Research in the Past: Selected
Projects
Statistical Analysis and Algorithms
for Achievable Resolution in Imaging
Local Detectors for High-Resolution
Spectral Analysis
A Cross-Distance
Analysis for ECG Classification
Multi-Channel
BioSignal Denoising Using Adaptive Filters
Statistical
Analysis and Algorithms for Achievable Resolution in Imaging
The problem of resolution has been of significant
interest in several scientific communities in science and engineering, for
example in imaging practice, astronomy, different applications in physics,
array processing and integrated circuit manufacturing.
By quantifying and understanding resolution limits for a
given imaging system, we can optimize our imaging system design as well as our
image processing algorithms. Moreover, the algorithms associated with the
proposed analytic framework are able to perform superiorly against other
widely-used approaches in retrieving information from acquired low-quality
images. An appealing benefit is ability to precisely detect and localize a
target of interest.
The results of our work extend, illuminate, and unify the
earlier works in this field using more modern tools in statistical signal
processing. Namely, we use locally optimal statistical tools, which lead to
more explicit, readily interpreted, and applicable results. The present results
clarify, arguably for the first time, the specific effects of the relevant
parameters on the definition of resolution, and its limits, as needed in practice.
Our approach has been to precisely define a quantitative measure of resolution
in statistical and information-theoretic terms. In contrast to earlier
definitions of resolution, there is little ambiguity in our proposed
definition, and all parameters (those related to camera lens and aperture
structure, noise variance, sampling rate, etc.) will be explicitly present in
the formulation.
Local Detectors for High-Resolution Spectral Analysis
Spectral estimation has a long history and significant
applications in communication and signal processing. In particular, the problem
in array signal processing arises in several contexts, including wave
direction-of-arrival estimation. In studying sensor array systems (such as in
Radar and Sonar systems), resolving power of the receiving antenna array has
been consistently used as a performance figure for such systems. The common
question in this area has been to investigate the relationship between required
SNR (Signal power to Noise power Ratio) and resolution. Resolution in this
context is identified as the ability to distinguish whether the received
(noisy) signal is originated from a single transmitting source or from two
distinct (but closely spaced) sources. Clearly, in array processing practice,
it is of a major interest to design high-resolution detectors/estimators with
ability to accurately localize closely-spaced transmitting sources.
Traditionally, subspace methods have
been employed to obtain spectral estimates. However, these methods are proven
to be non-optimal and in particular for the case where the number of signal
snapshots (observations) is limited, these approaches fail dramatically.
The problem of interest concerns with the case where the
separation between transmitting sources is small (in other words the incoming
waves have been traveling in slightly different directions). We have
effectively used this fact to set up ÒlocalÓ detectors/estimators.
Mathematically speaking the proposed framework is based on a series expansion
which revolves around the value of Òseparation=0Ó. This leads to a local
model-based approach which enables us to first establish a relationship between
SNR and separation between transmitting sources and second to develop the
corresponding detection strategies that can be applied in practice. In other
words, the final obtained performance figure is simply the result of employing
these locally optimal detectors. In order to illustrate the relevance of the
results, we present comparisons against the general class of subspace methods.
We demonstrate that the proposed detectors yield significantly improved
performance in distinguishing the transmitting sources.
A Cross-Distance Analysis for ECG
Classification
We
presented a multi-stage algorithm for ECG beat classification into normal and
abnormal categories using a sequential beat clustering and a cross-distance
analysis algorithm. After clustering stage, a search algorithm is applied to
detect the main normal class. Then other clusters are classified based on their
distance from the main normal class.
The
key point is that in several ECG recording, all normal beats remain
morphologically very similar even during a long-term record. It also turns out
that in many applications,
number of normal beats is quite larger than the number of abnormal ones.
The
algorithm is developed for both 1-lead and 2- lead ECG. Evaluated results on
MIT-BIH database exhibit a classification error of less than 1% for 1-lead and
0.2% for 2-lead and clustering error of 0.2%.
Multi-Channel BioSignal Denoising
Using Adaptive Filters
Two
case studies were considered: multi-lead ECG recording and pulse oximetry data
acqusition used to determine the percentage of haemoglobin (Hb) which is
saturated with oxygen.