# Conjugate Gradient Hard Thresholding Pursuit Algorithm for Sparse Signal Recovery
## 4 Convergence Analysis of CGHTP
### Real-World Image Reconstruction
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{6}{c}{\(\boldsymbol{\tau=0.2}\)} \\ \hline  & **Algorithms** & **HTP** & **HTP(\(\boldsymbol{\alpha^{*}-0.5}\))** & **HTP(\(\boldsymbol{\alpha^{*}}\))** & **HTP(\(\boldsymbol{\alpha^{*}+0.5}\))** & **CGIHT** & **CGHTP** \\ \hline \multirow{3}{*}{PSNR (unitdB)} & Lenna & 12.814 & 16.783 & 18.471 & 17.516 & 8.584 & **21.708** \\  & Pens & 13.491 & 14.512 & 15.450 & 14.926 & 9.843 & **17.471** \\  & Pepper & 11.092 & 17.266 & 18.293 & 17.566 & 8.273 & **20.492** \\  & Baboon & 10.344 & 12.605 & 13.313 & 12.298 & 9.120 & **14.863** \\ \hline \multirow{3}{*}{Rerr} & Lenna & 0.877 & 0.281 & 0.217 & 0.244 & 0.610 & **0.102** \\  & Pens & 0.810 & 0.431 & 0.330 & 0.382 & 0.532 & **0.225** \\  & Pepper & 0.642 & 0.227 & 0.175 & 0.206 & 0.488 & **0.104** \\  & Baboon & 0.932 & 0.644 & 0.528 & 0.632 & 0.874 & **0.222** \\ \hline \multirow{3}{*}{Average Recovery (unitsecond)} & Lenna & 0.153 & 0.216 & 0.223 & 0.237 & 17.632 & **0.216** \\  & Pens & 0.144 & 0.197 & 0.212 & 0.228 & 17.537 & **0.205** \\ \cline{1-1}  & Pepper & 0.145 & 0.221 & 0.240 & 0.246 & 17.682 & **0.231** \\ \cline{1-1}  & Baboon & 0.140 & 0.192 & 0.211 & 0.196 & 17.45 & **0.203** \\ \hline \multicolumn{1}{c}{\(\boldsymbol{\tau=0.4}\)} \\ \hline  & **Algorithms** & **HTP** & **HTP(\(\boldsymbol{\alpha^{*}-0.5}\))** & **HTP(\(\boldsymbol{\alpha^{*}}\))** & **HTP(\(\boldsymbol{\alpha^{*}+0.5}\))** & **CGIHT** & **CGHTP** \\ \hline \multirow{3}{*}{PSNR (unitdB)} & Lenna & 26.943 & 28.171 & 28.256 & 28.139 & 20.603 & **28.467** \\  & Pens & 23.042 & 24.004 & 24.655 & 24.142 & 18.597 & **25.110** \\  & Pepper & 25.604 & 27.216 & 28.471 & 27.318 & 20.363 & **28.537** \\  & Baboon & 17.614 & 18.237 & 18.333 & 18.249 & 14.621 & **18.364** \\ \hline \multirow{3}{*}{Rerr} & Lenna & 0.021 & 0.017 & 0.016 & 0.017 & 0.045 & **0.015** \\  & Pens & 0.057 & 0.046 & 0.042 & 0.044 & 0.074 & **0.040** \\ \cline{1-1}  & Pepper & 0.029 & 0.022 & 0.021 & 0.022 & 0.048 & **0.021** \\ \cline{1-1}  & Baboon & 0.052 & 0.047 & 0.045 & 0.046 & 0.104 & **0.044** \\ \hline \multirow{3}{*}{Average Recovery (unitsecond)} & Lenna & 0.468 & 0.697 & 0.998 & 3.394 & 23.448 & **0.813** \\ \cline{1-1}  & Pens & 0.446 & 0.556 & 0.641 & 0.695 & 23.454 & **0.640** \\ \cline{1-1}  & Pepper & 0.459 & 0.725 & 1.110 & 4.321 & 23.637 & **0.812** \\ \cline{1-1}  & Baboon & 0.409 & 0.556 & 0.553 & 0.599 & 21.726 & **0.531** \\ \hline \multicolumn{1}{c}{\(\boldsymbol{\tau=0.6}\)} \\ \hline  & **Algorithms** & **HTP** & **HTP(\(\boldsymbol{\alpha^{*}-0.5}\))** & **HTP(\(\boldsymbol{\alpha^{*}}\))** & **HTP(\(\boldsymbol{\alpha^{*}+0.5}\))** & **CGIHT** & **CGHTP** \\ \hline \multirow{3}{*}{PSNR (unitdB)} & Lenna & 29.924 & 31.133 & 31.164 & 31.145 & 27.376 & **31.392** \\  & Pens & 26.566 & 27.957 & 28.319 & 28.273 & 24.331 & **28.633** \\ \cline{1-1}  & Pepper & 29.207 & 30.867 & 31.028 & 30.891 & 27.363 & **31.297** \\ \cline{1-1}  & Baboon & 19.527 & 19.544 & 19.584 & 19.496 & 17.351 & **20.257** \\ \hline \multirow{3}{*}{Rerr} & Lenna & 0.013 & 0.010 & 0.010 & 0.010 & 0.019 & **0.009** \\ \cline{1-1}  & Pens & 0.032 & 0.024 & 0.023 & 0.024 & 0.045 & **0.022** \\ \cline{1-1}  & Pepper & 0.016 & 0.011 & 0.010 & 0.011 & 0.023 & **0.009** \\ \cline{1-1}  & Baboon & 0.040 & 0.039 & 0.038 & 0.039 & 0.048 & **0.038** \\ \hline \multicolumn{1}{c}{Average} & Lenna & 1.451 & 22.223 & 54.121 & 61.064 & 102.059 & **3.064** \\ \cline{1-1} Recovery & Pens & 1.436 & 1.823 & 2.980 & 19.836 & 109.281 & **3.186** \\ \cline{1-1} Time & Pepper & 1.559 & 24.761 & 56.593 & 62.299 & 94.708 & **3.140** \\ \cline{1-1} (unitsecond) & Baboon & 1.342 & 1.753 & 1.896 & 2.135 & 102.794 & **1.814** \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Reconstruction results of Lenna, Pens, Pepper, and Baboon images at different sampling rates by HTP, CGIHT, and CGHTP.