Tomography - Science method

Ahmad Bakir I will try! Thank you very much!

Hi,

a way to solve sparse matrices in tomography are SIRT or ART algorithms

Van Der Sluis, A., Van Der Vorst, H.A.

Numerical solution of large, sparse linear algebraic systems arising from tomographic problems.

(1987) Seismic tomography, pp. 49-83. 

You can find applications also in the works of Aldo Vesnaver, Gualtiero Boehm and myself such as

doi: 10.1111/j.1365-246X.1996.tb05274.x

10.1111/j.1365-2478.2006.00563.x

10.3997/1873-0604.2017037

and references therein

Many wishes

Cryo-electron tomography (cryo-ET) is a technique that allows the study of the 3D structure of cells and tissues at near-native conditions⁴. It can provide unprecedented insights into the inner working of molecular machines in their native environment, as well as their functional relevant conformations and spatial distribution within biological cells or tissues¹.

The field of structure elucidation by cryo-ET has evolved rapidly in recent years, thanks to the advances in instrumentation, sample preparation, image processing, and data analysis. Some of the current trends and challenges in the field are:

- Achieving higher resolution and better contrast for cryo-ET images, by using phase plates, direct electron detectors, and improved alignment and reconstruction algorithms¹³.

- Developing new methods and protocols for cryo-ET sample preparation, such as cryo-focused ion beam milling, cryo-correlative light and electron microscopy, and cryo-electron microscopy of vitreous sections¹⁴.

- Applying cryo-ET to study a wide range of biological systems and processes, such as viruses, bacteria, organelles, cytoskeleton, membrane proteins, and macromolecular complexes¹²³.

- Integrating cryo-ET with other complementary techniques, such as mass spectrometry, X-ray crystallography, nuclear magnetic resonance, and computational modeling, to obtain a comprehensive understanding of the structure and function of biological macromolecules¹⁵.

- Disseminating and standardizing cryo-ET data and structures in public databases, such as the Protein Data Bank (PDB) and the Electron Microscopy Data Bank (EMDB), to facilitate data sharing and reproducibility⁵.

(1) Cryo-electron Tomography Sample Preparation - Thermo Fisher Scientific. https://www.thermofisher.com/us/en/home/electron-microscopy/life-sciences/sample-preparation/techniques/cryo-tomography.html.

(2) High-resolution in situ structure determination by cryo-electron .... https://www.nature.com/articles/s41596-021-00648-5.pdf.

(3) Cryo-electron tomography: 3-dimensional imaging of soft matter. https://pubs.rsc.org/en/content/articlehtml/2011/sm/c0sm00441c.

(4) JoF | Free Full-Text | Preliminary Structural Elucidation of β-(1,3 .... https://www.mdpi.com/2309-608X/7/2/120/htm.

(5) Evolution of standardization and dissemination of cryo-EM structures .... https://www.jbc.org/article/S0021-9258%2821%2900338-0/pdf.

(6) undefined. https://doi.org/10.1038/s41596-021-00648-5.

(7) undefined. https://doi.org/10.3390/jof7020120.

Dear Martin,

A little shameless self-promotion of our result on Fredkin gate and measuring purity/overlap:

Stárek, et al., npj Quantum Information 4, 35 (2018), https://www.nature.com/articles/s41534-018-0087-x

Generally speaking, nonlinear functions of a quantum state (density matrix) can be measured by interfering multiple copies of the state and applying parity detection:

Filip, PRA 65, 062320 (2002),

Ekert et al. PRL 88, 217901 (2002).

The same holds for entanglement characterization:

Horodecki, PRL 90, 167901 (2003),

Fiurášek & Cerf, PRL 93, 063601 (2004).

Experimental tests for bipartite states:

Walborn et al. Nature 440, 1022 (2006),

Islam et al. Nature 528, 77 (2015).

Best,

Miroslav

Danilo Andrade De Jesus

Hi Danilo. Unfortunately, no. We could only get some preliminary results using TOPCON using 7line raster mode. however, we could not achieve a full field of the retina.

Dear Ashish Kumar Agrawal ,

I tghink you are on the right way;

in case of non-sufficient collimation and non-sufficient detector shielding the scattered radiation affects the detector signal, especially via an offset (background) and its correlated noise onto its output.

Monochromatic and whlte beam are produced by different means and will thus cause different ambient x-ray scatter levels, which for example in the case of strong absorbing samples will contribute a non-negligible contributions to the detector output.

I my x-ray set-ups I always checked this scatter offset in the detector signal by

a) putting a beam stop just behind the sample

and

b) just in front of the detector window.

In case (a) you will see how much x-ray scatter will enter in total the detector; and in case (a+b) you will see how much scatter enters the detector passing the housing/shielding. The difference of these signals [ (a) - (a+b) ] will give you the scatter contributions passing through the detector window.

