# X-ray Spectral Estimation using Dictionary Learning

## TL;DR

This paper introduces a dictionary learning-based spectral estimation method for X-ray CT systems that accurately estimates spectral response without initial guesses, improving over existing methods.

## Contribution

The paper presents a novel dictionary-based spectral estimation approach using MAP estimation with sparsity and simplex constraints, outperforming state-of-the-art methods.

## Key findings

- Accurate spectral estimates achieved without initial guesses.
- Method outperforms existing techniques in cross-validation experiments.
- Demonstrated effectiveness on real ALS datasets.

## Abstract

As computational tools for X-ray computed tomography (CT) become more quantitatively accurate, knowledge of the source-detector spectral response is critical for quantitative system-independent reconstruction and material characterization capabilities. Directly measuring the spectral response of a CT system is hard, which motivates spectral estimation using transmission data obtained from a collection of known homogeneous objects. However, the associated inverse problem is ill-conditioned, making accurate estimation of the spectrum challenging, particularly in the absence of a close initial guess. In this paper, we describe a dictionary-based spectral estimation method that yields accurate results without the need for any initial estimate of the spectral response. Our method utilizes a MAP estimation framework that combines a physics-based forward model along with an $L_0$ sparsity constraint and a simplex constraint on the dictionary coefficients. Our method uses a greedy support selection method and a new pair-wise iterated coordinate descent method to compute the above estimate. We demonstrate that our dictionary-based method outperforms a state-of-the-art method as shown in a cross-validation experiment on four real datasets collected at beamline 8.3.2 of the Advanced Light Source (ALS).