Medical Image Classification Using the Discriminant Power Analysis (DPA) of Discrete Cosine Transform (DCT) Coefficients

Medical imaging systems are very important in medicine domain. They assist specialists to make the final decision about the patient’s condition, and strongly help in early cancer detection. The classification of mammogram images represents a very important operation to identify whether the breast cancer is benign or malignant. In this chapter, we propose a new computer aided diagnostic (CAD) system, which is composed of three steps. In the first step, the input image is pre-processed to remove the noise and artifacts and also to separate the breast profile from the pectoral muscle. This operation is a difficult task that can affect the final decision. For this reason, a hybrid segmentation method using the seeded region growing (SRG) algorithm applied on a localized triangular region has been proposed. In the second step, we have proposed a features extraction method based on the discrete cosine transform (DCT), where the processed images of the breast profiles are transformed by the DCT where the part containing the highest energy value is selected. Then, in the feature’s selection step, a new most discriminative power coefficients algorithm has been proposed to select the most significant features. In the final step of the proposed system, we have used the most known classifiers in the field of the image classification for evaluation. An effective classification has been made using the Support Vector Machines (SVM), Naive Bayes (NB), Artificial Neural Network (ANN) and k-Nearest Neighbors (KNN) classifiers. To evaluate the efficiency and to measure the performances of the proposed CAD system, we have selected the mini Mammographic Image Analysis Society (MIAS) database. The obtained results show the effectiveness of the proposed algorithm over others, which are recently proposed in the literature, whereas the new CAD reached an accuracy of 100%, in certain cases, with only a small set of selected features.

Spread Option Pricing on Single-Core and Parallel Computing Architectures

This paper introduces parallel computation for spread options using two-dimensional Fourier transform. Spread options are multi-asset options whose payoffs depend on the difference of two underlying financial securities. Pricing these securities, however, cannot be done using closed-form methods; as such, we propose an algorithm which employs the fast Fourier Transform (FFT) method to numerically solve spread option prices in a reasonable amount of short time while preserving the pricing accuracy. Our results indicate a significant increase in computational performance when the algorithm is performed on multiple CPU cores and GPU. Moreover, the literature on spread option pricing using FFT methods documents that the pricing accuracy increases with FFT grid size while the computational speed has opposite effect. By using the multi-core/GPU implementation, the trade-off between pricing accuracy and speed is taken into account effectively.

On the Zap Integral Operators over Fourier Transforms

We devote the current chapter to describe a class of integral operators with properties equivalent to a killer operator of the quantum mechanics theory acting over a determined state, literally killing the state but now operating over some kind of Fourier integral transforms that satisfies a certain Fredholm integral equation, we call this operators Zap Integral Operators (ZIO). The result of this action is to eliminate the inhomogeneous term and recover a homogeneous integral equation. We show that thanks to this class of operators we can explain the presence of two extremely different solutions of the same Generalized Inhomogeneous Fredholm equation. So we can regard the Generalized Inhomogeneous Fredholm Equation as a Super-Equation with two kinds of solutions, the resonant and the conventional but coexisting simultaneously. Also, we remember the generalized projection operators and we show they are the precursors of the ZIO. We present simultaneous academic examples for both kinds of solutions.

Fourier Transform Infrared Spectroscopy of the Animal Tissues

Animal tissues are extensively used as scaffolds for tissue engineering and regenerative therapies. They are typically subjected to decellularization process to obtain a cell-free extracellular matrix (ECM) scaffolds. It is important to identify chemical structure of the ECM scaffolds and Fourier transform infrared (FTIR) appears to be a technique of choice. In this chapter, FTIR spectra of native and decellularized buffalo aortae, buffalo diaphragms, goat skin, and native bovine cortical bone are presented. The transmittance peaks are that of organic collagen amide A, amide B, amide I, amide II and amide III chemical functional groups in both native and decellularized aortae, diaphragms and skin. In bone, the transmittance peaks are that of inorganic ν1, ν3 PO43−, OH− in addition to organic collagen amide A, amide B, amide I, amide II and amide III chemical functional groups. These important transmittance peaks of the tissue samples will help researchers in defining the chemical structure of these animal tissues.