From the strength of that value you might decide to improve your collimation, and from the signal level of (a + b) you may decide to improve your detector shielding...

Good luck and

best regards

G.M.

The Landweber and MART (Multiplicative Algebraic Reconstruction Technique) regularization methods are commonly used in image reconstruction and signal processing applications. Although specific implementations may vary, I can provide you with a general guideline to create MATLAB functions for these regularization methods:

1. Landweber Regularization:

The Landweber regularization method is an iterative algorithm for solving ill-posed inverse problems. Here's a basic MATLAB function that implements the Landweber method:

```matlab

function x = landweber(A, b, iterations, stepsize)

% A: System matrix

% b: Measured data vector

% iterations: Number of iterations

% stepsize: Step size or regularization parameter

[m, n] = size(A);

x = zeros(n, 1); % Initialize the solution vector

for iter = 1:iterations

% Update the solution using Landweber iteration formula

x = x - stepsize * A' * (A * x - b);

end

```

You need to provide the system matrix `A`, the measured data vector `b`, the number of iterations, and the step size (regularization parameter). The function updates the solution iteratively using the Landweber iteration formula.

2. MART Regularization:

The MART regularization method is an iterative technique commonly used in computed tomography (CT) image reconstruction. Here's a simple MATLAB function for implementing the MART algorithm:

```matlab

function x = mart(A, b, iterations)

% A: System matrix

% b: Measured data vector

% iterations: Number of iterations

[m, n] = size(A);

x = zeros(n, 1); % Initialize the solution vector

for iter = 1:iterations

% Update the solution using MART iteration formula

x = x .* (A' * (b ./ (A * x + eps))) ./ (A' * ones(m, 1));

end

```

You need to provide the system matrix `A`, the measured data vector `b`, and the number of iterations. The function performs the MART iterations, updating the solution based on the MART iteration formula.

Note: These are basic implementations, and you may need to modify them based on the specific problem you are solving. Additionally, consider incorporating suitable stopping criteria and handling specific constraints if required.

Remember to adapt these functions to your specific problem and matrix representations. Also, ensure that you have the necessary system matrix `A` and measured data vector `b` appropriately defined before using these functions.

The purpose of the normal vector (n) in equations that describe the behaviour of surface sensors is to specify the direction in which the sensor is sensitive to incoming signals or perturbations. For example, in the case of seismic waves, the normal vector of a surface sensor is used to determine the direction of the particle motion that induces a voltage or current in the sensor.

a

The normal vector is also used to calculate the geometric factor, which is a correction factor that accounts for the geometry of the sensor and the direction of the incoming wavefield. In general, the normal vector (n) is an important parameter in equations that describe the behaviour of surfaces and surfaces sensors, as it determines the orientation and sensitivity of the sensor with respect to the surrounding environment.

____________________________________________________________________________

Acquiring the value of the adjoint state utilizing the boundary condition involves a multi-step process that has a significant impact on the final outcome.

To begin with, it is essential to derive the adjoint equation from the forward problem and apply the appropriate boundary conditions for deriving the adjoint state. Here are the steps that need to be followed:

Derive the adjoint equation: Starting from the forward problem, which could be the wave equation or any other relevant problem, the adjoint equation can be derived. This is achieved by taking the derivative of the forward problem concerning the model parameters and subsequently applying the adjoint operator. It is crucial to note that the adjoint equation possesses a structure similar to the forward problem. The only difference is that the time is reversed, and a new source term, which is derived from the misfit function, is added.

Define the initial condition for the adjoint equation: The initial condition for the adjoint equation is typically the zero state. This means that the adjoint state is zero at the final time, and this condition ensures causality. The zero state corresponds to the fact that the adjoint state is generated by the mismatch between the observed and modelled data.

Apply the boundary conditions: In the same manner as the forward problem, the adjoint equation requires boundary conditions to be well-posed. It is essential to base the boundary conditions for the adjoint equation on the corresponding conditions of the forward problem. For instance, if the forward problem has Dirichlet or Neumann boundary conditions, the adjoint equation will also have the same type of boundary conditions applied at the same locations.

Solve the adjoint equation: With the adjoint equation, initial condition, and boundary conditions properly defined, the next step involves solving the adjoint equation. This can be accomplished through various numerical methods such as finite differences, finite elements, or spectral methods. Solving the adjoint equation enables the derivation of the adjoint state, which can be further used to compute the gradient of the objective function concerning the model parameters.

It is crucial to keep in mind that the steps outlined above may vary depending on the problem, the forward model, and the numerical methods used. The key to obtaining the adjoint state is to derive the adjoint equation and apply the appropriate initial and boundary conditions.

