Forward Modeling Image Analysis

The forward modeling analysis approach (sometimes called “analysis by synthesis”) involves optimizing the parameters of a model, in order to minimize the differences between a synthetic radiograph and the actual data. Essentially, it solves a computer vision problem through the application of computer graphics and function optimization. This approach has been shown to perform well, especially under the highly constrained conditions commonly found in scientific imaging experiments.

Physics-Based Constraints in the Forward Modeling Analysis of Time-Correlated Image Data

LA-UR-12-26815

LANL P-21

This work is supported by The Advanced Radiography Science Campaign (C3), PM E. Mullen.

Results

UNCLASSIFIED

James L. Carroll and Christopher D. Tomkins

IntroductionWe study the application of physics based constraints on the forward modeling analysis of hydrodynamic explosive data. These constraints impose a temporal regularization, restricting the space of potential reconstructions to the space of physically realizable solutions, thus improving the quality of density reconstructions produced. We study the potential applicability of this approach to experiments at Los Alamos National Laboratory’s DARHT facility with simulated data.

Slide 1

Phase 2: “Second Axis”

Phase 1: “First Axis”

Lab Space and Control Rooms

Firing Point

Optics and Detector Bunker

t2t1 t3 t4

Prior knowledge provides additionalconstraints at each time SOLUTION:

Evaluated Density

DATA:Transmission(experiment)

Data constrain solution at each time

Now, physics-based constraints on the evolution of the time-series data will also constrain the (global) solution

t2t1 t3 t4

The forward-modeling framework makes possible a global optimization procedure

Concept: Can we learn something about the solution at time 3 (blue) from the data at surrounding times?

Approach: use physics to constrain solution at each time based upon time-series of data.

WHEN WILL THIS APPROACH HAVE GREATEST VALUE?

When certain conditions are met:

1) Must have the time between measurements (Dt) on the order of a relevant time scale of the flow; and

2) Must have non-perfect data (due to noise, background levels, etc).

time

t1t2t3t4t5

Consider an evolving interface:

Data must be correlated in time

Perfect data might render the information in the time series un-necessary, while noisier data should add value to global optimization.

These physics-based constraints will maximize information extracted from each dataset

Time Step 1 Time Step 2 Time Step 3 Time Step 4

Physics Model: Radius Evolving through Time

• Degrees of Temporal Freedom:• 1: • 2:• 3:• 4: …• n:

Conclusions• For all degrees of freedom:

• Time series advantage first grows as the signal to noise level drops, then falls in extreme noise

• Time series analysis acts as regularization, and delays the onset of overfit as noise is added• This regularization can involve the imposition of physics

based constraints on the space of acceptable solutoins• Time series analysis provides improvement even when the

problem is underconstrained• Time series analysis involves a more complex optimization

problem than does static analysis, converging more slowly

Application

DARHT is the USA’s premiere hydrodynamics testing facility, providing two intense energy radiographic views of explosives driven dynamic

Static Cylinder Set-up Static Cylinder shot Static Cylinder Radiograph

High Explosives (HE) driven experiments to study material properties under intense pressures and high velocities.• Radiographs of chosen instants during dynamic conditions.• Metals and other materials may flow like liquids under the high temperatures and pressures produced by HE.

Time Series Constraints

Methodology

Unobserved Starting Position Time Step 1 Time Step 2 Time Step 3 Time Step 4

Simulated Radiographs:

True Densities:

Signal To Noise Levels Tested:

The principle challenge is to summarize this vast body of data in order to draw meaningful conclusions. Each experiment in the 5X8array resulted in a graph like the one shown on the right. From this matrix of results, we extracted the following summary information:

Fina

l Err

or

Signal To Noise Ratio

Adv

anta

ge

Signal to Noise Ratio

DARHT

experiments. Axis 2, which was completed in 2009, has the capability of producing and imaging four distinct pulses. This provides a view of the dynamics of the experiments through time. The purpose of our research is to explore potential analysis techniques to make better use of this temporal time series information.

We tested 1 through 5 degrees of temporal freedom, and 8 different noise levels, resulting in a 5X8 matrix of experiments, each tested with 12 different numbers of optimization steps (up to 300,000), for both an independent forward modeling analysis, and a dynamic time series analysis, each averaged over 100 independent runs.

• Final Model Error• Advantage (the difference between the time series

approach and the independent analysis approach)• The number of optimization steps before the optimization

subjectively “converged” • The noise level where optimization harmed the solution

instead of improving it (the “overfit point”). This summary information is presented in the following graphs: