Phase imaging is gaining importance due to its applications in fields like biomedical imaging and material characterization. In biomedical applications, it can provide quantitative information missing in label-free microscopy modalities. One of the most prominent methods in phase quantification is the Transport-of-Intensity Equation (TIE). TIE often requires multiple acquisitions at different defocus distances, which is not always feasible in a clinical setting due to hardware constraints. To address this issue, we propose the use of chromatic aberrations to induce the required through-focus images with a single exposure, effectively generating a through-focus stack. Since the defocus distance induced by the aberrations is small, conventional TIE solvers are insufficient to address the resulting artifacts. We propose Zero-Mean Diffusion, a modified version of diffusion models designed for quantitative image prediction, and train it with synthetic data to ensure robust phase retrieval. Our contributions offer an alternative TIE approach that leverages chromatic aberrations, achieving accurate single-exposure phase measurement with white light and thus improving the efficiency of phase imaging. Additionally, we present a new class of diffusion models that are well-suited for quantitative data and have a sound theoretical basis. To validate our approach, we employ a widespread brightfield microscope equipped with a commercially available color camera. We apply our model to clinical microscopy of patients' urine, obtaining accurate phase measurements.

Inverse problems aim to determine parameters from observations, a crucial task in engineering and science. Lately, generative models, especially diffusion models, have gained popularity in this area for their ability to produce realistic solutions and their good mathematical properties. Despite their success, an important drawback of diffusion models is their sensitivity to the choice of variance schedule, which controls the dynamics of the diffusion process. Fine-tuning this schedule for specific applications is crucial but time-consuming and does not guarantee an optimal result. We propose a novel approach for learning the schedule as part of the training process. Our method supports probabilistic conditioning on data, provides high-quality solutions, and is flexible, proving able to adapt to different applications with minimum overhead. This approach is tested in two unrelated inverse problems: super-resolution microscopy and quantitative phase imaging, yielding comparable or superior results to previous methods and fine-tuned diffusion models. We conclude that fine-tuning the schedule by experimentation should be avoided because it can be learned during training in a stable way that yields better results. The code is available on https://github.com/casus/cvdm

The susceptibility of super paramagnetic iron oxide (SPIO) particles makes them a useful contrast agent for different purposes in MRI. These particles are typically quantified with relaxometry or by measuring the inhomogeneities they produced. These methods rely on the phase, which is unreliable for high concentrations. We present in this study a novel Deep Learning method to quantify the SPIO concentration distribution. We acquired the data with a new sequence called View Line in which the field map information is encoded in the geometry of the image. The novelty of our network is that it uses residual blocks as the bottleneck and multiple decoders to improve the gradient flow in the network. Each decoder predicts a different part of the wavelet decomposition of the concentration map. This decomposition improves the estimation of the concentration, and also it accelerates the convergence of the model. We tested our SPIO concentration reconstruction technique with simulated images and data from actual scans from phantoms. The simulations were done using images from the IXI dataset, and the phantoms consisted of plastic cylinders containing agar with SPIO particles at different concentrations. In both experiments, the model was able to quantify the distribution accurately.