# Parameter Search Algorithms for Microwave Radar-Based Breast Imaging: Focal Quality Metrics as Fitness Functions

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## Abstract

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## 1. Introduction

- that sufficient contrast exists between cancerous and healthy tissues [5];

- estimating from signals that have propagated through the imaging domain;
- and via parameter search based on properties of the reconstructed images.

## 2. Methods

- the exact propagation path, $C(\mathbf{s},\mathbf{r})$, is not known as the tissue composition of the imaging volume is unknown in a screening context;
- human breast tissues are dispersive, but the frequency-dependent propagation speed for each tissue is not known exactly, $c\left(\omega \right)$;
- the propagation speed, $c(\mathbf{r},\omega )$, along the propagation path is also unknown as this depends on the exact tissue composition of the imaging volume.

- the propagation path is assumed as the straight-line path from the antenna, $\mathbf{s}$, to the point of interest, $\mathbf{r}$. This has been found to have a minimal impact on accuracy, at worst 3 mm [35];
- the propagation speed is generally assumed to be defined at the centre frequency of the illumination pulse, ${\omega}_{c}$;
- the propagation speed is assumed to not vary spatially in the entire imaging domain. Although a preliminary numerical study indicated that localisation accuracy could be improved by adapting the propagation delay depending on paths within the breast, this is not practical in realistic scenarios [11].

- A set of backscattered signals, $S\left(t\right)$, is beamformed into the set of images, $\mathcal{I}=\left\{{I}_{{\epsilon}_{r}}\phantom{\rule{3.33333pt}{0ex}}\right|\phantom{\rule{3.33333pt}{0ex}}{\epsilon}_{r}\in {\epsilon}_{r}^{\mathrm{range}}\}$ using a range of assumed average dielectric properties ${\epsilon}_{r}^{\mathrm{range}}$;
- Given a measure of image quality, ${\Phi}$, apply the measure to the the set of images to determine the relative quality of the images where ${\Phi}\left({I}_{{\epsilon}_{r}}\right)=\left\{{\Phi}\left({I}_{{\epsilon}_{r}}\right)\phantom{\rule{3.33333pt}{0ex}}\right|\phantom{\rule{3.33333pt}{0ex}}{I}_{{\epsilon}_{r}}\phantom{\rule{3.33333pt}{0ex}}\in \phantom{\rule{3.33333pt}{0ex}}\mathcal{I}\}$;
- Determine the optimal average dielectric properties, and hence the optimal image, by optimising the relative quality curve, ${\Phi}\left({I}_{{\epsilon}_{r}}\right)$, such that the estimated best-case average dielectric properties, ${\epsilon}_{r}^{{B}^{\prime}}$, are determined as, ${\epsilon}_{r}^{{B}^{\prime}}=\text{}\mathrm{arg}\text{}\mathrm{max}\text{}{\Phi}\left({\epsilon}_{r}\right)$.

#### 2.1. Effect of Incorrect Estimation

#### 2.2. Evaluating Suitable Metrics

- the accuracy ($\Delta {\epsilon}_{r}$): the difference between the best-case effective average dielectric properties, ${\epsilon}_{r}^{{B}^{\prime}}$, and the true average dielectric properties, ${\epsilon}_{r}^{B}$;
- the localisation error, $\Delta \mathbf{r}$: the difference between the apparent location of the scatterer when reconstructing images with the effective average dielectric properties and the location when reconstructing images with the true average dielectric properties;
- the signal-to-clutter ratio (SCR) of the reconstructed image, $\mathrm{SCR}({I}_{{\epsilon}_{r}^{{B}^{\prime}}})$;
- the signal-to-mean ratio (SMR) of the reconstructed image, $\mathrm{SMR}({I}_{{\epsilon}_{r}^{{B}^{\prime}}})$.