Although I wrote the mathematics of the two x-ray anodes to make resection and intersection back in 1978, I am not an expert in CT mathematical modeling. Therefore, if you know each voxel's x, y, and z coordinates, then a horizontal section is to pick up all voxels with the same z-value. A profile section picks up all voxels with the same y-value, and a cross-section picks up all voxels with the same x-value. If you need a higher resolution than the voxel size, you make more sections around the location of interest and do interpolation.

Actually, there are many tools that you can develop the code. But when we talk about the CNN, it about the long journey of learning. It cannot get on the spot. Maybe you can read some intro what is machine learning, what is deep learning.

For QST, you need an entangled photon source that generates signal and idler pair photons, two polarization controllers for aligning bases (H/V, D/A, R/L), two polarization beam splitters, a dual-channel single photon counter to measure coincidence counts (CC), and some code to compute the QST from the CC. The most important thing is that you must obtain CCs for 36 combinations of polarization bases of H/V, D/A, and R/L. Here is the detailed explanation (see page 30): http://research.physics.illinois.edu/QI/Photonics/tomography-files/tomo_chapter_2004.pdf

Dear Tim Schwope

You can use (origin pro) program

Sincerely

Sample - Implant imbeded in bone.

Thank you sir Gordon L Warren

Hello Mahyar Radak

The question you mention is very broad! As for which is so-called "better", it really depends what type of tumour you are testing for or evaluating. As we know, different types of tumours are better analysed with different types of PET scans and I know my colleagues generally think they (PET scans) are all the same but you and I know that is not true. Most commonly, they expect if someone is said to have had a PET scan, it most commonly refers to using F18-FDG and clinicians are often surprised when it turned out to be something else (!)

In fact you can use any impedance meter to measure the skin impedance All what you need is to stick two metallic probes on the skin and measure the impedance between the two electrodes by this impedance meter. There are many RLC meters that measures the impedance of the skin where it is equivalent to a parallel combination of a resistance and a capacitance. You have to press the electrodes against the skin to avoid the existence of air gaps between the electrode and the skin. You can use salty solutions to wet the electrodes. In this way you will get reproducible results.

You can also use the impedance measuring method in the paper at the given link:

Article Four Voltmeter Vector Impedance Meter Based on Virtual Instrumentation

I used this method to measure the skin impedance and it gave good results.

Best wishes

Some of publications of downsampling for volumetric data:1_ Optimal distribution_preserving downsampling for a large biomedical data.

https://www.ncbi.nib.gov>Pmc

2_ Downsampling method for medical datasets_Core.

https://Core.ac.Uk> download>pdf

Dear Qamar Ul Islam

Thank you, Qamar,

Notice what we derive from our models. I also derived the equation of state of the Universe. They are very simple since the expansion is the Lightspeed expansion of a known hyperspherical shell volume.

We use different paradigms. They used Friedman-Lemaitre and I used the Hypergeometrical Universe Theory.

I provided evidence refuting Einstein's equations here:

and rebutted L-CDM here:

Hence it is not clear what can I use from their work. That said, I benefit from learning prior art and will reference their work in my paper.

Notice that I created the 3D galaxy density map for the whole Universe. My paradigm is trivial. The transition of Blackholium to Neutronium generated hyperspherical harmonic acoustic oscillations. While in the Neutronium phase (superfluid neutron matter), these waves froze in space due to the sudden change in the velocity of sound.

My job was to find where Earth was within the hyperspherical hypersurface and derive the hyperspherical harmonic acoustic spectral composition. No undefined nonsense related to "Gravitational Waves", or "Quantum Fluctuations".

It is very easy to understand that if suddenly an orbital degree of freedom (neutron orbital angular momentum) is allowed, sound waves would be triggered.

Notice that the last image (CMB_Best) is a simulation and you can compare it with the actual Planck Satellite Observation (CMB_SMICA):

Feel free to ask questions.

Thanks,

Marco Pereira

Assuming you have a full CT data set (sufficient projections to meet 180+cone angle criteria), you need some type of reconstruction algorithm first. Typically people use Feldkamp based recons, of which there are algorithms available for Matlab to easily do this. However, if you built the system yourself, you need calibration first, which is a bit more complex (but there are published ways on how to do this also). if you don't meet that criteria, then it is a limited angle sampling problem, which is more along tomosynthesis reconstruction.

Thabk you very much for your reply @HrvojeTkalcic

Well, I never heard of OCT until this minute, but a fiber rotator is generally for selecting the axis of polarization entering (exiting) a polarization maintaining (PM) fiber. A couple minutes with Google and I see polarization sensitive OCT is a thing, so I think that is the idea. If the light source is polarized, the scattering tissue can change the polarization. Different tissues give different polarization effects, so being able to change what polarization you are observing provides extra tissue differentiation and contrast.

