Image Quality of Decomposition Based On Near-Infrared Transmission Using The Gram-Schmidt Process

Near-infrared tomography (NIR) is highly developed. The weakness of NIR tomography is that it displays all tissue in a single image. To display a single image of a specific tissue from various tissues with unknown thickness, an inverse matrix decomposition method is used. The image decomposition results are not good. To overcome this, use the Gram-Schmidt process. The aim of this study is to measure the quality of the decomposition results using the Gram-Schmidt process.The indicators used to measure the quality of the decomposition results are the MSE and PSNR values. Using the Gram-Schmidt process results in a better decomposition process because it maximizes the independent linear properties by creating mutually orthogonal column vectors.

The Lambert-Beer equation performs a natural logarithmic operation, producing a linear relationship between intensity level, attenuation coefficient, and thickness. By varying three different wavelengths and three different materials, three linear equations are obtained. The solution to these three linear equations can be expressed in matrix form. This equation produces a 3x3 matrix of attenuation coefficients. The rows of the matrix represent the differences in attenuation coefficient values ​​for the three materials at a single wavelength, while the columns represent the differences in attenuation coefficient values ​​due to different wavelengths within the same material. By solving this inverse matrix, the thickness of a specific material can be determined at a single pixel. This thickness value can be used to create an image reconstruction that can decompose the material's composition.
The results show that the 780 nm-830 nm- 980 nm wavelengths successfully decomposed margarine and PVC. Meanwhile, the 780 nm-808nm-980 nm wavelengths successfully decomposed silicone rubber. The Gram-Schmidt process is able to improve the quality of a decomposition image