Expectation inequality of a function with standard normal variable as input
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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
asked Nov 27 at 9:15
vi11
11
add a comment |
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0
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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
asked Nov 27 at 9:15
vi11
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
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
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
asked Nov 27 at 9:15
vi11
11
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
normal-distribution expected-value
asked Nov 27 at 9:15
vi11
11
asked Nov 27 at 9:15
vi11
11
edited Nov 28 at 11:47
asked Nov 27 at 9:15
vi11
11
asked Nov 27 at 9:15
vi11
11
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
add a comment |
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
add a comment |
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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