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At first I thought it is just simple Hermitian Property of the FFT that is used.

But the Phase Correction need to be done so that we account for the assymetry and also for the assumption that Image is real.

Now I understood why we need those Extra K-space lines and for 256 Y Res we need to acquire little moree than 128 lines … i.e around 160 linjes

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**The Multiplication with 2 is because of the Real and Imaginary Portion**

**FrameSize = Size of One View** *( da_xres *2*point_size )*

**here Point_size is if each element is a captured as 32 bit or 16 bit , related to Extended Dynamic Range**

**Echo_Size = Size of Data for a single Echo ( FrameSize * da_yres)**

**slice_size = Size of Data for a single Slice** *(n_echos * Echo_Size)*

**mSlice_size = Size of the data in one acquisition** *( N-Slices_in_1_pass * slice_size)*

**Way a P FIle has Data **

*Acq1 *

*Â Â Â Â Â rec1 :Â ** Slice1 :Echo 1 (All Views) :Echo2(All Views) : Echo 3 (All Views) ……….*

*Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Slice2 :Echo 1 (All Views) :Echo2(All Views) : Echo 3 (All Views) ……….*

*Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Slice 3: Echo 1 (All Views) :Echo2(All Views) : Echo 3 (All Views) ……….*

*Â Â Â Â Â rec2 :Â Slice1 :Echo 1 (All Views) :Echo2(All Views) : Echo 3 (All Views) ……….*

*Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Slice2 :Echo 1 (All Views) :Echo2(All Views) : Echo 3 (All Views) ……….*

*Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Slice 3: Echo 1 (All Views) :Echo2(All Views) : Echo 3 (All Views) ……….*

Â Â Â rec3 :Â * Slice1 :Echo 1 (All Views) :Echo2(All Views) : Echo 3 (All Views) ……….*

*Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Slice2 :Echo 1 (All Views) :Echo2(All Views) : Echo 3 (All Views) ……….*

*Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Slice 3: Echo 1 (All Views) :Echo2(All Views) : Echo 3 (All Views) ……….*

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If B is the matrix and v is theÂ eigen vector with an eigen value k.

B * v = k*v

if k < 0 then its rotated by 180 degrees.Â the Eigen vector is shrunk by k.

If B is a symetric matrix then it has linearly independent eigen vectors.

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I almost forgot lot of math I read , about positive definite matrices, or steepest decent methods …. I need to Brush up on lot of them … ahem ahem … Here is a good paper or a tutorial that is talking about the basics of optimization without much pain

The Paper on painless conjugate Gradient method is painless-conjugate-gradient

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With my discussion with RV , he was talking abt using CS and PI together.Â The idea here is to use the PI to give an initial estimate image rather than using the zero filled Density correctedÂ image as the initial estimate.

When I went through the abstracts I found a similar (I should say same) idea as part of the abstract ..

The abstract is here Â 01488Â

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Let **phi** be the transform in which the image m is sparse

let **y** be the undersampled k-space

**FFTU** be the Fourier Transform operator based on the sampling pattern

Then we want to minimize of l1 norm of **phi*m **

with the constraintÂ **| FFTU*m – y| < epsilon**

SO here sparsity is important because we are trying to minimize and sparsity helps …

Now why is the incoherence needed ? Looks like the incoherence doesnt give any visible artifacts ,

so we should ensure that the sampling pattern is incoherent …

Point spread function gives good estimate of coherence i.e incoherence ….

Point spread function is Fourier Transform of the filter i.e the sampling pattern we have.

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Generating a PDF based on the radius of the unit circle

create a linspace from -1 to 1based on the no.of Points neededÂ (1-r).^p

If its a uniform pdf then lets say its 1 every where. then sum(pdf(:)) gives row*col.

Now we want to generate a pdf such that sum(pdf(:)) = row * col * sampling rate;

use the distance from the centre to create the pdf.

The code is genpdf1

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I got through the idea of using the sparsity of the transform domain and reducing the degrees of freedom and arrive at this sparse elements with a relatively small set of sampled points.

Some one said that nyquist was a pessimist as he gave the upper bound. Now we are interested in the lower bound …..

A decently good tutorial (Though I didnt understand the head or tail of UUP or RIP … Need to spend more time)

http://www.ee.duke.edu/ssp07/Tutorials/ssp07-cs-tutorial.pdf

This blog seemed to cover lot on CS …. I spent some time on the links provided …

http://igorcarron.googlepages.com/cs

At present I m reading this article called sparseMRI , where cs is used to get the Scan Time optimization on the cartesian Grid for angiogram images … sparsemri1

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This is a good article on CPU /GPU/CELL/FPGA … Its interesting ….

I m not sure where my company is headed

Â

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