## 3. Focal Quality Metrics

- the Discrete Cosine Transform (${\varphi}^{\mathrm{F}}$);
- image gradient (${\varphi}^{\mathrm{G}}$);
- Laplacian approximation (${\varphi}^{\mathrm{L}}$);
- image statistics (${\varphi}^{\mathrm{S}}$);
- and the Discrete Wavelet Transform (${\varphi}^{\mathrm{W}}$).

- variance;
- contrast;
- entropy;
- and the central moment.

## 4. Experimental Evaluation

## 5. Results

- the effect of incorrectly estimating the effective average dielectric properties is analysed using simplified theoretical PSFs and then experimental PSFs;
- next, promising FQMs from each family are selected by evaluating all FQMs described using a variety of targets in a homogeneous breast phantom;
- finally, the best performing metrics in the homogeneous phantoms are analysed in increasingly complex and dielectrically heterogeneous scenarios using an experimental prototype imaging system.

#### 5.1. Effect of Incorrect Parameter Estimation

- in general, the maximum amplitude of the PSF is when the effective average dielectric properties, ${\epsilon}_{r}^{\prime}$, is equal to the true average dielectric properties, ${\epsilon}_{r}$;
- if the effective average dielectric properties are underestimated (i.e., $\sqrt{\frac{{\epsilon}_{r}^{\prime}}{{\epsilon}_{r}}}<1$), the apparent location of the scatterer moves towards the edge of the imaging domain (closer to R). This localisation error is due to reflections appearing to come from closer than their true origin and the channels closest to the scatterer are dominant in the coherent summation;
- conversely, if the effective average dielectric properties are overestimated, the apparent location of the scatterer moves towards the centre of the imaging domain (closer to 0). This localisation error is due to reflections appearing to come from further away than their true origin;
- the number of sidelobes increases as the estimate of the effective average dielectric properties increases; in other words, there is higher spatial frequency content in PSFs with over-estimated effective average dielectric properties, $\sqrt{\frac{{\epsilon}_{r}^{\prime}}{{\epsilon}_{r}}}>1$;
- it can be seen that as the effective average dielectric properties are overestimated, the width of the peak decreases.
- the localisation error is greater when underestimating the effective average dielectric properties compared to overestimation.

- the maximum amplitude of the images with incorrectly estimated effective average dielectric properties is much lower than the ideal image, 40% when underestimated and 9% when overestimated;
- the apparent location of the scatterer moves towards the edge of the imaging domain when the effective average dielectric properties are underestimated, i.e., $\sqrt{\frac{{\epsilon}_{r}^{\prime}}{{\epsilon}_{r}}}<1$;
- the apparent location of the scatterer moves towards the centre of the imaging domain when the effective average dielectric properties are overestimated, i.e., $\sqrt{\frac{{\epsilon}_{r}^{\prime}}{{\epsilon}_{r}}}>1$;
- the area of the response decreases as the estimated effective average dielectric properties increase.
- The localisation error when overestimating the properties is less than when underestimating the properties.

#### 5.2. Initial Evaluation

#### 5.3. Detailed Analysis

- can be calculated easily from the image using simple and well-known kernels in two and three dimensions;
- have a well-understood method of action as differentiation is analogous to high-pass filtering;
- and identify the optimal image in heterogeneous phantoms with different tumour sizes.

## 6. Conclusions and Future Work

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**Block diagram of the proposed imaging system. Focal quality metrics are used in a parameter-search algorithm to identify the best-case average dielectric properties, ${\epsilon}_{r}^{{B}^{\prime}}$. The proposed algorithm is described: from a set of images reconstructed with different average dielectric properties estimates, select the image that the measure of image quality, ${\Phi}$, weights most highly.

**Figure 2.**The acquisition system, example phantom and targets are shown here. (

**a**) shows the 2-port VNA connected to the 24-port switching matrix. The antennas are shown housed in the 3D printed radome; (

**b**) shows the five spherical and smooth tumour models used for evaluation of the FQMs; (

**c**) shows the interior of the phantom with 10% glandular content. Three other similar phantoms with 0%, 20% and 30% glandular content were used in this study. All dimensions are in mm.

