# Presentation: 694493

## Plasmasphere Feature Tracking via Tomographic Backprojection

- T. S. Newman	  R. Kandimalla    N. Santhanam
- C. Wang    H. Zhang    D. Gallagher‡
- Dept. of Computer Science
- University of Alabama in Huntsville
- ‡ Nat’l Space Science and Technology Center / MSFC

## Organization

-   The Problem
-   Related Work
-   New Approach
-   Results and Analysis
-   Conclusion

## The Problem I

-   Specific Problem:
- Plasmasphere Density Reconstruction
- N 2D  --> True 3D
-   Wider Application:
- Limited-Angle Volume Reconstruction
- e.g., large-object scanning

## The Problem II: Data

-  The 2D Views
- IMAGE EUV
- External, Global Views
- 84o x 90o  FOV
- 150x140 pixels
- Every 10 min.
- He+: 30.4 nm

## The Problem III: Sample View

- from http://euv.lpl.arizona.edu/euv/

-  May 24,2000

## The Problem IV: Constraints

-  Moving Target
- --> Few Images
-  Shadow
-  Airglow

## Related Work: Methods

-  Popular Tomographic Reconstruction
- Filtered Backprojection
- Many views!
-  Algebraic Reconstruction
- Alternative

## Related Work: ART I

-  Typical ART Scenario

- camera

- pixel

- slice *k*

- slice *k*+1

## Related Work: ART I

-  Typical ART Scenario

- camera

- pixel

- slice *k*

- slice *k*+1

**Point-sampling**

## Related Work: ART I

-  Typical ART Scenario

- camera

- pixel

- slice *k*

- slice *k*+1

- slice 1

- slice 2

- slice 3

- slice 4

- 2D cut-away view

- camera

**Point-sampling**

## Related Work: ART II

-  Intensity Distribution:
- Unknowns (*X*): intensity values of samples
- Coefficients (*A*): beam-cell intersection weights
- Pixel values (*P*)

**              ***A*                         *X*           *P*

## Related Work: ART III

-  Simul. Alg. Recon. Tech. (SART)
- Initialize unknowns vector (*X*) (Zeroes?)
- Update *X* iteratively
- Average the corrections of all beams in a view:

- * Already-computed unknowns aid

## The New Approach’s Framework

*Volume-sampling* traversal mechanism
- 3D rectilinear grid
- Each region: cell
- From each image’s pixel:
- Generate beam
- Find intersected cells
- Pixel intensity: accumulate particles along beam
- Multiple views

- Beam-Cell Intersection

## SVD and New Approach

- A is Sparse, Nearly Singular
- Singular Value Decomposition?

- where:  *A* is *MxN*
- 		     *U* is *MxN* column-orthogonal
- 		     *W* is *NxN* diagonal
- 	         *V * is *NxN* orthogonal
- Column-ortho.:
- Row-ortho.:
- Key point: obtain *U*, *W*, *V*

- Used by Few
- -RAM!

## SVD and New Approach

- A is Sparse, Nearly Singular
- Singular Value Decomposition?

- where:  *A* is *MxN*
- 		     *U* is *MxN* column-orthogonal
- 		     *W* is *NxN* diagonal
- 	         *V * is *NxN* orthogonal
- Column-ortho.:
- Row-ortho.:
- Key point: obtain *U*, *W*, *V*

- Used by Few
- -RAM!
- -Slow!

## The New Approach: Hybrid Lanczos

-  Lanczos:
- Effective, indirect SVD method
- Tri-diagonalizes
- Fewer operations than standard SVD
-  Hybrid (Lanczos+SART):
- Lanczos as initial estimate
- SART to refine

- * Improves accuracy (Zhang + Newman, 2003)

## Incorporating Physical Constraints

-  Reducing Unknowns:
- North-to-South Symmetry
- Plasma Density Empirical Model
- Plasmapause Exploitation

##  Symmetric cells: same intensity
About equator
Solve one set
Advantages:
Less unknowns
Over-determined 
=> More accurate

