Fig. 1. The 50% recovery probability logistic regression curves for matrix ensembles (a) $\mathscr {N}$ with $n=2^{12}$, (b) $\mathscr {S}_7$ with $n=2^{18}$,

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Fig. 1. The 50% recovery probability logistic regression curves for matrix ensembles (a) $\mathscr {N}$ with $n=2^{12}$, (b) $\mathscr {S}_7$ with $n=2^{18}$, and (c) $DCT$ with $n=2^{20}$. From: CGIHT: conjugate gradient iterative hard thresholding for compressed sensing and matrix completion Inf Inference. 2015;4(4):289-327. doi:10.1093/imaiai/iav011 Inf Inference | © The authors 2015. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.

Fig. 2. Algorithm selection maps for matrix ensembles (a) $\mathscr {N}$ with $n=2^{12}$, (b) $\mathscr {S}_7$ with $n=2^{18}$, and (c) $DCT$ with $n=2^{20}$. From: CGIHT: conjugate gradient iterative hard thresholding for compressed sensing and matrix completion Inf Inference. 2015;4(4):289-327. doi:10.1093/imaiai/iav011 Inf Inference | © The authors 2015. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.

Fig. 3. Average recovery time ratio for CGIHT (a–c), CGIHT restarted (d–f), CGIHT projected (g–i) and FIHT (j–l) compared with the fastest recovery time among all algorithms. Matrix Ensembles: $\mathscr {N}$ with $n=2^{12}$ (left panels), $\mathscr {S}_7$ with $n=2^{18}$ (center panels), $DCT$ with $n=2^{20}$ (right panels). From: CGIHT: conjugate gradient iterative hard thresholding for compressed sensing and matrix completion Inf Inference. 2015;4(4):289-327. doi:10.1093/imaiai/iav011 Inf Inference | © The authors 2015. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.

Fig. 4. Average recovery time (ms) dependence on $\rho $ for $\delta \approx 0.287$; (a) $\mathscr {N}$ with $n=2^{12}$, (b) $\mathscr {S}_7$ with $n=2^{18}$, and (c) $DCT$ with $n=2^{20}$. Vertical scale in $\log (\hbox {ms})$. From: CGIHT: conjugate gradient iterative hard thresholding for compressed sensing and matrix completion Inf Inference. 2015;4(4):289-327. doi:10.1093/imaiai/iav011 Inf Inference | © The authors 2015. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.

Fig. 5. The 50% recovery probability logistic regression curves with $n=2^{11}$ and $r=1,10$ for matrix ensembles (a) $\mathscr {N}$, (b) $\mathscr {S}_7$, and (c) ${\rm DCT}$. From: CGIHT: conjugate gradient iterative hard thresholding for compressed sensing and matrix completion Inf Inference. 2015;4(4):289-327. doi:10.1093/imaiai/iav011 Inf Inference | © The authors 2015. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.

Fig. 6. Average recovery time (ms) dependence on $\rho $ for $\delta \approx 0.287$ with $n=2^{11}$ and $r=10$; (a) $\mathscr {N}$, (b) $\mathscr {S}_7$, and (c) $DCT$. Vertical scale in $\log (\hbox {ms})$. From: CGIHT: conjugate gradient iterative hard thresholding for compressed sensing and matrix completion Inf Inference. 2015;4(4):289-327. doi:10.1093/imaiai/iav011 Inf Inference | © The authors 2015. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.

Fig. 7. The 50% recovery probability logistic regression curves for matrix completion algorithms: CGIHT, CGIHT projected, FIHT and NIHT. Horizontal axis $\delta $ and vertical axis $\rho $ as defined in (3.7). (a) $\mathscr {G}$ with $m = n =80$, and (b) $\mathscr {E}$ with $m=n=800$. From: CGIHT: conjugate gradient iterative hard thresholding for compressed sensing and matrix completion Inf Inference. 2015;4(4):289-327. doi:10.1093/imaiai/iav011 Inf Inference | © The authors 2015. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.

Fig. 8. (a) Average convergence rate and (b) average recovery time (s) of CGIHT, CGIHT projected, FIHT and NIHT for problem class $(\mathscr {E},N)$ with $m=n=2000$, $p=0.1\times mn$ and $r$ ranging from 1 to 96. Horizontal axis $\rho $ defined in (3.7) and convergence rate of left panel defined in (3.8). Vertical scale for (b) is $\log (\hbox {s})$. From: CGIHT: conjugate gradient iterative hard thresholding for compressed sensing and matrix completion Inf Inference. 2015;4(4):289-327. doi:10.1093/imaiai/iav011 Inf Inference | © The authors 2015. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.

Fig. 9. The 50% recovery probability logistic regression curves: (a) CGIHT for ensemble $(\mathscr {N},B)$ with $n=2^{12}$ (black) and the analytic $\ell ^1$ regularization phase transition [31], (b) CGIHT for ensemble $(\mathscr {G},N)$ with $n=m=80$ (black) and the analytic Schatten-1 regularization phase transition [1, 38], and (c) the same as (b) with a different vertical axis. From: CGIHT: conjugate gradient iterative hard thresholding for compressed sensing and matrix completion Inf Inference. 2015;4(4):289-327. doi:10.1093/imaiai/iav011 Inf Inference | © The authors 2015. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.