**Figure 3.**The theoretical point spread function (PSF) is analysed here. (

**a**) shows the one-dimensional PSF for various values of $\sqrt{\frac{{\epsilon}_{r}^{\prime}}{{\epsilon}_{r}}}$. Localisation error increases as the difference between ${\epsilon}_{r}^{\prime}$ and ${\epsilon}_{r}$ grows. The number of sidelobes decreases as $\sqrt{\frac{{\epsilon}_{r}^{\prime}}{{\epsilon}_{r}}}$ decreases; (

**b**) shows the apparent location of the scatterer as $\sqrt{\frac{{\epsilon}_{r}^{\prime}}{{\epsilon}_{r}}}$ varies; As the effective average dielectric properties are overestimated ($\sqrt{\frac{{\epsilon}_{r}^{\prime}}{{\epsilon}_{r}}}>1$), the apparent location is closer to the centre (0) compared to the true location. As the effective average dielectric properties are underestimated ($\sqrt{\frac{{\epsilon}_{r}^{\prime}}{{\epsilon}_{r}}}<1$), the apparent location is closer to the skin (R) compared to the true location. In both (

**a**,

**b**), the true location is at $T=0.2R$.

**Figure 4.**Coronal slices of the experimental PSF at the tumour location. The maximum intensity of images (

**a**,

**c**) are 40% and 9% of image (

**b**). The normalised images with linear colour scales are displayed so that features can be more clearly identified. Images (

**a–c**) are reconstructed with $\sqrt{\frac{{\epsilon}_{r}^{\prime}}{{\epsilon}_{r}}}\in \{0.5,1,1.5\}$ respectively. The location of the point scatterer is marked with the circle.

**Figure 5.**Shown are coronal, sagittal and transverse slices of images of the tumour model ${T}_{4}$. (

**a**,

**b**) are in a phantom with 10% glandular structures by volume and (

**c**,

**d**) are in a phantom with 30% glandular structures by volume. (

**a**,

**c**) are the images selected by the Gaussian Energy, ${\varphi}_{\mathrm{GSS}}^{\mathrm{G}}$; and (

**b**,

**d**) are the images selected by the Modified Laplacian, ${\varphi}_{\mathrm{M}}^{\mathrm{L}}$. The actual target location is marked by the dotted, red ellipse in each slice.

**Table 1.**Summary of the names, abbreviations and methods of action. $\mathrm{var}\left[X\right]$ represents the variance of X across the imaging area, and $\u2329X\u232a$ represents the mean of X across the imaging area.

Name | Equation |
---|---|

AC–DC Ratio [71] | ${\varphi}_{\mathrm{R}}^{\mathrm{F}}=\u2329\frac{{\sum}_{(n,m)\ne (0,0)}{F}_{x,y}{(n,m)}^{2}}{{F}_{x,y}{(0,0)}^{2}}\u232a$ |

AC–DC Reduced Ratio [72] | ${\varphi}_{\mathrm{RR}}^{\mathrm{F}}=\u2329\frac{{\sum}_{(n,m)\in {P}_{r}}{F}_{x,y}{(n,m)}^{2}}{{F}_{x,y}{(0,0)}^{2}}\u232a$ |

Absolute Gradient [73] | ${\varphi}_{\mathrm{DMA}}^{\mathrm{G}}=\u2329{\mathrm{max}}_{D\in \{X,Y\}}\left|{I}_{D}^{D}(x,y)\right|\u232a$ |

Squared Gradient [73] | ${\varphi}_{\mathrm{DMS}}^{\mathrm{G}}=\u2329{\mathrm{max}}_{D\in \{X,Y\}}{\left|{I}_{D}^{D}(x,y)\right|}^{2}\u232a$ |

