Biomedical Signal and Image Processing

Kayvan Najarian, Robert Splinter

• Publisher: CRC Press
• Year: 2016
• ISBN:
  9781000218817
• Edition: 2
• Topic: Computer Science
• Subtopic: Digital Media
• Index: Computer Science

Written for senior-level and first year graduate students in biomedical signal and image processing, this book describes fundamental signal and image processing techniques that are used to process biomedical information. The book also discusses application of these techniques in the processing of some of the main biomedical signals and images, such as EEG, ECG, MRI, and CT. New features of this edition include the technical updating of each chapter along with the addition of many more examples, the majority of which are MATLAB based.

Part I

Introduction to Digital Signal and Image Processing

1 Signals and Biomedical Signal Processing

1.1 INTRODUCTION AND OVERVIEW

The most fundamental concept that is frequently used in this book is a “signal.” It is imperative to clearly define this concept and to illustrate different types of signals encountered in signal and image processing. In this chapter, different types of signals are defined, and the fundamental concepts of signal transformation and processing are presented while avoiding detailed mathematical formulations.

1.2 WHAT IS A “SIGNAL”?

The definition of a signal plays an important role in understanding the capabilities of signal processing. We start this chapter with the definition of one-dimensional (1-D) signals. A 1-D signal is an ordered sequence of numbers that describes the trends and variations of a quantity. The consecutive measurements of a physical quantity taken at different times create a typical signal encountered in science and engineering. The order of the numbers in a signal is often determined by the order of measurements (or events) in “time.” A sequence of body temperature recordings collected in consecutive days forms an example of a 1-D signal in time. The characteristics of a signal lie in the order of the numbers as well as the amplitude of the recorded numbers, and the main task of all signal processing tools is to analyze the signal in order to extract important knowledge that may not be clearly visible to the human eyes.

We have to emphasize the point that not all 1-D signals are necessarily ordered in time. As an example, consider the signal formed by the recordings of the temperature simultaneously measured at different points along a metal rod where the distance from one end of the rod defines the order of the sequence. In such a signal, the points that are closer to the origin (one end of the metal rod) appear earlier in the sequence, and, as a result, the concept that orders the sequence is “distance in space” as opposed to time. However, due to abundance of time signals in many areas of science, in the literature of signal processing, the word “time” is often used to describe the axis that identifies order. In this book, without losing the generality of the results or concepts, we use the concept of time as the ordering axis, knowing that, in some signals, time should be replaced by other concepts such as space.

Many examples of biological 1-D signals are heavily used in medicine and biology. Recording of the electrical activities of the heart muscles, called electrocardiogram (ECG), is widely considered as the main diagnostic signal in assessment of the cardiovascular system. Electroencephalogram (EEG) is a signal that records the electrical activities of the brain and is heavily used in diagnostics of the central nervous system (CNS).

Multidimensional signals are simply extensions of the 1-D signals mentioned earlier, i.e., a multidimensional signal is a multidimensional sequence of numbers ordered in all dimensions. For example, an image is a two-dimensional (2-D) sequence of data where numbers are ordered in both dimensions. In almost all images, the numbers are ordered in space (for both dimensions). In a gray-scale image, the value of the signal for a given set of coordinates (x, y), i.e., g(x, y), identifies the image brightness level at those coordinates. There are several important types of image modalities that are heavily used for clinical diagnostics among which magnetic resonance imaging (MRI), computed tomography (CT), ultrasonic images, and positron emission tomography (PET) are the most commonly used ones. These imaging systems will be introduced in separate chapters dedicated to each image modality.

1.3 ANALOG, DISCRETE, AND DIGITAL SIGNALS

Based on the continuity of a signal in time and amplitude axes, the following three types of signals can be recognized:

1.3.1 ANALOG SIGNALS

These signals are co...