One would expect that the material covered in Biomedical Signal and Image Processing would primarily be about biomedical signal and image processing, the title of the book. However, it is spotty in its comprehensiveness and there are entire chapters devoted to peripheral topics. There are no citations given for any of the material and no reference texts are shown.

In terms of comprehensiveness, the first chapter, Introduction to Digital Signal and Image Processing is helpful to the discussion. Basic introductory materials about signal and image processing are provided. In the second chapter however, which is devoted to the Fourier Transform, a very important concept in biomedical engineering, details are lacking. The reader is provided the definition of the Fourier transform. The following equation is provided:

G\left(f\right)={\int}_{-\infty}^{+\infty}{e}^{-j2\mathit{\pi ft}}\mathit{dt}

(2.1)

The frequency variable *f*, imaginary number *j*, and continuous signal *g(t)* are defined in the text. However other variables lack explanation. What is the purpose of the exponential function in the transformation equation, for example? What is the purpose of *2π* and *t*? How is the exponential related to the sine waves that are used for signal transformation? How does it work to convert a signal to basis functions and power spectrum? Instead of explaining these concepts, the authors devote a large portion of the chapter to transforming simple mathematical functions.

The two-dimensional discrete Fourier transform is also described briefly in this chapter. What I would like to have seen is a description of the relationship between biomedical image and the two-dimensional Fourier transform that results. It would have been interesting to see images with visibly periodic patterns and their Fourier representation, then work up to real biological images which may have periodic components, and show their transformation. This is done for example, in a popular bioimaging text[1].

I expected toward the end of the chapter to see a section on the Fast Fourier Transform and the Cooley-Tukey algorithm, but no such information is provided on this topic. Knowledge of the method would have been helpful toward understanding the mathematics of Fourier analysis. It is also a question that appears on many graduate level examinations including PhD qualifiers.

The book then shifts to image processing techniques, which are covered briefly in Chapter 3, entitled Image Filtering, Enhancement, and Restoration, and in Chapter 4, Edge Detection and Segmentation of Images. The basic aspects of contrast enhancement, histogram equalization, masking, low and high pass filtering, edge detection, and image segmentation are provided. These two chapters provide most of the image processing information that is covered in the book. Yet most image processing texts are much larger and more comprehensive[1]. These two chapters can be used as a basic introduction to image processing only.

Very important to biomedical engineering is the topic of wavelets, which is considered in chapter 5. The authors lead into the concept by describing the short-time Fourier transform, which is helpful and clear. They show how windowing at short intervals is useful to capture time-variant information, and how the analysis window size is very important for interpreting time-variant events. There are suitable illustrations for this purpose. The concept of using analysis windows other than the rectangular type is also introduced. The authors mention triangular and trapezoidal analysis windows, and that more weight would be assigned to the central part of the window when these shapes are used. However this is the only place in the book where these windows are mentioned at all, and they are not described. The concept of weighting and how window type affects the analyzed signal should be detailed.

The actual description of wavelets is very good in my opinion. The authors nicely describe the relationship of scale and shift for wavelet transformation, and how this relates to the short-time Fourier transform. However I would have preferred to see more information about the mother wavelet and what it does. Why exactly are there different mother wavelets that are used for transformation? How does the choice of mother wavelet affect the result? If one chooses one particular mother wavelet over another, can it significantly affect the time-frequency information that is obtained? Can it affect the conclusions that are reached by implementing wavelet analysis for biomedical application? If so, why then are wavelets useful when the results and conclusions depend upon the choice of mother wavelet? If the results and conclusions are robust to mother wavelet choice, why and how? These are the kind of need-to-know topics that would be very helpful to present in any text that is more conceptually oriented and geared toward students.

The authors also mention in the chapter that a continuous time series signal can be reconstructed from discrete wavelet coefficients. How can this be? Is it because the mother wavelet itself is a continuous function? It would be helpful to see an example of how this works.

The authors then explain the difference between a frame and a basis. They state that it can be proven that there exists bounded positive values A and B such that Eq. 5.10 is valid (see Figure 1). Note this equation is blurry. But more importantly, what are A.E_{x} and B.E_{x}? As a reader, I would like to know. What does this notation mean? Is it a mathematical shorthand or a typo? Particularly for undergraduate level students, this should be explained.