Brenner Gradient [60,73,74,75] | ${\varphi}_{\mathrm{BMS}}^{\mathrm{G}}=\u2329{\mathrm{max}}_{D\in \{X,Y\}}{\left|{I}_{D}^{B}(x,y)\right|}^{2}\u232a$ |

Gradient Energy [66,76,77] | ${\varphi}_{\mathrm{DSS}}^{\mathrm{G}}=\u2329{I}_{X}^{D}{(x,y)}^{2}+{I}_{Y}^{D}{(x,y)}^{2}\u232a$ |

Gaussian Energy [78,79] | ${\varphi}_{\mathrm{GSS}}^{\mathrm{G}}=\u2329{I}_{X}^{G}{(x,y)}^{2}+{I}_{Y}^{G}(x,y)\u232a$ |

Tenengrad Mean [69,74,77,80,81] | ${\varphi}_{\mathrm{TM}}^{\mathrm{G}}=\u2329{\mathrm{max}}_{D\in \{X,Y\}}{I}_{D}^{T}{(x,y)}^{2}\u232a$ |

Tenengrad Variance [80] | ${\varphi}_{\mathrm{TV}}^{\mathrm{G}}=\mathrm{var}\left[{\mathrm{max}}_{D\in \{X,Y\}}{I}_{D}^{T}\right]$ |

Laplacian Energy [63,69,70,82] | ${\varphi}_{\mathrm{E}}^{\mathrm{L}}=\u2329\left|L\ast I(x,y)\right|\u232a$ |

Modified Laplacian [83] | ${\varphi}_{\mathrm{M}}^{\mathrm{L}}=\u2329\left|{L}_{x}\ast I(x,y)\right|+\left|{L}_{y}\ast I(x,y)\right|\u232a$ |

Diagonal Laplacian [84] | ${\varphi}_{\mathrm{D}}^{\mathrm{L}}=\u2329{\varphi}_{\mathrm{M}}^{\mathrm{L}}(x,y)+\phantom{\rule{-0.166667em}{0ex}}\phantom{\rule{-0.166667em}{0ex}}\phantom{\rule{-0.166667em}{0ex}}\phantom{\rule{-0.166667em}{0ex}}{\displaystyle \sum _{n\in \{1,2\}}}\phantom{\rule{-0.166667em}{0ex}}\phantom{\rule{-0.166667em}{0ex}}\left|{L}_{dn}\ast I(x,y)\right|\u232a$ |

Laplacian Variance [80] | ${\varphi}_{\mathrm{V}}^{\mathrm{L}}=\mathrm{var}\left[L\ast I\right]$ |

Variance [65,66,67,68,73,74,75,77,81,85] | ${\varphi}_{\mathrm{V}}^{\mathrm{S}}=\mathrm{var}\left[I(x,y)\right]$ |

Normalised Variance [72,73,74] | ${\varphi}_{\mathrm{VN}}^{\mathrm{S}}=\frac{1}{\u2329I(x,y)\u232a}\mathrm{var}\left[I(x,y)\right]$ |

Localised Variance [80] | ${\varphi}_{\mathrm{VL}}^{\mathrm{S}}=\mathrm{var}\left[{L}_{v}(x,y)\right]$ |

Contrast [86] | ${\varphi}_{\mathrm{C}}^{\mathrm{S}}=\u2329{\displaystyle \sum _{i\in W}}{\displaystyle \sum _{j\in W}}I(x,y)\phantom{\rule{-0.166667em}{0ex}}-\phantom{\rule{-0.166667em}{0ex}}I(x+i,y+j)\phantom{\rule{-0.166667em}{0ex}}\u232a$ |

Mean Ratio [81] | ${\varphi}_{\mathrm{R}}^{\mathrm{S}}=\u2329\mathrm{max}\left\{\frac{\mu (x,y)}{I(x,y)},\frac{I(x,y)}{\mu (x,y)}\right\}\u232a$ |

Entropy [65,73,74,75,85,87] | ${\varphi}_{\mathrm{HE}}^{\mathrm{S}}=H\left({I}_{H}\right)$ |

