8
Biomedical Signal and Image Processing
questions: “On average, how often can a failure occur?” and “Is there any visible
periodicity in the failure pattern?” If we identify a specific frequency at which
machine failures often occur, we can simply schedule regular periodic checkups
before the expected time for possible machine failures. This can also help us identify potential reasons and causes for periodic failures and therefore associate failures to some physical events such as the regular weariness of a belt in the machine.
Fourier transform (FT) is a transformation designed to describe a signal in frequency domain and highlight the important knowledge in the frequency variations
of the signal. The usefulness of the knowledge contained in frequency domain
explains the importance of FT. Other transformations commonly used in signal
and image processing literature (such as wavelet transform) describe a signal in
other domains that are often a combination of time and frequency.
It has to be emphasized that the information contained in a signal is exactly the
same in all domains, regardless of the specific domain definition. This means that
different transformations do not add/delete any information to/from a signal, and the
same exact information can be discovered from a signal in each of these domains.
The key point to realize the popularity of different types of transformations in signal
processing is the fact that each transform can highlight a certain type of information
(which is different from adding new knowledge to it). For example, the frequency
information is much more visible in Fourier domain than in time domain, while the
exact same information is also contained in the time signal. In other words, while
the frequency information is entirely contained in the time signal, such information might be more difficult to notice or more computationally intensive to extract
in time domain. The reason for this clarification is the answers often students give
to the following tricky question: “Assume a signal is given in both time and Fourier
domains. Which domain does give more information about the signal?” The authors
have asked this question to their students, and almost always half of the students
identify the time domain as the more informative domain while the remaining half
go with the Fourier domain, and almost never does anyone realize that the answer
to this tricky question is simply “neither!” The choice of the domain only affects
the visibility, representation, and highlighting of certain characteristics, while the
information contained in the signal remains the same in all domains. It is important
for the readers to keep this fact in mind when we discuss different transformations
in the following chapters.
1.5 SIGNAL PROCESSING FOR FEATURE EXTRACTION
Once certain characteristics of a signal are identified using appropriate transformations, these characteristics or features are used to evaluate the signal and the system
producing the signal. As an example, once using image processing techniques, a
region of a CT image is highlighted and identified as a tumor, then one can easily perform some measurements over the region (such as measuring the size of the
tumor) and identify the malignancy of the tumor. As mentioned in the Preface, one
of the main functions of biomedical signal and image processing is to define and
extract measures that are vital for diagnostics of biomedical systems.
Biomedical Signal and Image Processing
questions: “On average, how often can a failure occur?” and “Is there any visible
periodicity in the failure pattern?” If we identify a specific frequency at which
machine failures often occur, we can simply schedule regular periodic checkups
before the expected time for possible machine failures. This can also help us identify potential reasons and causes for periodic failures and therefore associate failures to some physical events such as the regular weariness of a belt in the machine.
Fourier transform (FT) is a transformation designed to describe a signal in frequency domain and highlight the important knowledge in the frequency variations
of the signal. The usefulness of the knowledge contained in frequency domain
explains the importance of FT. Other transformations commonly used in signal
and image processing literature (such as wavelet transform) describe a signal in
other domains that are often a combination of time and frequency.
It has to be emphasized that the information contained in a signal is exactly the
same in all domains, regardless of the specific domain definition. This means that
different transformations do not add/delete any information to/from a signal, and the
same exact information can be discovered from a signal in each of these domains.
The key point to realize the popularity of different types of transformations in signal
processing is the fact that each transform can highlight a certain type of information
(which is different from adding new knowledge to it). For example, the frequency
information is much more visible in Fourier domain than in time domain, while the
exact same information is also contained in the time signal. In other words, while
the frequency information is entirely contained in the time signal, such information might be more difficult to notice or more computationally intensive to extract
in time domain. The reason for this clarification is the answers often students give
to the following tricky question: “Assume a signal is given in both time and Fourier
domains. Which domain does give more information about the signal?” The authors
have asked this question to their students, and almost always half of the students
identify the time domain as the more informative domain while the remaining half
go with the Fourier domain, and almost never does anyone realize that the answer
to this tricky question is simply “neither!” The choice of the domain only affects
the visibility, representation, and highlighting of certain characteristics, while the
information contained in the signal remains the same in all domains. It is important
for the readers to keep this fact in mind when we discuss different transformations
in the following chapters.
1.5 SIGNAL PROCESSING FOR FEATURE EXTRACTION
Once certain characteristics of a signal are identified using appropriate transformations, these characteristics or features are used to evaluate the signal and the system
producing the signal. As an example, once using image processing techniques, a
region of a CT image is highlighted and identified as a tumor, then one can easily perform some measurements over the region (such as measuring the size of the
tumor) and identify the malignancy of the tumor. As mentioned in the Preface, one
of the main functions of biomedical signal and image processing is to define and
extract measures that are vital for diagnostics of biomedical systems.