Dear Ziqiang Cui,

Within the classical framework, one can minimize the error between measurements and calculated values, in function of the multiphase electrical properties. There are different optimization algorithms which deal with non-linearity, with the most popular being Gauss-Newton, Simulated Annealing and Kalman filtering. Of these three, Simulated Annealing requires a large processing time and Kalman filtering may be suitable for real time (depending on other aspects).

Some time ago I used SSA and KDE - they require some fine-tuning, but are capable of giving good results.

I think you need to try simplest approaches first to see if they give acceptable results for your dataset.

Marie-Christine Zdora and Alexander Rack We've decided to fix the samples in formalin and are considering embedded it in agarose. Thank you very much!

Follow

the neutron imaging limit is about 1um in a good day, seems you need SEM analysis

You should distinguish two different cases:1. The stationary traveltime is a minimum. Then you minimize the traveltime. 2. The stationary traveltime is a saddle point. Then you minimize the traveltime gradient squared. In both cases, the conjugate gradient method can be used to minimize the target functions, among other optimization methods

We have done quite a bit of imaging of various tissues in our lab and we have never air-dried. You can keep your tissues in formalin rather than switching them to ethanol or another organic solvent if you prefer. This will prevent shrinkage which can also cause artifact. You can prepare the sample in a tube of any size, fill it with your solvent, and parafilm any areas of potential leakage. Just make sure that you also affix the tube to the mount properly to avoid leakage in the scanner. Depending on your machine, you can also leave your mouse in tact and perform imaging. There are many other routes you can go from there.

Hi Denis Korneev and Andreas Müller,

You can also try Dragonfly (https://www.theobjects.com/dragonfly/index.html) from Object Research Systems, it is free for non commercial use.

Dragonfly has many segmentation tools from active shape to deep neural networks. The following video, (https://www.youtube.com/watch?v=1WVlskyuw94) is a deep learning tutorial.

Do not hesitate to contact me if you want more information.

Thank you everybody for your answers, I appreciate it greatly.

Danilo Rastovic,

Computerized Tomography (CT) uses algebraic reconstruction technique (ART) which can be considered as an iterative solver of a system of linear equations. However, there exists nonlinear iterative algorithms for CT such as multiplicative algebraic reconstruction technique (MART) and experiments have shown that it can indeed further optimize CT algorithms resulting in greater image quality and dose reduction:

To answer your second question, it can be online, offline or even hybrid depending on the case.

In addition to producing lovely pictures, tomography can help with understanding the mechanism of fracture and characterising the surface.

We generally use the areal surface roughness parameters (see ISO 25178-2) to compare surfaces

Emmanuel Cosnard,

You may find useful the following reference:

Vo-Dinh - Biomedical Photonics Handbook, 2nd ed. Vol. I

Chapter 2 Optical Properties of Tissue Table 2.2

oops..

Tomographic inversion SHOULD fit if you do it right.

Inversion is a model process. Tomography is a model..

SO if you doit right IT WILL WORK. There should be NO BIAS..

If there is THEN you have issues with the assumption, equations, calibration. Develop simply check points along the entire data path and include anisotropy (?)

I would assume your inversion is properly benchmarked?

Dear Rafael Campo ,

CT primarily delivers the mean linear attenuation coeffcient (µ), which is the product of the mass-attenuation coefficient (µ/rho) and the density (rho):

µ=(µ/rho)*rho.

By the way: bulk Copper has got higher density than Fe and in addition has got higher atomic number, which also leads to higher mass-attenuation coefficient compared to Iron .

You might now draw new conclusions.....

Yizhou Lu , Thanks for your recommendation.

I have skimmed over the book , while the book is introducing the iteration between x-ray and matters, it's more related to the application of x-ray in material science. The last chapter is the absorption and phase contrast imaging of x-ray, but there seems no phase retrieval related content in the book. Anyway, thanks you!

Let me try.