Central Moment [41,88] | ${\varphi}_{\mathrm{ACM}}^{\mathrm{S}}={\sum}_{k}\left|k-\u2329I\u232a\right|{P}_{k}$ |

Absolute Detail Sum [41,87,89] | ${\varphi}_{\mathrm{AS}}^{\mathrm{W}}=\u2329{\displaystyle \sum _{n\in \{\mathrm{LH},\mathrm{HL},\mathrm{HH}\}}}\left|{W}_{\mathrm{n}}^{1}(x,y)\right|\u232a$ |

Detail Variance [87,89] | ${\varphi}_{\mathrm{V}}^{\mathrm{W}}=\u2329{\displaystyle \sum _{n\in \{\mathrm{LH},\mathrm{HL},\mathrm{HH}\}}}\mathrm{var}\left[{W}_{\mathrm{n}}^{1}\right]\u232a$ |

Detail–Coarse Ratio [41,87] | ${\varphi}_{\mathrm{R}}^{\mathrm{W}}=\u2329\frac{{W}_{\mathrm{LH}}^{1}{(x,y)}^{2}+{W}_{\mathrm{HL}}^{1}{(x,y)}^{2}+{W}_{\mathrm{HH}}^{1}{(x,y)}^{2}}{{W}_{\mathrm{LL}}^{1}{(x,y)}^{2}+{W}_{\mathrm{LL}}^{2}{(x,y)}^{2}+{W}_{\mathrm{LL}}^{3}{(x,y)}^{2}}\u232a$ |

**Table 2.**Evaluation of performance of all metrics in homogeneous scenarios. Ranks are shown in parentheses, within each method of action for each individual criterion. Two overall ranks are shown, first within each method of action and then for all metrics (local/global). The top performing metrics are shown in

**bold**.

Metric | $\mathbf{\Delta}{\mathit{\epsilon}}_{\mathit{r}}$ | $\mathbf{\Delta}\mathit{r}$ | SMR$\left({\mathit{I}}_{{\mathit{\epsilon}}_{\mathit{r}}^{{\mathit{B}}^{\prime}}}\right)$ | SCR$\left({\mathit{I}}_{{\mathit{\epsilon}}_{\mathit{r}}^{{\mathit{B}}^{\prime}}}\right)$ | Ranks |
---|---|---|---|---|---|

${\varphi}_{\mathbf{R}}^{\mathbf{F}}$ | 2.5 (1) | 10.9 (1) | 7.6 (1) | 3.8 (1) | (1/21) |

${\varphi}_{\mathrm{RR}}^{\mathrm{F}}$ | 3.0 (2) | 13.3 (2) | 5.0 (2) | 2.5 (2) | (2/22) |

${\varphi}_{\mathbf{GSS}}^{\mathbf{G}}$ | 1.4 (2) | 4.6 (1) | 18.3 (1) | 8.5 (1) | (1/2) |

${\varphi}_{\mathrm{DMA}}^{\mathrm{G}}$ | 1.3 (1) | 6.6 (2) | 16.7 (2) | 8.0 (2) | (2/7) |

${\varphi}_{\mathrm{TM}}^{\mathrm{G}}$ | 1.4 (3) | 7.4 (3) | 14.5 (3) | 7.1 (3) | (3/8) |

${\varphi}_{\mathrm{DMS}}^{\mathrm{G}}$ | 1.5 (4) | 7.4 (4) | 14.5 (4) | 7.1 (4) | (4/10) |

${\varphi}_{\mathrm{DSS}}^{\mathrm{G}}$ | 1.5 (4) | 7.4 (4) | 14.5 (4) | 7.1 (4) | (4/10) |

${\varphi}_{\mathrm{BMS}}^{\mathrm{G}}$ | 1.5 (6) | 7.6 (6) | 14.5 (6) | 7.1 (6) | (6/15) |

