# Radar-Based Microwave Breast Imaging Using Neurocomputational Models

## Abstract

**:**

## 1. Introduction

- In this study, conventional imaging was carried out utilizing CSAR-based numerical data and an MP-based algorithm.
- For imaging, both the matching-pursuit-based method and the neurocomputational models utilized raw, unprocessed real-valued, and complex-valued numerical data. Computed or measured scattered electric field data can therefore be applied directly to models without preprocessing.
- RV-DNN and RV-CNN models are proposed, followed by two combined neurocomputational models (RV-MWINet and CV-MWINet) employing the proposed CNN model structure, which combines the U-Net structure. The images generated by the proposed models are compared to those generated by the matching-pursuit algorithm. The study demonstrates that the processing and generation speeds of the proposed models are faster than those of conventional imaging techniques, and that the resulting images are of higher quality.
- By placing a screw in the sand and an unhealthy tumor phantom in a healthy phantom, a total of 12 measurements were taken in the range of 1 GHz to 10 GHz, using the measurement setup. In order to train the CV-MWINet model, measurement data were added to the dataset obtained from simulated data. Also, the performance of the proposed model on both simulated and measured data is discussed.

## 2. The Forward Problem Based on the Circular Synthetic Aperture Radar (CSAR) Principle

**r**), and collects backscattered electric field data from this domain. This method assumes that the imaging domain is entirely encompassed by the radiation pattern of the antenna. Thus, the electric field measurements backscattered from the imaging domain contain information about the target object. The backscattered electric field data obtained in accordance with the structure depicted in Figure 1 comprise information regarding skin and tumors.

_{0}, f, ε

_{r}, μ

_{r}, c, and

**R**(ϕ) denote the amplitude of the electric field, frequency, relative permittivity, magnetic permeability, the phase velocity of the wave, and the Euclidean distance function between the scatterer and antenna. For most common materials, μ

_{r}is considered as 1. For the sake of simplicity, the imaging field is considered to be homogenous, and the tumor and skin are supposed to be discrete perfect scatterers. The angle-dependent Euclidean distance in the expression given in Equation (1) is calculated by Equation (2) [38].

_{m}), which can be determined using Equation (3) [38].

## 3. Phantom Fabrication and Measurement

_{11}) was measured at a total of 90 angles for a total of 360 degrees. Figure 3 depicts the dielectric constant measurement graph of the phantoms manufactured as shown in Figure 2a.

## 4. Microwave Imaging (MWI) Using Deep Learning (DL) Models

#### 4.1. Similarities between DL and Non-Linear Electromagnetic Scattering

_{0}, ${H}_{0}^{\left(1\right)}$ and χ represent the index of the scattering, the wavenumber of the background medium, the first-kind zeroth-order Hankel function, and the contrast function, respectively.

**r**= (x, y) and

**r**’ = (x’, y’) indicate the field and source positions, respectively, and are evaluated as

**r**,

**r**’ ∈ Ω. In computational imaging, the imaging region surrounded by antennas and whose content is unknown is regarded as being divided into pixels. The values of the pixels provide information related to the contrast values. Consequently, the value of the scattered electric field to be used in the imaging process is computed using Equation (6) [20].

**G**in Equations (6) and (7). Iteratively applying Equations (6) and (7) yields the expression given in Equation (8) for the (t+1)th stage of the contrast function [20].

**D**is utilized to describe a sparse transformation process like a wavelet. The contrast function at time t + 1 can be defined as in Equation (10) [20].

**P**

_{(t)}and

**b**

_{(t)}in Equation (11) are given in Equations (13) and (14) [20].

**P**and

**b**in Equation (12) correspond to the weights and bias values of fully connected NNs. The indices (t) of these parameters represent the neural network layers. This similarity and relationship demonstrate that DL models are applicable to non-linear electromagnetic scattering challenges.

#### 4.2. Deep Neural Network-Based (DNN-Based) Imaging

_{i}, N, W

_{ij}, x

_{j}, and b

_{i}

^{h}represent the output value of the element, the number of inputs to the element, the weight coefficients at the input of the element, the values at the input of the element, and the bias value, respectively. The parameter σ represents the activation function, and the rectified linear unit (ReLU) activation function used in this study is given in Equation (16).