If you understand TD-OCT, it is great. So you understand that the wider the bandwidth of the light source, the shorter the coherence length (higher resolution of OCT image). That means if you use infinity bandwidth, you will have infinitely short coherence length and the signal would be only exactly at dz=0 (d_obj = d_ref). So now, let consider in other way. Start limit your bandwidth. You shall find that signal oscillation does not disappear so rapidly as before, so there is some vicinity of positions around dz=0 at which you still can see the signal. If you reduce bandwidth more and more up to exactly single wavelength you find that no matter how far you are from condition dz=0, there is always high signal (it varies as cosine signal due to interference of ref and obj light while moving the ref mirror). Ok then, so let detect this single wavelength signal by using a spectrometer in SD-OCT. What you will see is a single pixel which amplitude varies as cosine while moving reference mirror. Nothing special. So let's include a second wavelength in your light source so now you have a two-wavelength laser. Let the second wavelength differ not so much. Consider SD-OCT with a spectrometer having field of view of 100nm and having 2048 pixels operating at 1050nm center wavelength. So the second wavelength would be 1000nm + 100nm/2048 = 1000,05nm. How the signal will look like? Signal at first pixel still follows cosine cos[k(1000nm)*dz(t)]. The signal at the second pixel also shows a cosine according to cos[k(1000,05nm)*dz(t)]. As you see the phase (argument of cosine) would be slightly different. Assume dz=1mm then phase of the first pixel k1*dz=6283.2 and the second pixel k2*dz=6282.9, so it differs by 0.3 rad (17 deg), correct? You can check that at the 2048th pixel (1100nm) the phase is 5712. Now just calculate phase and cosine(phase) for each of 2048 pixel in excel and make a graph. You will see nice cosine fringe spanning along the pixels - this is your virtual spectrometer. Now put very small dz like 10um. You would see a fringe pattern which has just a single period along all pixels. At dz=0 all phases are zero and cosine(0)=1 for all wavelengths. That means in SD-OCT you see no signal! This is curious because in TD-OCT you observe maximal signal at exactly dz=0, right? Yes. Because in TD-OCT you observe a sum of all electric fields of all wavelengths by using a single photodiode. That means peaks and valleys of electric fields must match each other to produce highest interference signal. Since the peaks and valleys of electric field of all wavelenghts match perfectly (are highly coherent), they produce highest interference signal exactly at dz=0.

For dz > 0 phases of all wavelengths differs too much and corresponding electric fields rapidly loose the coherence, so the sum of them quickly decay to ~zero. As you saw in above virtual spectrometer considerations, at dz=1mm a two very close wavelengths (1000 and 1000.05) differs already by 17 deg. That means a wavelength in 10th pixel is at phase 170deg vs 1st pixel, at 20th pixel it is ~360deg. So you have one oscillation at 20 pixels, ~100 oscillations at 2048 pixels. At spectrometer you still observe nice interference fringes. But if you sum all of them (to simulate signal at TD-OCT - this is how TD-OCT observe signal) you will find that signal is zero! Sum of cosine signal along 100 oscillations would always give ~0 value. But if you observe a signal at spectrometer which has less than one oscillation, sum of it is > 0 and is highest when all pixels have 1.0 :). This is the all magic of TD and SD OCT :).

One digression. In TD-OCT if you don't move the ref mirror, signal from a photodiode is constant in time because neither k nor dz don't depend on time. To observe a signal you need to make k(t) or dz(t). In TD-OCT you can only make dz(t) by moving ref mirror so the signal at photodiode start changing oscillating with cost(k*dz(t)). Please note that you may also make k(t) - this is Swept-Source OCT where the wavelength of the swept laser is changing over the time. In SS-OCT you also use a single photodiode but you don't observe all wavelengths at once anymore like in TD-OCT. So SS-OCT is just "time-spectrometer" OCT :). I hope you will have better understanding now.

unfortunately, this research is over. However, you could be collaborate with others who having same topic right this one. Good luck

CBCT over CT and other methods

International Association of the Seismology and Physics of the Earth's Interior (IASPEI)

Hi Iago,

I am trying to apply Tikhonov regularization to minimize the cost function in Seismic Travel Time Inversion.

In order to construct the L curve, how to I choose the Tikhonov parameters? I have attached the paper given to me to code the cost function. Please have a look at equation number 5.

I greatly appreciate your help.

You can check by applying travelling sales person algorithm.

Hi,

If your reconstruction problem is underdetermined, you need to either (1) make your reconstructed image smaller (fewer pixels, lower resolution), (2) increase the number of measurements, or (3) incorporate a priori information about your image (smoothness, total variation. etc) to regularize the reconstruction.

Hope this helps,

Guillem

Hi David, I can say I know who to contact and they can be shared but not publicly for example....

Saptaparnee Chaudhuri to calculate the covariance matrix, you can use Opencv method:

calcCovarMatrix(const Mat* samples, int nsamples, Mat& covar, Mat& mean, int flags, int ctype=CV_64F)

to find the inverse of the matrix:

invert(InputArray src, OutputArray dst, int flags=DECOMP_LU)

all these functions are ready implemented in OpenCV, which is a very powerful library for C++.

Dear prof. Raul Perez-Lopez,

we have developed portable CCC-based muon detectors for speleological applications in Wigner RCP, Budapest, Hungary. If you are interested in the application of this technology, please feel free to contact me. My e-mail address is the following: olah.laszlo@wigner.mta.hu

Best regards,

Laszlo Olah

not for FIB but the logic is close...