${\varphi}_{\mathrm{TV}}^{\mathrm{G}}$ | 1.9 (7) | 8.9 (7) | 11.8 (7) | 5.7 (7) | (7/18) |

${\varphi}_{\mathbf{M}}^{\mathbf{L}}$ | 1.5 (1) | 7.3 (1) | 14.5 (1) | 7.0 (4) | (1/9) |

${\varphi}_{\mathrm{D}}^{\mathrm{L}}$ | 1.5 (3) | 7.3 (2) | 14.5 (2) | 7.0 (3) | (2/12) |

${\varphi}_{\mathrm{E}}^{\mathrm{L}}$ | 1.5 (3) | 7.6 (4) | 14.4 (4) | 7.0 (2) | (4/16) |

${\varphi}_{\mathrm{V}}^{\mathrm{L}}$ | 1.5 (3) | 7.6 (4) | 14.4 (4) | 7.0 (2) | (4/16) |

${\varphi}_{\mathbf{ACM}}^{\mathbf{S}}$ | 0.7 (1) | 5.2 (1) | 17.1 (2) | 8.3 (1) | (1/1) |

${\varphi}_{\mathrm{V}}^{\mathrm{S}}$ | 0.8 (2) | 5.5 (3) | 17.1 (3) | 8.3 (2) | (2/3) |

${\varphi}_{\mathrm{VL}}^{\mathrm{S}}$ | 1.3 (5) | 5.9 (4) | 17.5 (1) | 8.2 (3) | (3/4) |

${\varphi}_{\mathrm{VN}}^{\mathrm{S}}$ | 1.3 (4) | 5.2 (2) | 16.4 (5) | 7.9 (5) | (4/6) |

${\varphi}_{\mathrm{C}}^{\mathrm{S}}$ | 1.3 (3) | 6.6 (5) | 16.7 (4) | 8.1 (4) | (4/5) |

${\varphi}_{\mathrm{R}}^{\mathrm{S}}$ | 2.3 (6) | 9.8 (6) | 7.5 (7) | 3.6 (7) | (6/20) |

${\varphi}_{\mathrm{HE}}^{\mathrm{S}}$ | 2.4 (7) | 11.0 (7) | 7.8 (6) | 3.9 (6) | (6/19) |

${\varphi}_{\mathbf{V}}^{\mathbf{W}}$ | 1.5 (2) | 7.3 (1) | 14.5 (1) | 7.0 (1) | (1/12) |

${\varphi}_{\mathrm{AS}}^{\mathrm{W}}$ | 1.5 (2) | 7.3 (2) | 14.5 (2) | 7.0 (2) | (2/14) |

${\varphi}_{\mathrm{R}}^{\mathrm{W}}$ | 5.0 (3) | 31.0 (3) | 0.0 (3) | 0.0 (3) | (3/23) |

**Table 3.**$\Delta \mathbf{r}$, $\mathrm{SMR}({I}_{{\epsilon}_{r}^{{B}^{\prime}}})$ and $\mathrm{SCR}({I}_{{\epsilon}_{r}^{{B}^{\prime}}})$ evaluated for spherical targets of increasing diameter in phantoms of increasing heterogeneity.

$\mathbf{\Delta}\mathit{r}$ (mm) | SMR$\left({\mathit{I}}_{{\mathit{\epsilon}}_{\mathit{r}}^{{\mathit{B}}^{\prime}}}\right)$ (dB) | SCR$\left({\mathit{I}}_{{\mathit{\epsilon}}_{\mathit{r}}^{{\mathit{B}}^{\prime}}}\right)$ (dB) | |||||||
---|---|---|---|---|---|---|---|---|---|