#### 4.3. Convolutional Neural Networks-Based (CNN-Based) Imaging

^{l}

^{+1}derived from Equation (17) belongs to the solution set ${\mathbb{R}}^{{H}^{l+1}\times {W}^{l+1}\times {D}^{l+1}}$.

^{l}represents the input of the lth layer, while x

^{l}

^{+1}represents the output of this layer, as well as the input of the (l + 1)th layer. f represents the kernel function for ${\mathbb{R}}^{H\times W\times {D}^{l}\times D}$, while the $\rho $ function is the activation function.

^{l}

^{+1}= H

^{l}– H + 1, W

^{l}

^{+1}= W

^{l}− W + 1 and D

^{l}

^{+1}= D. H × W represents the spatial span of each kernel, whereas D indicates the total number of kernels. The RV-CNN model developed in this study also employs the ReLU activation function derived from Equation (16). The RV-CNN model proposed in the study is shown in Figure 5.

#### 4.4. U-Net-Based Combined Neurocomputational Imaging Model

#### 4.5. Evaluation Metrics

_{I}parameter in the equation represents the maximum value of the pixels. In addition to PSNR, the UQI and SSIM metrics given in Equations (27) and (28) provide significant information about the generated images. The values of the variables used in Equations (27) and (28) are calculated by Equations (22)–(26).

_{1}and C

_{2}coefficients. The UQI value is achieved when C

_{1}and C

_{2}in the SSIM equation are both set to 0.

## 5. Numerical Results and Discussion

## 6. Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Simulation setup for two-dimensional breast tumor imaging (The red arcs from the antenna to the imaging field represent the propagating wave, the gray arrows the scattered field, and the red arrows the backscattered field).

**Figure 2.**(

**a**) Fantom fabrication, dielectric constant measurement of (

**b**) healthy and (

**c**) tumor phantoms and (

**d**) microwave measurement setup for two-dimensional breast tumor imaging.

**Figure 5.**The proposed RV-CNN model for microwave medical imaging (Input data is shown in red color).

**Figure 6.**The proposed MWINet model for microwave medical imaging (Input data is shown in red color).

**Figure 7.**Mean squared error (MSE) curves for training and validation phases of the proposed RV-DNN model.

**Figure 8.**Mean squared error (MSE) curves for training and validation phases of the proposed RV-CNN model.

**Figure 11.**Comparison of samples of microwave images generated by the proposed neurocomputational models for train data ((

**a**,

**g**,

**m**) are ground truth images).

**Figure 12.**Comparison of samples of microwave images generated by the proposed neurocomputational models for test data ((

**a**,

**g**,

**m**) are ground truth images).

**Figure 13.**Comparison of samples of microwave images generated by the proposed CV-MWINet model for measurement data (metal screw in fine dust).

**Figure 14.**Comparison of samples of microwave images generated by the proposed CV-MWINet model for measurement data (tumor phantom in healthy phantom).

