THREE-DIMENSIONAL BIOMEDICAL IMAGE DE-NOISING V. Musoko * and A. Proch´ azka * * Prague Institute of Chemical Technology Department of Computing and Control Engineering Technick´ a 1905, 166 28 Prague 6, Czech Republic Phone: +420-224 354 198 Fax: +420-224 355 053 e-mail : Victor.Musoko@vscht.cz, A.Prochazka@ieee.org Abstract: The paper presents the fundamental mathematical methods used in the analysis and processing of three-dimensional (3D) image objects. The methods to be discussed include 3D discrete Fourier transform (DFT) and Wavelet transform (WT). Firstly there is a need to generate an object for testing followed by its 3D visualization and the generation of the random noise. Computer visualization and processing is applied to the 3D biomedical image data. Keywords: Discrete Fourier Transform, Three-Dimensional visualization, Wavelet Transform, Biomedical Image Analysis, Image De-Noising 1. INTRODUCTION Several of today’s imaging techniques (Bilgin and Marcellin 2000) produce three-dimensional (3D) data sets. Medical imaging techniques, such as computer tomography (CT) and magnetic reso- nance (MR), generate multiple slices in a single examination, with each slice representing a differ- ent cross section of the body part being imaged. However when transmitting these image volumes there is a possibility that noise is encountered dur- ing image transmission as pixel drop-outs. Noise elimination forms a fundamental problem in im- age processing. The three-dimensional discrete Fourier transform is applied for noise rejection by the use of an appropriate window function in the frequency do- main. Wavelet transform allows the image volume decomposition and reconstruction using selected threshold levels. The paper compares efficiency of the proposed methods. A series of de-noising and enhancement experiments is performed to verify the efficiency of the methods using 3D image volumes corrupted with random noise. The ex- perimental results of the algorithms described are compared based on the quality of the de-noised image volumes. The algorithms are at first tested for the generated image objects and then applied to real magnetic resonance image (MRI) volumes for the biomedical 3D image applications. The paper is organized as follows: Sections 4 and 5 present a brief overview of Fourier and wavelet transform techniques and their applications to multidimensional data. In Section 6 simulated and MR volumes are used to test de-noising per- formance of the proposed algorithms. The per- formance of the algorithms are investigated and compared using the mean square error (MSE) and signal-noise-ratio (SNR) criteria. Section 7 summarizes the paper and provides some of the possible solutions to improve the de-noising. 2. BIOMEDICAL IMAGE VISUALIZATION Magnetic resonance imaging (MRI) is based on the absorption and emission of energy in the radio frequency range of the electromagnetic spectrum.