e d a ta m odel in (3.2.1) and th e resulting estim ators so th a t they can be successfully im p lem ented in practice.

In addition, it is w o rth n otin g th a t th e proposed m ultiple-carrier based estim ators in C hapter 3 have high co m p u tatio n al complexity. As a result, it would be interesting to look into how these m e th o d s can be im plem ented w ith lower com p utatio nal load.