Parameter | Value |
---|---|

Start Frequency (GHz) | 1 |

Stop Frequency (GHz) | 10 |

Frequency Count | 301 |

Skin Radius (cm) | 7 |

Gap Between Skin and Antenna (cm) | 2 |

Number of Tumor Scatterers | 1–3 |

Radius Range of Tumor Scatterers (cm) | 0.2–0.9 |

Rotation Angle Increment (°) | 4 |

Layer | Output Shape | Number of Parameters |
---|---|---|

Convolution 2D | (299, 89, 32) | 288 |

Batch Normalization | (299, 89, 32) | 128 |

Convolution 2D | (297, 86, 32) | 9216 |

Batch Normalization | (297, 86, 32) | 128 |

Maximum Pooling 2D | (99, 28, 32) | - |

Convolution 2D | (97, 26, 64) | 18,432 |

Batch Normalization | (97, 26, 64) | 256 |

Convolution 2D | (95, 24, 64) | 36,864 |

Batch Normalization | (95, 24, 64) | 256 |

Maximum Pooling 2D | (31, 8, 64) | - |

Convolution 2D | (29, 6, 128) | 73,728 |

Batch Normalization | (29, 6, 128) | 512 |

Convolution 2D | (27, 4, 128) | 147,456 |

Batch Normalization | (27, 4, 128) | 512 |

Convolution 2D | (25, 2, 128) | 147,456 |

Batch Normalization | (25, 2, 128) | 512 |

Flatten | 6400 | - |

Fully Connected #1 | 2048 | 13,107,200 |

Batch Normalization | 2048 | 8192 |

Fully Connected #2 | 2048 | 4,196,352 |

Fully Connected #3 | 16,384 | 33,570,816 |

**Table 3.**Performance metrics of the proposed neurocomputational models for 10-fold cross-validation using train data.

Parameters | RV-DNN | RV-CNN | RV-MWINet | CV-MWI-Net | |||||
---|---|---|---|---|---|---|---|---|---|

MSE | SSIM | MSE | SSIM | ACC | SIM | ACC | SSIM | ||

10-fold Cross-Validation | Fold #1 | 97.784 ± 45.153 | 0.918 ± 0.031 | 62.731 ± 33.540 | 0.897 ± 0.051 | 0.999 ± 0.001 | 1.000 ± 0.000 | 1.000 ± 0.000 | 1.000 ± 0.000 |

Fold #2 | 100.917 ± 47.951 | 0.925 ± 0.029 | 75.192 ± 42.959 | 0.893 ± 0.052 | 0.988 ± 0.005 | 0.998 ± 0.000 | 1.000 ± 0.000 | 1.000 ± 0.000 | |

Fold #3 | 102.443 ± 48.706 | 0.922 ± 0.030 | 65.007 ± 41.774 | 0.888 ± 0.054 | 0.998 ± 0.002 | 1.000 ± 0.000 | 1.000 ± 0.000 | 1.000 ± 0.000 | |

Fold #4 | 92.100 ± 43.208 | 0.925 ± 0.029 | 74.251 ± 48.942 | 0.886 ± 0.053 | 0.994 ± 0.004 | 0.999 ± 0.000 | 1.000 ± 0.000 | 1.000 ± 0.000 | |

Fold #5 | 101.076 ± 47.054 | 0.924 ± 0.031 | 61.865 ± 38.730 | 0.887 ± 0.054 | 0.998 ±0.001 | 1.000 ± 0.000 | 1.000 ± 0.000 | 1.000 ± 0.000 | |

Fold #6 | 92.854 ± 41.111 | 0.924 ± 0.031 | 79.385 ± 47.123 | 0.890 ± 0.058 | 1.000 ± 0.000 | 1.000 ± 0.000 | 1.000 ± 0.000 | 1.000 ± 0.000 | |

Fold #7 | 98.932 ± 46.810 | 0.924 ± 0.030 | 65.930 ± 49.868 | 0.891 ± 0.056 | 0.999 ± 0.001 | 1.000 ± 0.000 | 1.000 ± 0.000 | 1.000 ± 0.000 | |

Fold #8 | 98.564 ± 45.503 | 0.925 ± 0.030 | 61.795 ± 39.846 | 0.890 ± 0.052 | 0.999 ± 0.001 | 1.000 ± 0.000 | 1.000 ± 0.000 | 1.000 ± 0.000 | |

Fold #9 | 102.653 ± 49.134 | 0.921 ± 0.031 | 61.114 ± 43.199 | 0.892 ± 0.053 | 0.994 ± 0.004 | 1.000 ± 0.000 | 1.000 ± 0.000 | 1.000 ± 0.000 | |

Fold #10 | 93.116 ± 43.122 | 0.927 ± 0.030 | 71.750 ± 58.493 | 0.888 ± 0.057 | 0.996 ± 0.003 | 1.000 ± 0.000 | 1.000 ± 0.000 | 1.000 ± 0.000 | |

Average | 98.044 ± 45.775 | 0.924 ± 0.030 | 67.902 ± 44.447 | 0.890 ± 0.054 | 0.997 ± 0.002 | 1.000 ± 0.000 | 1.000 ± 0.000 | 1.000 ± 0.000 |