Dear Sir

I think the following papers will benefit you in your search

Best Regards

In the paper they used the Cray T3D with 128 processors. It was a shared memory machine, so it should translate nicely to the GPU.

[Be aware, this paper is about 20 years old so there are likely updates to this problem. Also, the parallel algorithm could have been solved in architecture or by modern compilers.]

Looking at the algorithms, there are sends and receives. These are

message passing algorithms and they do not translate as easily to the GPU, but it can be done.

I would say implement this in MPI first, but it also might not translate clearly. If you are going to compare results, you will need that baseline anyways. Also, If you have not already done this, implement the serial version.

Where are you having problems?

Well, I am sending you the links which will help you.

a) https://pdfs.semanticscholar.org/06ca/10c3ccede73159a4b6892b306644dbac39c4.pdf

b)citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.891.9855&rep=rep1...

c) https://arxiv.org/pdf/1712.08655

I am not sure that Sentinel-1 is entirely suitable for tomography. The six day revisit time will mean that you may have incoherent data with more than two images; you don't have the necessary control over incidence angles (or baselines).

Please use the built-in software for reconstruction. It should be optimized for your CT system.

The following open source (free) programs will allow you to do what you need, if one doesn't allow you to complete the process just export a 2D image stack in the required format for one of the other software packages;

ImageJ

Drishti

Blob3d

A quick Google search will lead you to the relevant websites.

dear Collins.

I write some comments to your answer without entering in the mathematical details supporting my answer, which constitutes an integration of Chris answer and an explanation of first Raed answer. In refraction tomography when we refere to " ray path coverage" to define "a measure of the model sampling", we really refer to the number of times that a ray between a source and a receiver hit, or cross, the pixels or the nodes of our model velocity grid (depends on our used parametrization). In fact, the tomographic software, or inversion procedure, give the hit counts or the derivative sums per pixel. The number of ray fractions per pixel indicates how many times the velocity parameter is involved in the inversion (properly propagation kernel or ray matrix of the system solving our problem). I nextly refer to "ray coverage" in this sense.

When the pixel or node have a coverage 0 the corresponding parameter is not involved in the inversion solution. In this case, even though the inversion procedure gives a solution, this is poor or bad constrained. On the other hand when the ray coverage is to high indicates that our velocity parameter is considered many time in our inversion. Although high ray coverage generally could indicate accuracy in parameter determination, some times they act as a solution attractor so that the solution could be also bad. It also depend on by the ray illumination direction of our pixel.

The best practice should be parametrize a model which has the "most homogeneous" value of hit counts or derivative sums. Sometimes it is better a solution obtained with few data and/or with low hit counts but homogeneous than a solution with many data with high hit counts but highly not homogeneous. A good practice is to calculate different model whith different grid dimension and analyze the hit counts; also using pixel with different dimension or using a variable grid dimension.

In your example, the external data, which not have reciprocal constraints, mainly contribute only in the deeper part (bottom) of your model but they are unconstrained in the external upper part of the model edges. If the external shots sample the deeper portion of model space that is not sampled with reciprocal shots they could reach instable parameter solution in the deeper part of model because they contribute partially and separately to whole solution with respect the part constrained by the reciprocal shots.

In the external part of the model (edge) the parameter are not (or partially) involved in the inversion, infact they are similar to those of the starting model that we suppose "good". In general we should limit the model space to the part where there are the minimum number of constrained pixels in the solution search (about 60-120 m). I advice you to consider in the inversion only the reciprocal shots in this distance range. Everthough, the external shots should be considered in the starting model construction to constrain the deeper model in the inverted model space (60-120 m). Obviously if you have "a priori robust" information about the edge of model you can insert it in the inversion.

Please send your proposal on ashishka@rrcat.gov.in.

We are doing X-ray micro-tomography using synchrotron radiation at Indore India

You might want to have a look at this a bit older mailings which list a lot of software as well:

I have,

You will find most of it documented in the MCNP Manual Vol II beginning at 3-151.  Appendix I explains the output lines but it is difficult to follow.

Here is my PTRAC card:

PTRAC FILE=ASC WRITE=all TYPE=p,e EVENT=col,bnk FILTER=150,icl

I am recording all bank and collision events of photons and electrons in volume 150.

Each line is one interaction of one particle.  The first number is the reaction type.

I "unpack" the PTRAC file by using MATLAB to search for a 150 at position 6, this is the volume.  Then look at the 2xxx number.  Appendix I lists the last two digits of this number as event type, i.e. 17 is a knock on electron.  The 2xxx indicates a bank. 1xxx is a source. 9xxx is the last event in the history,  Position 15 is the energy. Position 11,12, and 13 define the location X,Y, Z of the event.  etc. etc.