A major part of the wavelets chapter is devoted to the Quadrature Mirror Filter (QMF) algorithm, which in many cases is used to implement wavelet analysis. The authors’ diagram for QMF is shown in Figure 2. It is unclear from the text how and why this implementation can replace discreet shift and scale of the mother wavelet at multiple levels for wavelet analysis. The diagram in the book, reproduced in Figure 2, shows that the input signal is filtered by the QMF algorithm separately for both high and low pass content. Why? How do the high and low pass filters relate to shift and scale? We are told that the high and low pass form of the digital filter can be obtained from Equation 5.12, reproduced below:

g\left(n\right)=\left(2N-1-n\right)

(5.12)

but are not told what the variables n and N represent. It is important to define all variables as they are used in equations. Concerning the QMF algorithm diagram (Figure 2), the authors say:

‘As can be seen, once h(n) is chosen, g(n) is automatically defined. This means that even though in the block diagram of Figure 5.9 [shown in Figure 2 in this review] there are two filters, only one of them is selected and the other one is calculated from another.’

This statement is unclear to me. What is calculated from what? More detail is needed. The authors continue:

‘As evident from Figure 5.9 [shown in Figure 2 in this review], the signal transformation and decomposition can be repeated for as many levels as desired. If one wishes to terminate the operation at the first level, two coefficients are found, d1c (the high-pass coefficient on the first level) and a1c (the low-pass coefficient on the first level). … This would result in two new coefficients: d2c (the low-pass coefficient on the second level) and a2c (the high-pass coefficient on the second level).’

I am not sure if I understand this passage. If d1c is the high-pass coefficient on the first level, why is a2c the high-pass coefficient on the second level? Shouldn’t it be d2c? If not, the authors need to explain more clearly in the text why the variable associated with each type of filter changes letter. Similarly, if a1c is the low-pass coefficient on the first level, why is d2c the low-pass coefficient on the second level? The authors should explain how the coefficients work, and which of g(n) and h(n) is the high pass and low pass filter at each level.

The text then continues:

‘From the preceding equations, one can see that the mother wavelet of the operation is uniquely identified and represented by the filter h(n) or, in other words, the role of the mother wavelet is somehow replaced by h(n).’

Please explain how this works. The concept should not have to be understood just from the equations, but through the text as well.

The following chapter, Chapter 6, entitled ‘Other Signal and Image Processing Methods’ was of interest to me because I thought that some of the major additional methods used in signal and image processing would be discussed, such as eigenanalysis, linear predictive methods, and adaptive filtering. However they were not included. The authors devote a page to fractal dimension, which is helpful, but other aspects of nonlinear analysis and chaos theory are not presented – perhaps an entire chapter or more could be devoted to this field, which is quite important to signal and image processing. The cosine transform is then discussed. Here is another example of a transform, like the Fourier transform, for which it would be very useful to know the relationship of the equation to its sinusoidal basis. How is the cosine transform similar to or different from the Fourier transform? It would be an important question for me as a student. Why is only the cosine wave used for transformation? Is there a sine transform?

Several chapters are then devoted to peripheral topics. Chapter 7 is devoted to clustering and classification. Although pattern recognition may or may not be considered to be a branch of signal and image processing, it is sufficiently related that I agree with the authors that it merits a chapter. Topics such as k-means and the maximum likelihood methods are discussed. Part II of the book however, is mostly devoted to the physiologic aspects of biomedical signals. Although its title is ‘Processing of Biomedical Signals’ it really is short on processing and long on physiology. These chapters consist of Chapters 8–12, which are entitled, respectively, ‘Electrical Activities of the Cell’, ‘Electrocardiogram’, ‘Electroencephalogram’, ‘Electromyogram’, and ‘Other Biomedical Signals’. The authors concentrate on bioelectric signals, mostly to the exclusion of biomechanical, biomagnetic, and bioacoustic signals. Only Chapter 12, ‘Other Biomedical Signals’, provides brief descriptions of selected non-electrophysiologic signals – the blood pressure signal, magnetoencephalogram, and respiratory signals.

Part III of the book is entitled ‘Processing of Biomedical Images’. Similar to Part II, there is less description of processing methods, and more description of biomedical image formation. In this Part, the concepts behind the source of the image are discussed in great detail, in Chapters 14 – 18, which are respectively, Principles of Computed Tomography, X-Ray Imaging and Computed Tomography, Magnetic Resonance Imaging, Ultrasound Imaging, Positron Emission Tomography, and Other Biomedical Imaging Techniques. Though interesting, it would be helpful to learn more about actual image processing techniques, of which there are devoted many large textbooks and reference manuals.