5
votes
Accepted
How can we treat real signal as imaginary?
The MRI system is taking two sets of measurements: the in-phase and quadrature measurements. Both measurements are real. There is no way for a physical system to measure $i5 V$, we measure $5 V$.
The ...
- 25.9k
4
votes
How can we treat real signal as imaginary?
For historical reasons, the two primary types of complex numbers have names that are completely inaccurate. One type of number is referred to as "real" even though there's nothing ...
- 208
3
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Quadrature signal acquisition simulation
For a causal time domain signal, the Fourier Transform will be complex with the imaginary part as the Hilbert Transform of the real part.
This may be clearer by noting the following additional ...
- 53.9k
3
votes
Machine learning for denoising MRI images
My personal feeling is that you should do each things separately and compare the results. For example, take your MRI dataset and denoise using "standard algorithm 1", "standard algorithm 2" and "...
- 131
2
votes
Accepted
MRI image reconstruction - reduced scan pecentage
I would say no, there isn't. This is unmeasured information and you cannot compute it without additional information (ie some additionally sampled data, and maybe some compressed sensing algorithm). ...
- 1,736
2
votes
Accepted
What is the most likely imaging processing step associated with the term 'Riesz' in clinical MRI?
I think the answer is in the DICOM dictionary:
(0018,9064) k-space Filtering KSpaceFiltering CS 1
This corresponds to what I am reading on the metadata transmitted (...
- 453
2
votes
Accepted
Bloch equation: adding gradients
I am not sure if this is related, but this cross-product is part of the differential equation, something like $\frac{\textrm{d}M}{\textrm{d}t} = \gamma M \times B$... For a true infinitesimal $\textrm{...
- 1,736
2
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How can we treat real signal as imaginary?
In many situations, such as with these MRI calculations, we want to measure a gain and a phase shift. However, in many situations, phase shifts are difficult to measure directly. Instead, we measure ...
- 199
1
vote
Accepted
Why the T1 recovery & T2 decay are independent?
T2 decay is caused by the decohherence of spins and does not require any sort of energy transfer (the spins alignment with respect to the B0 filed does not change and spins remain in transverse plane,...
- 1,417
1
vote
How can we treat real signal as imaginary?
In wave mechanics, one often encounters solutions of the form $f(t) = A\cos(\omega t -\phi)$. If we have a constant $\omega$, then this gives a two-parameter family of functions. If we take $u = A\cos(...
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1
vote
How can we treat real signal as imaginary?
There's different semantics at play, and they're being mixed. This is not uncommon in signal processing, or in the STEM in general. You can either get perplexed and bothered, or you can just sit ...
- 12.9k
1
vote
How to reconstruct image from an Under Sampled MRI k-space data?
I was experiencing a similar problem (CS reco looked the same as the simple FT reco). What helped me was to normalize my data to max=1,
...
- 11
1
vote
Accepted
Effective field in MRI when solving for Bloch equations
In the rotating reference frame, $B_z$ from the static magnetic field $B_0$ is transformed away, hence $B_z = 0$ if no gradient field is applied. All gradients change the $B_z$ value, as you described ...
- 1,736
1
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What is the most likely imaging processing step associated with the term 'Riesz' in clinical MRI?
Focusing on the DICOM part, I've found this paper which supports your contention that it's more to do with directional filtering.
I suspect it refers to the (Adaptive Modified) Riesz Mean Filter.
...
- 25.9k
1
vote
Adding noise to real MRI data
Using real data is a way to validate the assumption that your algorithm will behave with real data in a similar way to the behavior with generated data.
In a general sense.
When we want to test an ...
- 2,393
1
vote
Accepted
Will the phase of the reconstructed data using a single MRI k-space point show any curvature?
Some courses tell that each point in k-space (spatial-frequency domain) represents a certain stripe pattern in spatial domain.
It does. A simpler way to think about what sort of "stripe pattern&...
- 10.7k
1
vote
From Fourier (k space) to wavelet domain in MRI sensing
The image $I$ is in spatial domain.
The sampled raw data, so-called kspace data $K$ stores the fourier coefficients of $I$:
$$
K = FI
$$
Here $F$ denotes the Discrete Fourier Transform matrix. $K \...
- 123
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