RBYRCT — Multiplicative Algebraic Reconstruction Technique (MART)
This repository hosts a reference implementation of the MART algorithm for use in Ray-by-Ray Computed Tomography (RBYRCT) — a next-generation imaging framework being developed by Janus Sphere Innovations.
RBYRCT integrates steerable X-ray beams and Janus spheres to focus radiation precisely where needed, enabling earlier detection of breast cancer with minimal dose.
✳️ Model Overview
MART is an iterative multiplicative update algorithm that reconstructs an image from sparse or photon-limited X-ray projections.
import numpy as np
def mart(A, b, x0, iters=20, eps=1e-8):
"""
A: projection matrix [M, N]
b: measured data [M]
x0: initial estimate [N]
"""
x = x0.copy()
row_sums = A.sum(axis=1) + eps
for _ in range(iters):
for i in range(A.shape[0]):
proj = A[i] @ x + eps
r = (b[i] + eps) / proj
x *= np.power(r, A[i] / row_sums[i])
x = np.clip(x, 0, None)
return x
📊 Inputs and Outputs
| Type | Description |
|---|---|
| Input: | 2D/3D X-ray projections (A, b) |
| Output: | Reconstructed image volume (x) |
| Parameters: | Iteration count, photon count, angular step |
🧠 Applications
- Low-dose breast cancer imaging
- Limited-angle tomography
- Sparse-view reconstruction
- Real-time diagnostic modeling
🧩 Linked Assets
| Type | Name | Description |
|---|---|---|
| Dataset | rbyrct-imaging-data |
Photon-limited X-ray projections |
| Space | strx-onephoton-demo |
Interactive reconstruction demo |
📜 Citation
Gordon, R., Ather, S.H., et al. (2024). Electronic Steering of X-rays (RBYRCT): A Plan to End Breast Cancer. Journal of Artificial Intelligence Research (JAIR).
💡 About Janus Sphere Innovations
Janus Sphere Innovations is an open-science company exploring the intersection of optics, AI, and life — from photon-limited tomography to quantum imaging.
“I know of no better life purpose than to perish in attempting the great and the impossible.” — F. Nietzsche