WARNING.  These output files are HUGE!  You will need a special editor.  I use EM Edit.

Also consider the DBNC card instead.

2017 4 52000 0 3 150 3 1

-0.22647E+00 0.23806E+00 0.19025E+01 0.50385E+00 -0.37274E+00 0.77923E+00 0.12040E+00 0.10000E+01 0.59373E-02

Best Regards - Gregg

Yes, you can differentiate. This link may help you. https://global.britannica.com/science/cell-biology/The-process-of-differentiation 

Hello:

Most DCM studies are actually performed using SPM, whose source engine is based on distributed dipole models (see e.g. link). DCM requires that you select a set fo regions of interest to perform causal inference testing on the resulting time series. So ion short, DCM can be applied on time series, regardless of how they have been obtained (distributed or equivalent dipoles) and therefore, you may use the tool subsequently to sLORETA et al. modeling.

Hope this helps.

Sylvain. 

yes i want this type of image

What type of material are those filling made of? 

If it is made of high Z number (Atomic number) like Metal then rest assured the defects are coming from those elements. 

Pls share an image to see the defects.

Dear Ahmad,

I have dealt with the similar question recently.

David Isaacson dealt with this question with respect to measurement precision in his work [1]:

Yours sincerely,

JC

The attached file is a pretty comprehensive treatment of the backprojection algorithm for SAR.

Dear Nikolaos,

In FWI,  I am using same parameter set including grid dimensions, frequencies and their interval and all other inversion parameters for invrting P-wave velocity using Visco-acoustic FWI for two crossed SBN lines (Wide-angle offshore data) stating from low frequency to high frequency.

the only difference between two SBN lines is that, One line having with 4ms & other having 8ms sampling data.

After FWI, We are observing very good agreement between synthetic & observed data in frequency domain at each frequency group, But at cross position we are not getting that much confident results as we have seen in comparison of data.

I want to know the justification for this type of FWI results.

Regards,

Damodara

Here is the source of information on the uses of Alexa Fluor dyes:

What type of "artifacts" are you referring to? The output of a Radon transform is a sinogram, i.e., something that is not supposed to be understood by a human observer. If you are talking about image noise (but noise is not an "artifact") after Radon inversion (e.g., by filtered back projection) this is usually attenuated by apodization windows during the ramp-filtering step.

Have a look at this: http://www.sciencedirect.com/science/article/pii/B9780444536327002124

Most seismic travel-time tomography approaches use the ray tracer as a way to identify the perturbed cells in the grid. Fat ray approximation may decrease resolution as adjacent cells can be hit (and thus subject to perturbation) around a specific ray path. Other than that, the results should be roughly the same if both ray tracers provide comparable responses.

For CIT using satellite-to-ground links as a primary dataset, the vertical profile is underdetermined. Therefore the datasets you and David suggested should be a good complement to data from Beacons or GPS. You can put these in either as a priori constraints or as observations as long as you account for the uncertainties. If you are using vertical basis functions, it makes sense to adjust these to be consistent with observations of the density-altitude profile before trying to ingest those observations. Zapfe et al. [2006] have a paper on that issue. 

As David mentioned, you need an optical forward model for airglow data, but Link and Cogger's [1988] formulation is quite straightforward for the 630.0-nm redline nightglow emission that occurs in the F-region. I think Tim Duly has coded it into Python with all the necessary supporting empirical models in Pyglow (which is open-access). Ultraviolet data are also available (e.g. 135.6-nm airglow) from DMSP/SSUSI and TIMED/GUVI and soon from NASA's ICON mission. The mutual neutralization term has to be accounted for in order to assimilate 135.6-nm properly. 

None of these datasets are especially good in the E-region (except the ISRs and ionosondes where we have them). This could be a problem for you if you are working at high latitudes, although it is also a problem elsewhere. In the high latitude case, I would suggest adding some a priori constraints from a particle precipitation model. 

Link, R., & Cogger, L. L. (1988). A reexamination of the OI 6300‐Å nightglow. Journal of Geophysical Research: Space Physics, 93(A9), 9883-9892.

Zapfe, B. D., Materassi, M., Mitchell, C. N., & Spalla, P. (2006). Imaging of the equatorial ionospheric anomaly over South America—A simulation study of total electron content. Journal of atmospheric and solar-terrestrial physics, 68(16), 1819-1833.

Optical coherence tomography should be well suited for that purpose. Although I saw some of papers dealing with fingertips (e.g. the vascular structure) I highly doubt, there is some kind of accessible database.

May I ask which kind of OCT device you are using? (wavelength, FOV and type)

Another question is: Which resolution do you need? (let's say pixel per gland)

Do you need B-scans or C-scans?