- About equator
- Solve one set
- Advantages:
- Less unknowns
- Over-determined
- => More accurate

- Symmetry Constraint

- Equator

- Unknowns

## Physical Constraints: Density Model

-  Symmetry and Empirical Data

- Solid lines: measurements
- Dashed lines: empirical model
- Figure adapted from Song et al.’s  “Development of empirical model for the plasmasphere”

## Reconstruction Exploiting the Model I

-  Quantized L shells;
- Solve these at equator
-  Per Cell: L values at corners
-  Distance-weighting of closest  L’s.
- 1 unknown / shell

-  Mean L (e.g., Lm = 1.875)
-  => Between L1 = 1.5 and L2 = 2

## Exploiting the Model II: Alternate Approach

- Solve nonlinear least-squares problem in order to fit parameters in in Nonlinear Model :
- Levenberg-Marquardt method* *

- Nonlinear Model of plasma density model

- A, B, R, D, γ :  parameters which decide plasma density in one MLT plane

## Plasmapause Exploitation

- <footer>

**Detecting Plasmapause****:**
- Find Earth Center
-        Template-matching (find airglow)
- Find Plasmapause (using snakes)
- Snake initialization
- Use Earth center
-  Snake Energy Minimization
- Voronoi Diagram to avoid loops
- Two-phase Approach

## Automated Boundary Localization

## Improved Edge Algorithm for Extracting Plasmapause in Eq. Plane

- For a position (r, θ, φ) along any LOS,
- L : defined by f (r, θ, φ; L) = 0
-  :  MLT, defined by g(r, θ, φ; ) = 0
- For each LOS, there is a (L, ) curve**.**
- c(θ, φ)= 0 : ‘cone’ of all LOS tangent to the plasmapause.
- All (L, )  curves drawn for LOS lying on the edge cone c(θ, φ)= 0 form an outer bound to the plasmapause in Equatorial plane

**Minimum L Algorithm:**
-       	For each LOS,  among all dipole field lines touching it, find field line w/ min. *L.*
*	*Compute field line’s *L *and MLT coordinates.
- 	(The (L, MLT) pairs define plasmapause in eq. plane.)

**Improved Edge Algorithm for Extracting Plasmapause in Eq. Plane**

## One Enlarged Result

## Synthetic Image Comparison

- <footer>

**Synthetic Image Comparison**

- plasmapause Roelof Edge Alg.

- plasmapause Min L Alg.

- plasmapause boundary

- synthetic image,
- Edge Alg.

- synthetic image Min L Alg.

- real image

- EUV image: 2001/161/11:29

**Conclusion****:**Min L Algorithm is better for non-convex plasmapause boundary.

## Results I

-  Test w/ Synthetic Datasets
- Synthetic plasmaspheric volume datasets
- Follow Carpenter-Anderson model
- Dipole Dataset 1: 16*18*8
- Dipole Dataset 2: 224*252*112, with noise

## Results: Experiment I

- SART vs. SVD-based vs. Hybrid Tech.
- Dipole Dataset 1
- 10 30 x 28 Images, 0-90o

- (b) Pure SART (V1)

- (c) SVD-Based (V2)

- (d) Hybrid (V3)

- (a) Dipole Dataset

_**Qualitative Results: Isosurfaces**_

## Experiment I (cont’d)

|  | Diff. Cells
(%) | Mean Abs. Diff. | Min. Diff. | Max. Diff. |
| --- | --- | --- | --- | --- |
| Pure SART (V1) | 55.1% | 3.3 | -24.58 | 22.42 |
| Lanczos SVD (V2) | 0% | 2.2x10-5 | -8x10-6 | 6.19x10-3 |
| Hybrid (V3) | 0% | 2.2x10-5
 | -8x10-6
 | 6.18x10-3 |

_**Quantitative Results**_

## Experiment II

-  Validate volume-sampling w/o noise
- Compared with point-sampling
- Same Dataset, Views
- Hybrid technique

- (a) Dipole Dataset

- (b) Volume-Sampling (V3)

- (c) Point-Sampling (V4)

