Expectation inequality of a function with standard normal variable as input












0














The article "PhaseLift: Exact and Stable Signal Recovery from Magnitude Measurements via Convex Programming" gives the proof of obtaining the solution for phase retrieval. Here, he used the result
$
boldsymbol{E}|(z_1^2 -1)1_{z_1^2 leq 2beta log(n)} | leq (2beta log(n))^{k-2}boldsymbol{E}(z_1^2 -1)^2
$



Where $boldsymbol{E} $ is the expectation and $ z_1 sim mathcal{N}(0,1)$. $beta $ is a constant and $n$ is the number of measurements taken which is also constant. It is present in page 19 of the article. How is this inequality obtained?
The link to the article https://arxiv.org/pdf/1109.4499.pdf


Edit:The inequality is used in page 19 of the paper










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  • Can you give us an idea where in the paper you're looking? I personally can't be bothered to look through 31 pages to try and get some context.
    – MRobinson
    Nov 27 at 9:21










  • Its on page 19. Sorry, I forgot to add that detail.
    – vi11
    Nov 27 at 9:24
















0














The article "PhaseLift: Exact and Stable Signal Recovery from Magnitude Measurements via Convex Programming" gives the proof of obtaining the solution for phase retrieval. Here, he used the result
$
boldsymbol{E}|(z_1^2 -1)1_{z_1^2 leq 2beta log(n)} | leq (2beta log(n))^{k-2}boldsymbol{E}(z_1^2 -1)^2
$



Where $boldsymbol{E} $ is the expectation and $ z_1 sim mathcal{N}(0,1)$. $beta $ is a constant and $n$ is the number of measurements taken which is also constant. It is present in page 19 of the article. How is this inequality obtained?
The link to the article https://arxiv.org/pdf/1109.4499.pdf


Edit:The inequality is used in page 19 of the paper










share|cite|improve this question
























  • Can you give us an idea where in the paper you're looking? I personally can't be bothered to look through 31 pages to try and get some context.
    – MRobinson
    Nov 27 at 9:21










  • Its on page 19. Sorry, I forgot to add that detail.
    – vi11
    Nov 27 at 9:24














0












0








0







The article "PhaseLift: Exact and Stable Signal Recovery from Magnitude Measurements via Convex Programming" gives the proof of obtaining the solution for phase retrieval. Here, he used the result
$
boldsymbol{E}|(z_1^2 -1)1_{z_1^2 leq 2beta log(n)} | leq (2beta log(n))^{k-2}boldsymbol{E}(z_1^2 -1)^2
$



Where $boldsymbol{E} $ is the expectation and $ z_1 sim mathcal{N}(0,1)$. $beta $ is a constant and $n$ is the number of measurements taken which is also constant. It is present in page 19 of the article. How is this inequality obtained?
The link to the article https://arxiv.org/pdf/1109.4499.pdf


Edit:The inequality is used in page 19 of the paper










share|cite|improve this question















The article "PhaseLift: Exact and Stable Signal Recovery from Magnitude Measurements via Convex Programming" gives the proof of obtaining the solution for phase retrieval. Here, he used the result
$
boldsymbol{E}|(z_1^2 -1)1_{z_1^2 leq 2beta log(n)} | leq (2beta log(n))^{k-2}boldsymbol{E}(z_1^2 -1)^2
$



Where $boldsymbol{E} $ is the expectation and $ z_1 sim mathcal{N}(0,1)$. $beta $ is a constant and $n$ is the number of measurements taken which is also constant. It is present in page 19 of the article. How is this inequality obtained?
The link to the article https://arxiv.org/pdf/1109.4499.pdf


Edit:The inequality is used in page 19 of the paper







normal-distribution expected-value






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Nov 28 at 11:47

























asked Nov 27 at 9:15









vi11

11




11












  • Can you give us an idea where in the paper you're looking? I personally can't be bothered to look through 31 pages to try and get some context.
    – MRobinson
    Nov 27 at 9:21










  • Its on page 19. Sorry, I forgot to add that detail.
    – vi11
    Nov 27 at 9:24


















  • Can you give us an idea where in the paper you're looking? I personally can't be bothered to look through 31 pages to try and get some context.
    – MRobinson
    Nov 27 at 9:21










  • Its on page 19. Sorry, I forgot to add that detail.
    – vi11
    Nov 27 at 9:24
















Can you give us an idea where in the paper you're looking? I personally can't be bothered to look through 31 pages to try and get some context.
– MRobinson
Nov 27 at 9:21




Can you give us an idea where in the paper you're looking? I personally can't be bothered to look through 31 pages to try and get some context.
– MRobinson
Nov 27 at 9:21












Its on page 19. Sorry, I forgot to add that detail.
– vi11
Nov 27 at 9:24




Its on page 19. Sorry, I forgot to add that detail.
– vi11
Nov 27 at 9:24















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