**Table 4.**Performance metrics of the proposed neurocomputational models for 10-fold cross-validation using test data.

Parameters | RV-DNN | RV-CNN | RV-MWINet | CV-MWINet | |||||
---|---|---|---|---|---|---|---|---|---|

MSE | SSIM | MSE | SSIM | ACC | SSIM | ACC | SSIM | ||

10-fold Cross-Validation | Fold #1 | 185.183 ± 124.598 | 0.914 ± 0.030 | 157.868 ± 108.600 | 0.915 ± 0.030 | 0.995 ± 0.004 | 1.000 ± 0.000 | 0.992 ± 0.005 | 0.999 ± 0.001 |

Fold #2 | 207.658 ± 136.553 | 0.912 ± 0.033 | 162.565 ± 107.290 | 0.910 ± 0.033 | 0.987 ± 0.005 | 0.998 ± 0.000 | 0.993 ± 0.005 | 0.999 ± 0.001 | |

Fold #3 | 195.671 ± 132.356 | 0.911 ± 0.032 | 156.713 ± 109.397 | 0.910 ± 0.027 | 0.993 ± 0.004 | 0.999 ± 0.001 | 0.993 ± 0.004 | 0.999 ± 0.001 | |

Fold #4 | 200.928 ± 137.845 | 0.919 ± 0.027 | 163.380 ± 109.841 | 0.906 ± 0.032 | 0.992 ± 0.005 | 0.999 ± 0.001 | 0.993 ± 0.004 | 0.999 ± 0.001 | |

Fold #5 | 181.389 ± 119.239 | 0.916 ± 0.031 | 152.357 ± 107.160 | 0.915 ± 0.028 | 0.993 ± 0.004 | 0.999 ± 0.000 | 0.993 ± 0.005 | 0.999 ± 0.001 | |

Fold #6 | 216.705 ± 140.831 | 0.912 ± 0.030 | 178.969 ± 122.073 | 0.909 ± 0.033 | 0.993 ± 0.005 | 0.999 ± 0.001 | 0.993 ± 0.005 | 0.999 ± 0.001 | |

Fold #7 | 202.940 ± 135.807 | 0.915 ± 0.029 | 168.076 ± 117.404 | 0.910 ± 0.032 | 0.993 ± 0.004 | 0.999 ± 0.001 | 0.994 ± 0.004 | 0.999 ± 0.000 | |

Fold #8 | 187.140 ± 126.529 | 0.914 ± 0.024 | 150.096 ± 112.963 | 0.911 ± 0.030 | 0.995 ± 0.004 | 1.000 ± 0.000 | 0.994 ± 0.004 | 0.999 ± 0.000 | |

Fold #9 | 198.709 ± 135.104 | 0.914 ± 0.028 | 164.587 ± 112.925 | 0.913 ± 0.028 | 0.991 ± 0.006 | 0.999 ± 0.001 | 0.992 ± 0.005 | 0.999 ± 0.001 | |

Fold #10 | 197.682 ± 123.131 | 0.916 ± 0.029 | 166.285 ± 111.977 | 0.910 ± 0.029 | 0.993 ± 0.004 | 0.999 ± 0.001 | 0.993 ± 0.005 | 0.999 ± 0.001 | |

Average | 197.401 ± 131.199 | 0.914 ± 0.030 | 162.089 ± 111.963 | 0.911 ± 0.030 | 0.993 ± 0.005 | 0.999 ± 0.001 | 0.993 ± 0.004 | 0.999 ± 0.001 |

Scenarios | Materials | Distance from the Center (cm) |
---|---|---|

#1 | Metal screw in fine sand | 0 |

#2 | 2 | |

#3 | 4 | |

#4 | 6 | |

#5 | Tumor phantom in healthy phantom | 0 |

#6 | 2 | |

#7 | 4 | |

#8 | 5.5 |

Metrics/Models | Train Data | Test Data | Avgs. ± Stds. | ||||||
---|---|---|---|---|---|---|---|---|---|

1 Tumor | 2 Tumor | 3 Tumor | 1 Tumor | 2 Tumor | 3 Tumor | All Train Set | All Test Set | ||

PSNR (dB) | MP-Based Algorithm | 25.87656 | 24.14579 | 22.83756 | 19.78088 | 23.12839 | 22.51522 | – | – |

