**5. Simulation result of image reconstruction**

The reconstructed image can be obtained using the Levenberg–Marquardt algorithm by providing optical flux, scattering coefficient, and absorption coefficient values, which are then compared to distinguish between normal soft tissue and cancer-affected tissue. The forward mesh has more nodes to extract all of the optical parameters of the tissue, whereas the inverse mesh has fewer nodes for reconstruction. As shown in **Figure 1**, the forward mesh has 1097 nodes and 2095 elements, and the reverse mesh has 286 nodes and 522 elements.

**Figure 2** depicts the reconstruction based on absorption and scattering coefficient measurements. The image is reconstructed using optical properties of human tissue such as absorption coefficient and scattering coefficient (and (r) = 2). The reconstructed image is based on the absorption and scattering coefficient values. It is possible to predict normal tissue and cancer-affected tissue by examining the reconstructed image with absorption and scattering coefficients. When the absorption and scattering coefficients are higher, the tumor is classified as malignant or benign soft tissue tumor.

The split Bregman algorithm with sparsity regularization efficiently solves the DOT image reconstruction problem. **Figure 3** depicts a Spilt Bregman reconstruction from scattering coefficients. The scattering coefficient value distinguishes the variation of abnormal tissue to normal tissue. According to **Figure 3**, the abnormal tissue scattering coefficient ranges from 150 to 210, whereas the normal tissue scattering coefficient ranges from 0 to 20. When compared to other reconstruction algorithms, the Bregman algorithm produces more accurate results. The reconstructed image's

**Figure 1.** *Mesh diagram of inverse problem.*

*Soft Tissue Image Reconstruction Using Diffuse Optical Tomography DOI: http://dx.doi.org/10.5772/intechopen.102463*

**Figure 2.** *Levenberg–Marquardt regularization and standard reconstruction.*

**Figure 3.** *Spilt Bregman regularization with sparsity reconstruction.*

resolution is determined by calculating the signal-to-noise ratio (SNR), contrast-tonoise ratio (CNR), relative solution error norm (RE), and CPU time. SNR is calculated as follows:

$$\text{SNR} = \mathbf{10} \log\_{10} \left( \frac{P\_{signal}}{P\_{noise}} \right) \tag{20}$$

The CNR is a metric used to assess image quality. The mean and standard deviation values are used to calculate it. CNR is calculated as follows:

$$\text{CNR} = \frac{\text{S}\_A - \text{S}\_B}{\sigma\_0} \tag{21}$$


**Table 1.**

*Performance analysis of reconstruction algorithms.*

**Figure 4.** *Performance analysis of reconstruction algorithms.*

where are the image signal intensities and is the standard deviation of pure image noise. The Relative solution error norm is computed as follows:

$$E = \frac{\left\|\mu\_{\mathcal{S}} - \mu\_{\mathcal{S}}^{true}\right\|\_{2}}{\left\|\mu\_{\mathcal{s}}^{true}\right\|\_{2}}\tag{22}$$

**Table 1** compares parameters used to evaluate the performance of reconstruction algorithms. The Split Bregman method has a higher SNR than the Gauss Newton algorithm and improves CNR more than the Gauss Newton method. To achieve better performance, the RE of a reconstructed image should be low. Because the Gauss Newton method has a high RE value, it is not an optimal solution for image reconstruction. Finally, when compared to the Gauss Newton method, the Split Bregman method requires less CPU time to execute. The graph of the performance analysis of the Split Bregman and Gauss Newton algorithms is shown in **Figure 4**.
