| Summary: | Human body tissue disease diagnosis will become more accurate if transmittance images, such as X-ray images, are separated according to each constituent tissue. This research proposes a new image decomposition technique based on the matrix inverse method for biological tissue images. The fundamental idea of this research is based on the fact that when <i>k</i> different monochromatic lights penetrate a biological tissue, they will experience different attenuation coefficients. Furthermore, the same happens when monochromatic light penetrates <i>k</i> different biological tissues, as they will also experience different attenuation coefficients. The various attenuation coefficients are arranged into a unique <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>k</mi><mo>×</mo><mi>k</mi></mrow></semantics></math></inline-formula>-dimensional square matrix. <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>k</mi></mrow></semantics></math></inline-formula>-many images taken by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>k</mi></mrow></semantics></math></inline-formula>-many different monochromatic lights are then merged into an image vector entity; further, a matrix inverse operation is performed on the merged image, producing <i>N</i>-many tissue thickness images of the constituent tissues. This research demonstrates that the proposed method effectively decomposes images of biological objects into separate images, each showing the thickness distributions of different constituent tissues. In the future, this proposed new technique is expected to contribute to supporting medical imaging analysis.
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