# Single-Shot Compressed Imaging via Random Phase Modulation
## 4 Compressed Imaging Using Random Phase Modulation
### Single-Shot Compressed Imaging with Fourier-Domain Single Random Phase Mask (CI-FSRPM)
Although the RecPC method has the highest SNR (especially sparse gradient images, such as the Phantom images), the reason is the subsampling type is  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multicolumn{1}{c}{**Phantom**} & \multicolumn{2}{c}{**CI-DRPM**} & \multicolumn{2}{c}{**RecPC**} & \multicolumn{2}{c}{**CI-FSRPM**} \\ \hline \multicolumn{1}{c}{**Subsampling Type**} & \multicolumn{2}{c}{**Integral Subsampling**} & \multicolumn{2}{c}{**Random Location**} & \multicolumn{2}{c}{**Integral Subsampling**} \\ \hline \multicolumn{1}{c}{**Solver**} & \multicolumn{2}{c}{**tvqc\_logbarrier**} & \multicolumn{2}{c}{**RecPF\_Circ**} & \multicolumn{2}{c}{**IST**} & \multicolumn{2}{c}{**GPSR**} \\ \hline
**Size** & **SNR/dB** & **Time/s** & **SNR/dB** & **Time/s** & **SNR/dB** & **Time/s** & **SNR/dB** & **Time/s** \\ \hline
256 \(\times\) 256 & 22.55 & 824 & 39.43 & 3.92 & 12.15 & 3.03 & 12.21 & 2.92 \\ \hline
512 \(\times\) 512 & 24.85 & 2629 & 39.90 & 11.99 & 23.38 & 8.78 & 23.41 & 10.47 \\ \hline
768 \(\times\) 768 & 26.81 & 6788 & 41.24 & 20.83 & 25.98 & 14.28 & 26.08 & 23.47 \\ \hline
1024 \(\times\) 1024 & 27.38 & 12,558 & 41.44 & 38.26 & 32.52 & 22.39 & 32.68 & 45.14 \\ \hline
1280 \(\times\) 1280 & 27.62 & 25,507 & 41.96 & 55.27 & 34.00 & 27.41 & 34.04 & 52.93 \\ \hline
1536 \(\times\) 1536 & - & - & 42.10 & 87.31 & 37.46 & 30.57 & 37.47 & 72.61 \\ \hline
1792 \(\times\) 1792 & - & - & 42.36 & 111.4 & 37.53 & 33.13 & 37.26 & 86.49 \\ \hline
**Cameraman** & \multicolumn{2}{c}{**CI-DRPM**} & \multicolumn{2}{c}{**RecPC**} & \multicolumn{2}{c}{**CI-FSRPM**} \\ \hline
**Subsampling Type** & \multicolumn{2}{c}{**Integral Subsampling**} & \multicolumn{2}{c}{**Random Location**} & \multicolumn{2}{c}{**Integral Subsampling**} \\ \hline
**Solver** & \multicolumn{2}{c}{**tvqc\_logbarrier**} & \multicolumn{2}{c}{**RecPF\_Circ**} & \multicolumn{2}{c}{**IST**} & \multicolumn{2}{c}{**GPSR**} \\ \hline
**Size** & **SNR/dB** & **Time/s** & **SNR/dB** & **Time/s** & **SNR/dB** & **Time/s** & **SNR/dB** & **Time/s** \\ \hline
256 \(\times\) 256 & 20.22 & 624.7 & 23.30 & 7.97 & 20.74 & 1.52 & 20.74 & 3.19 \\ \hline
512 \(\times\) 512 & 25.47 & 3033 & 32.12 & 20.35 & 29.74 & 3.85 & 29.73 & 6.53 \\ \hline
768 \(\times\) 768 & 26.88 & 6732 & 34.18 & 33.49 & 32.96 & 6.28 & 32.98 & 12.18 \\ \hline
1024 \(\times\) 1024 & 28.93 & 13,719 & 37.35 & 55.43 & 36.75 & 9.05 & 36.62 & 20.64 \\ \hline
1280 \(\times\) 1280 & 29.58 & 24,939 & 38.37 & 77.87 & 37.50 & 10.54 & 37.39 & 32.95 \\ \hline
1536 \(\times\) 1536 & - & - & 39.85 & 120.6 & 38.88 & 14.04 & 38.59 & 40.33 \\ \hline
1792 \(\times\) 1792 & - & - & 40.37 & 144.8 & 39.08 & 18.50 & 38.76 & 56.22 \\ \hline
**Lena** & \multicolumn{2}{c}{**CI-DRPM**} & \multicolumn{2}{c}{**RecPC**} & \multicolumn{2}{c}{**CI-FSRPM**} \\ \hline
**Subsampling Type** & \multicolumn{2}{c}{**Integral Subsampling**} & \multicolumn{2}{c}{**Random Location**} & \multicolumn{2}{c}{**Integral Subsampling**} \\ \hline
**Solver** & \multicolumn{2}{c}{**tvqc\_logbarrier**} & \multicolumn{2}{c}{**RecPF\_Circ**} & \multicolumn{2}{c}{**IST**} & \multicolumn{2}{c}{**GPSR**} \\ \hline
**Size** & **SNR/dB** & **Time/s** & **SNR/dB** & **Time/s** & **SNR/dB** & **Time/s** & **SNR/dB** & **Time/s** \\ \hline
256 \(\times\) 256 & 20.98 & 624.7 & 24.33 & 6.86 & 23.57 & 1.35 & 23.51 & 2.73 \\ \hline
512 \(\times\) 512 & 26.24 & 2838 & 32.35 & 19.43 & 32.00 & 3.17 &by random sampling with a random position rather than random demodulation, which severely limits its practical application.