Generally the first thing to do is to organize your data in some sort of database. A popular and free earthquake database software is SEISAN.

Once your data is stored and organized you will have to detect the events. This can be done manually or automatically. The most common approach is to use an STA/LTA detector.

Once you have a list of events you can start picking. This can also be done manually (by visually scanning the timeseries and manually picking the data) or automatically (by sending the timeseries through a picking algorithm, as in the paper posted by Tetsuo). 

Whether you pick manually or automatically will depend on how much time you have and what kind of tomography study you are planning.

here is another reference for automatic picking: http://www.bssaonline.org/content/92/5/1660.short

Dear Neha Baraiya

Thank you so much. You are so nice. :)

Hengda

Code will give you interpolated (spherical harmonic fitted) TEC maps on a 2.5x5.0 lat x lon grid in two-hour temproal resolution. Rather than just using the CODE maps, however, you can also look at the IONEX TEC maps generated by each of the global analysis centers (IGS, CODE, JPL, ESA, etc...). The CODE, IGS, and JPL maps are generally considered the more reliable. ftp://cddis.gsfc.nasa.gov/gnss/products/ionex/

Instructions on how to navigate their ftp and about the data format can be found here: http://cddis.gsfc.nasa.gov/Data_and_Derived_Products/GNSS/atmospheric_products.html#iono

You can also try Anthea Coster's Madrigal TEC maps, which don't use any interpolation (leaving you to choose how you want to interpolate the data). You can get that data here: http://madrigal.naic.edu/ No account is needed but they do ask for your email an institution information for their records.

Electron density is another beast all together. There doesn't really exist a reliable electron density model out there. The IRI has it's issues at high and low latitudes and the TIEGCM (http://www.hao.ucar.edu/modeling/tgcm/) isn't really at the stage where it can be considered for operational use. There are assimilation models out there, but none of them are openly available or run regularly.

For a formal evaluation, you may want to consider case-studies and seeing if you can get any of your data near one of the North American Incoherent Scatter Radars, which can get accurate, high-resolution electron density information. Poker Flat or Millstone Hill would probably be ideal. Poker Flat is a phased array scanning many beam directions at once and has a bunch of GPS receivers in its vicinity. Millstone Hill is in the central mid-latitudes with excellent range and is covered by an even larger array of GPS receivers. The ISR data can be retrieved from the same Madrigal site I posted a link to above. (They're also hosting an ISR Summer School in Europe this summer that you may be interested in attending -room, board, and flights are generally covered-). http://amisr.com/workshop

Alternatively, I'll be publishing my empirical electron density model for 60+ Magnetic Latitudes later this month. I'll send you the model as soon as I've finished optimizing it, if you want. Until then you can try the IRI and just see what kind of results you get. You can also scale IRI NmF2 to match map TEC, which may work OK at mid latitudes (big issues at high latitudes though).  

ImageJ can be used and is Java scriptable. But you have to be more specific. What sort of data do you have and what is is that you want to measure. What is the scientific question that you need answered?

-Peter

thank you very much Bagus. Very appreciate that !! It's really helpful

Dear Safal,

Many OCT machines come with a built-in measurement algorithm that can automate thickness and volume measurements. Automated layer detection is quite complex mathematically and it appears most OCTs use proprietary software for this purpose that varies greatly in terms of function and ongoing support. I could not find any freely available source or script for automated OCT measurement during my studies.

The best place to start is to find out the system name of the OCT you are working with and check to see whether the bundled software is sufficient for your needs. For my research, the software on the machine we used (Spectralis HRA+OCT; Heidelberg Engineering) was not suitable, so instead I manually measured thicknesses using custom scripts in ImageJ and excel VBA. This was tedious but not difficult.

Regards,

Felix Aplin

Many parameters will have an effect on the resolution of your tomograms. Not only the imaging system and the reconstruction but also the sample itself are important. In cryo-ET -if you get everything right- radiation damage will become the limiting factor. Here an overview article on all paramters that need to be considered to reach this:

Yes, and here is why. To solve the wave propagation problem "asymptotically" we search for solutions of the Helmholtz equation under the so-called travel-time approximation (Rytov or WKB) that looks like u(x)=A(x)exp{i P(x)/omega) where omega is the temporal frequency. Once we substitute this ansatz into the Helmholtz equation and group the the terms by powers of omega, we obtain the eikonal equation for the phase P(x). So, in order to find an asymptotic solution that satisfies the Helmholtz equation within accuracy of O(1), phase of the above ansatz must satisfy  the eikonal equation but the amplitude can be arbitrary. However, once we equate to zero the terms of order O(omega),  we obtain the so-called  transport equation that involves both the amplitude A(x) and phase P(x). Thus, amplitudes have higher-order (i.e., smaller) effect under the travel-time approximation.