## Experiment II: Quantitative Results

|  | Diff. Cells(%) | Mean Abs. Diff. | Min. Diff. | Max. Diff. |
| --- | --- | --- | --- | --- |
| Volume-Sampled (V3)  | 0% | 2.2x10-5 | -8x10-6 | 6.18x10-3 |
| Point-Sampled (V4) | 0.5% | 5.1x10-3 | -0.35 | 0.41 |

## Experiment III

- Validate volume-sampling w/ noise
- Vs. point-sampling
- Dipole Dataset 2, 10 views
- Hybrid technique

- (a) Noisy Dataset

- (b) Lo-res Sampling

- (c) Volume-Sampling (V5)

- (d) Point-Sampling(V6)

## Experiment III: Quantitative Results

|  | Diff. Cells(%) | Mean Abs. Diff. | Min. Diff. | Max. Diff. |
| --- | --- | --- | --- | --- |
| Volume-Sampled (V5)  | 67.4% | 4.03 | -21.95 | 55.66 |
| Point-Sampled (V6) | 57.3% | 11.17 | -197.02 | 359.21 |

## Experiment IV: Empirical Model I

- Dipole Dataset 2
- Recovered at 36x32x16
- 10 150x140 images, 0-90o

- Isosurface, Synthetic Dipole Volume

- Lanczos Alone, No Empirical Model

- New method

- alpha = 4

## Fitting parameters in plasma density 

-  model using real images

- EUV image: 2001/159/18:07
- Longitude parts: 18
- Parameters number: 72
- Volume size 128*144*64
- The number of Pixels in selected region: 6848

***Initial guess: ***
**a[1]=5000.0;a[2]=0.200;a[3]=0.0300;a[4]=5.000;**
**a[5]=5000.0;a[6]=0.200;a[7]=0.0300;a[8]=5.000;**
**a[9]=5000.0;a[10]=0.200;a[11]=0.0300;a[12]=5.000;**
**......**** ****a[61]=5000.0;a[62]=0.200;a[63]=0.0300;a[64]=5.000;**
**a[65]=5000.0;a[66]=0.200;a[67]=0.0300;a[68]=5.000;**
**a[69]=5000.0;a[70]=0.200;a[71]=0.0300;a[72]=5.000;**

- Green: Selected region to fit in image

## The number of Pixels in selected region: 6848

- <footer>

**a[1]=8513.4;a[2]=-3.213;a[3]=1.3961;a[4]=4.005;**
**a[5]=4908.3;a[6]=0.340;a[7]=0.3157;a[8]=4.151;**
**a[9]=3808.1;a[10]=5.908;a[11]=-2.0125;a[12]=4.859;**
**......**
**a[61]=9318.5;a[62]=-8.299;a[63]=2.4683;a[64]=3.998;**
**a[65]=6694.3;a[66]=-5.691;a[67]=1.7878;a[68]=4.616;**
**a[69]=10043.7;a[70]=-3.447;a[71]=1.4214;a[72]=4.050****;**

- Average error per pixel =  6.79
- (The range of intensity of pixels is from 0 to 835.044.)

**Fitted image after 135 iterations**

**Real image**

- (135 Iterations)

## Web-based Tool

- <footer>

## Step 1:

- <footer>

- Input parameters in reconstructing volume.

- Step 2:
- Upload EUV images; Select method to get plasmapause in image.

## Step 3:

- <footer>

- Draw plasmapause boundary in EUV image.

- Step 4:
- Display plasmapause at equatorial plane; download plasmapause file.

## Ongoing Work

-  Improve Reconstruction
- More physical constraints
- Rotational Effects
- Handle Noise
-  Volume Visualization of Plasmasphere
-  Feature Tracking
- Time-Variant Phenomena
-  Community Accessibility to Tools

## Conclusion

- New Plasmapause Localization Techniques and Tools
- New hybrid reconstruction technique
- Recovery from limited views
- Volume-sampling
- Lanczos SVD-based processing
- Initialize SART with vector from Lanczos
- Physical Constraints