## 4 Numerical Experiments
### Reconstruction Results  
The illustrating reconstructions are presented for two phase test-objects with the invariant amplitudes equal to 1 and the phases: \"truncated Gaussian\" and \"logo\" of Tampere University of Technology (TUT), \(100\times 100\) pixels both. The wrapped and absolute phases of these test-objects are shown in Figure 2. The TUT logo and truncated Gaussian phases are very different, the first one is discontinuous binary and the second one is piecewise-smooth continuous. The both test-objects are taken with a high peak-value of the absolute phase equal to \(35\pi\) rad, that corresponds to about 35 reference wavelength \(\lambda^{\prime}\) in variations of the profile \(h_{o}\). We demonstrate the performance of the WM-APR algorithm for this quite difficult test-objects provided very noisy Poissonian observations. The noisiness of observations is illustrated by values of \(SNR\) (Equation (11)) and \(N_{photon}\) (Equation (12)). The accuracy of the object reconstruction is characterized by Relative Root-Mean-Square Error (\(RRMSE\)) calculated as \(RMSE\) divided by the root of the mean square power of the true signal:  
\[RRMSE_{\varphi}=\frac{\sqrt{||\phi_{est}-\varphi_{true}||_{2}^{2}}}{\sqrt{|| \varphi_{true}||_{2}^{2}}}, \tag{24}\]  
In this criterion the phase estimate is corrected by the mean value of the error between the estimate and true absolute phase. It is the standard approach to evaluation of the accuracy for the phase retrieval, where the phase is estimated within an invariant error. Note, that values of \(RRMSE\) are identical for accuracy of the phase and the profile \(h_{o}\). It happens because these variables are different only by the invariant factors, which are the same in nominator and denominator of \(RRMSE\). Figure 3 shows the performance of the developed WM-APR algorithm for different noise levels by a dependence of \(RRMSE\) from the noisiness parameter \(\chi\). The \(RRMSE\) curves for truncated Gaussian and logo TUT are given for different numbers of experiments \(S=7\) and \(S=4\), respectively. They demonstrate a similar behavior: go down for growing \(\chi\) and take values about 0.1 at \(\chi=40\), what corresponds to the very noisy observed data with a low value of \(SNR=5.6\) dB and small mean photon number \(N_{photon}=1.42\). Figure 2: Wrapped and absolute phases of the investigated test-objects: truncated Gaussian and TUT logo, the reference wavelength \(\lambda^{\prime}=\lambda_{3}\). _RRMSEs_ for the logo TUT and Gaussian phases are shown in Figure 4 as functions of the experiment number \(S\) and \(SNR\) after 300 iterations. Nearly horizontal areas (dark blue in color images) correspond to high-accuracy reconstructions with small values of \(RRMSE\), for other areas \(RRMSE\) values are much higher and the accuracy is not so good. As it can be seen from these maps, reconstruction results for logo TUT demonstrate good small \(RRMSE\) values in wide ranges of \(SNR\) and \(S\), while truncated Gaussian has such small \(RRMSE\) values only for \(S\geq 7\) and \(SNR>5\). It can be explained by a complex structure of the wrapped phase of the truncated Gaussian phase. It follows from Figure 4, that some improvement in the accuracy can be achieved at the price of the larger number of experiments \(S\). In what follows, we provide the images of the reconstructed absolute phases obtained for the iteration number \(T=300\), \(S=4\) and \(S=7\) for logo TUT and truncated Gaussian objects, respectively. The high iteration number \(T=300\) is governed by complexity of reconstruction from the CFA mosaic observations, where each pixel of the sensor captures only one red, green or blue color-channel information. It means that the color information is subsampled with the subsampling ratio 50% for green and 25% for red and blue channels. The missed color-information is restored for each pixel of the sensor (demosaiced) in the iterations of the algorithm as defined by Equations (15)-(17).