${\varphi}_{\mathrm{GSS}}^{\mathrm{G}}$ | ${\varphi}_{\mathrm{M}}^{\mathrm{L}}$ | ${\varphi}_{\mathrm{ACM}}^{\mathrm{S}}$ | ${\varphi}_{\mathrm{GSS}}^{\mathrm{G}}$ | ${\varphi}_{\mathrm{M}}^{\mathrm{L}}$ | ${\varphi}_{\mathrm{ACM}}^{\mathrm{S}}$ | ${\varphi}_{\mathrm{GSS}}^{\mathrm{G}}$ | ${\varphi}_{\mathrm{M}}^{\mathrm{L}}$ | ${\varphi}_{\mathrm{ACM}}^{\mathrm{S}}$ | |

10% het. | |||||||||

d = 5.3 | 12 | 11 | 12 | 1.9 | 1.7 | 1.9 | 15.6 | 15.7 | 15.6 |

d = 7.8 | 14 | 14 | 14 | 3.9 | 3.6 | 3.9 | 17.8 | 17.8 | 17.8 |

d = 10.9 | 1 | 1 | 1 | 1.5 | 1.9 | 1.9 | 16.6 | 16.6 | 16.6 |

d = 13.1 | 2 | 63 | 2 | 0.5 | 2.9 | 0.5 | 14.3 | 14 | 14.3 |

d = 20.2 | 8 | 8 | 8 | 2.3 | 1.9 | 2.3 | 13.7 | 13.7 | 13.7 |

20% het. | |||||||||

d = 5.3 | 83 | 83 | 83 | 3.5 | 3.5 | 3.5 | 14.9 | 14.9 | 14.9 |

d = 7.8 | 21 | 76 | 21 | 1.1 | 0.7 | 1.1 | 14.6 | 14 | 14.6 |

d = 10.9 | 45 | 52 | 45 | 0.9 | 0.8 | 0.9 | 12.8 | 12.8 | 12.8 |

d = 13.1 | 3 | 4 | 3 | 3.8 | 3.6 | 3.8 | 17.9 | 17.9 | 17.9 |

d = 20.2 | 7 | 8 | 7 | 2.4 | 2.5 | 2.4 | 15.5 | 15.6 | 15.5 |

30% het. | |||||||||

d = 5.3 | 36 | 16 | 36 | 0.1 | 0.6 | 0.1 | 11.8 | 10.4 | 11.8 |

d = 7.8 | 21 | 21 | 21 | 0.2 | 0.2 | 0.2 | 12.1 | 12.1 | 12.1 |

d = 10.9 | 29 | 29 | 29 | 0.5 | 0.9 | 0.5 | 11.9 | 12.1 | 11.9 |

d = 13.1 | 39 | 28 | 39 | 0.6 | 1 | 0.6 | 13 | 11.1 | 13 |

d = 20.2 | 13 | 9 | 13 | 1.2 | 1.3 | 1.2 | 16.5 | 15.6 | 16.5 |

© 2017 by the authors. 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 (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

O’Loughlin, D.; Oliveira, B.L.; Elahi, M.A.; Glavin, M.; Jones, E.; Popović, M.; O’Halloran, M. Parameter Search Algorithms for Microwave Radar-Based Breast Imaging: Focal Quality Metrics as Fitness Functions. *Sensors* **2017**, *17*, 2823.
https://doi.org/10.3390/s17122823

**AMA Style**

O’Loughlin D, Oliveira BL, Elahi MA, Glavin M, Jones E, Popović M, O’Halloran M. Parameter Search Algorithms for Microwave Radar-Based Breast Imaging: Focal Quality Metrics as Fitness Functions. *Sensors*. 2017; 17(12):2823.
https://doi.org/10.3390/s17122823

**Chicago/Turabian Style**

O’Loughlin, Declan, Bárbara L. Oliveira, Muhammad Adnan Elahi, Martin Glavin, Edward Jones, Milica Popović, and Martin O’Halloran. 2017. "Parameter Search Algorithms for Microwave Radar-Based Breast Imaging: Focal Quality Metrics as Fitness Functions" *Sensors* 17, no. 12: 2823.
https://doi.org/10.3390/s17122823