## 2 Principle of Radar-Based Algorithms  
The mechanism of the microwave imaging is based on the difference in the dielectric property (relative permittivity and conductivity) for healthy and malignant tissues [35]. The dielectric property is an inherent characteristic of the tissue that characterises the transmission, absorption and reflection of electromagnetic energy. An array of antennas is used to penetrate the targeted tissue, and the reflected and transmitted signals are stored. These signals are used as input to imaging algorithms. The most common microwave imaging algorithm used in medicine is CMI. These methods are usually referred to as radar-based methods. It uses the reflected or transmitted signals from the imaged object to reconstruct the resulting image using different beamformers [36]. These beamformers calculate the energy from a focal point and integrate the information to reconstruct an energy map. The basic principle of a radar-based algorithm is to thoroughly delay and sum the signals to reconstruct the image. Each antenna in the microwave imaging system transmits a signal to each focal point in the imaging domain, and the reflected and transmitted signals are stored. The time delay is calculated for each measured signal from the antenna to the focal point and back to the transmitting antenna (monostatic mode) or and receiving antenna (multistatic mode). In time delay calculation, the propagation speed of the signals depends on the relative permittivity of the medium. The signals are thoroughly delayed and summed to calculate energy. When the energy distribution of the whole imaging area for each antenna is obtained, a 2D image is formed. DMAS is an extended version of the DAS algorithm. It produces more accurate and high-resolution results. Similar to DAS, the reflected or transmitted signals are first aligned and then summed to reconstruct the image. The signal energy corresponding to each pixel in the resulting images is equal to the square of the sum of the product of the signal. DMAS increases the sample size by multiplying the signals in pairs before summation, as shown in Figure 1, significantly increasing its computation time. The DMAS algorithm performs a correlation process for each focal point to obtain data with a high degree of similarity. The improvement in the accuracy of the resulting images is due to the substantial increase in the sample size. The observations are shifted according to focal points in the imaging domain using delay values calculated as follows:  
\[\tau(r_{0})=\frac{|t_{x}-r_{0}|+|r_{x}-r_{0}|}{C_{0}/\sqrt{\varepsilon_{r}}} \tag{1}\]  
where \(\tau(r_{0})\) is the delay factor for a focal point \(r_{0}\) for the signal transmitted by an antenna located at \(t_{x}\) and receiving antenna located at \(r_{x}\), \(C_{0}\) denotes the speed of light in space and \(\varepsilon_{r}\) is the relative permittivity of the human head. Assume that there are M observations (\(S_{i}[k]\); \(i=1..M\), \(k=1..L\)), each with L samples, shifted using (1). Then, the output of DAS is as follows:  
\[I_{DAS}=\sum\limits_{k=1}^{L}\left(\sum\limits_{i=1}^{M}S_{i}[k]\right)^{2} \tag{2}\]  
where \(S_{i}[K]\) is the \(i\)th delayed signal  
On the other hand, the output of DMAS is as follows:  
\[I_{DMAS}=\sum\limits_{k=1}^{L}\left(\sum\limits_{i=1}^{M}\sum\limits_{ \begin{subarray}{ c}j=1\\ j\
eq 1\end{subarray} }^{M}S_{i}[k]S_{j}[k]\right) \tag{3}\]  
where \(M\) is the total number of received signals and \(S_{i}[K]\) and \(S_{j}[K]\) are delayed signals according to the positions of the transmitter and receiver antennas. DAS requires M summations and one multiplication for \(M\) observations to estimate the desired value. On the other hand, the DMAS method requires \(M^{2}\) multiplications and \(M^{2}\) summations, increasing the computations and requiring \(M\) times longer to reconstruct an image.