MatRecon — Physics-Guided CT Material Decomposition

The problem

Investigating how spatial material-composition maps can be inferred from CT measurements using physics-constrained inverse methods. A forward model predicts measurements from a material distribution; the inverse problem asks which material distributions are consistent with the measurements. These questions are related, but a differentiable simulator does not automatically make the inverse problem well posed.

The mathematical idea

A schematic spectral transmission model integrates energy-dependent attenuation along a ray:

Here $S(E)$ represents the incident spectrum and detector weighting, and $\mu(x,E)$ is the attenuation field. This expression illustrates the modeling question; it is not a specification of every implementation detail.

Methods

• Differentiable spectral CT forward modeling
• Polychromatic X-ray attenuation
• Numerical projection operators
• Gradient-based inverse optimization
• Material identifiability and non-uniqueness analysis

The goal is material decomposition, not generating synthetic CT images. The forward simulator is a supporting component of the inverse problem.

Validation

An important numerical check compares the forward operator and its adjoint through the inner-product identity $\langle Ax,y\rangle=\langle x,A^*y\rangle$. Gradient checks and decomposition benchmarks address different parts of the problem.

Identifiability and limitations

This is ongoing research. A small measurement residual need not imply correct material recovery, and reliable material recovery from real clinical CT has not been demonstrated. Spectral information, measurement geometry, noise, and the chosen material basis all affect what can be recovered. Benchmark values and experiment figures are not included here because validated artifacts have not yet been supplied.

Next questions

Which ambiguities arise from the physics, and which come from discretization or optimization? Which additional measurements would distinguish otherwise similar material configurations?

The code repository predates the project's current name and is still called CTsynth.