RV-DNN Model | 23.0948 | 22.02725 | 17.7845 | 23.76579 | 18.924 | 21.27754 | 20.37510 ± 2.89746 | 20.52958 ± 2.93180 | |

RV-CNN Model | 23.62187 | 22.1329 | 19.95046 | 21.513 | 20.54329 | 19.71726 | 21.22355 ± 2.27647 | 21.38717 ± 2.62633 | |

RV-MWINet Model | 42.35213 | 34.39235 | 34.32751 | 37.00931 | 35.94595 | 34.00697 | 34.68058 ± 3.24353 | 34.57853 ± 3.53797 | |

CV-MWINet Model | 217.02188 | 207.71069 | 209.097967 | 210.92949 | 207.84857 | 206.52970 | 209.09540 ± 3.56411 | 209.46525 ± 3.59434 | |

UQI | MP-based Algorithm | 0.914 | 0.92553 | 0.90138 | 0.82 | 0.91924 | 0.89136 | – | – |

RV-DNN Model | 0.74023 | 0.73941 | 0.71659 | 0.74554 | 0.72334 | 0.73738 | 0.72929 ± 0.01239 | 0.72974 ± 0.1239 | |

RV-CNN Model | 0.74212 | 0.73895 | 0.72828 | 0.73449 | 0.73098 | 0.72887 | 0.73380 ± 0.00854 | 0.73426 ± 0.00957 | |

RV-MWINet Model | 0.9995 | 0.99792 | 0.99783 | 0.9986 | 0.99842 | 0.99758 | 0.99759 ± 0.00172 | 0.99750 ± 0.00211 | |

CV-MWINet Model | 0.99118 | 0.967916 | 0.966361 | 0.98312 | 0.96825 | 0.95368 | 0.96754 ± 0.01632 | 0.96995 ± 0.01479 | |

SSIM | MP- Based Algorithm | 0.82675 | 0.84876 | 0.80792 | 0.67093 | 0.83687 | 0.78471 | – | – |

RV-DNN Model | 0.75538 | 0.74624 | 0.7142 | 0.75802 | 0.7257 | 0.73583 | 0.73705 ± 0.02006 | 0.73754 ± 0.01913 | |

RV-CNN Model | 0.75643 | 0.72977 | 0.725 | 0.74177 | 0.7018 | 0.72572 | 0.73220 ± 0.01953 | 0.73457 ± 0.02198 | |

RV-MWINet Model | 0.99878 | 0.99291 | 0.99312 | 0.99642 | 0.99473 | 0.99159 | 0.99295 ± 0.00396 | 0.99302 ± 0.00419 | |

CV-MWINet Model | 1.00000 | 1.00000 | 1.00000 | 1.00000 | 1.00000 | 1.00000 | 1.00000 ± 0.00000 | 1.00000 ± 0.00000 |

Mesh Points | 9061 Points | 16,105 Points | |
---|---|---|---|

Train Data | 1 Tumor | 189.96657 s | 385.11506 s |

2 Tumor | 186.09587 s | 391.25924 s | |

3 Tumor | 184.26689 s | 337.86427 s | |

Test Data | 1 Tumor | 180.65272 s | 386.98390 s |

2 Tumor | 185.19212 s | 370.29391 s | |

3 Tumor | 184.13824 s | 376.40420 s | |

Avgs. ± Stds. | 185.05210 ± 3.03536 s | 374.6534 ± 19.55980 s |

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© 2023 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Bicer, M.B.
Radar-Based Microwave Breast Imaging Using Neurocomputational Models. *Diagnostics* **2023**, *13*, 930.
https://doi.org/10.3390/diagnostics13050930

**AMA Style**

Bicer MB.
Radar-Based Microwave Breast Imaging Using Neurocomputational Models. *Diagnostics*. 2023; 13(5):930.
https://doi.org/10.3390/diagnostics13050930

**Chicago/Turabian Style**

Bicer, Mustafa Berkan.
2023. "Radar-Based Microwave Breast Imaging Using Neurocomputational Models" *Diagnostics* 13, no. 5: 930.
https://doi.org/10.3390/diagnostics13050930