Projection Embedded Diffusion Bridge for CT Reconstruction from Incomplete Data

Reconstructing CT images from incomplete projection data remains challenging due to the ill-posed nature of the problem. Diffusion bridge models have recently shown promise in restoring clean images from their corresponding Filtered Back Projection (FBP) reconstructions, but incorporating data consistency into these models remains largely underexplored. Incorporating data consistency can improve reconstruction fidelity by aligning the reconstructed image with the observed projection data, and can enhance detail recovery by integrating structural information contained in the projections. In this work, we propose the Projection Embedded Diffusion Bridge (PEDB). PEDB introduces a novel reverse stochastic differential equation (SDE) to sample from the distribution of clean images conditioned on both the FBP reconstruction and the incomplete projection data. By explicitly conditioning on the projection data in sampling the clean images, PEDB naturally incorporates data consistency. We embed the projection data into the score function of the reverse SDE. Under certain assumptions, we derive a tractable expression for the posterior score. In addition, we introduce a free parameter to control the level of stochasticity in the reverse process. We also design a discretization scheme for the reverse SDE to mitigate discretization error. Extensive experiments demonstrate that PEDB achieves strong performance in CT reconstruction from three types of incomplete data, including sparse-view, limited-angle, and truncated projections. For each of these types, PEDB outperforms evaluated state-of-the-art diffusion bridge models across standard, noisy, and domain-shift evaluations.

Evaluating GPT's Programming Capability through CodeWars' Katas

In the burgeoning field of artificial intelligence (AI), understanding the capabilities and limitations of programming-oriented models is crucial. This paper presents a novel evaluation of the programming proficiency of Generative Pretrained Transformer (GPT) models, specifically GPT-3.5 and GPT-4, against coding problems of varying difficulty levels drawn from Codewars. The experiments reveal a distinct boundary at the 3kyu level, beyond which these GPT models struggle to provide solutions. These findings led to the proposal of a measure for coding problem complexity that incorporates both problem difficulty and the time required for solution. The research emphasizes the need for validation and creative thinking capabilities in AI models to better emulate human problem-solving techniques. Future work aims to refine this proposed complexity measure, enhance AI models with these suggested capabilities, and develop an objective measure for programming problem difficulty. The results of this research offer invaluable insights for improving AI programming capabilities and advancing the frontier of AI problem-solving abilities.