Nadav Torem

Nadav Torem, Roi Ronen, Yoav Y. Schechner et al.

In diverse microscopy modalities, sensors measure only real-valued intensities. Additionally, the sensor readouts are affected by Poissonian-distributed photon noise. Traditional restoration algorithms typically aim to minimize the mean squared error (MSE) between the original and recovered images. This often leads to blurry outcomes with poor perceptual quality. Recently, deep diffusion models (DDMs) have proven to be highly capable of sampling images from the a-posteriori probability of the sought variables, resulting in visually pleasing high-quality images. These models have mostly been suggested for real-valued images suffering from Gaussian noise. In this study, we generalize annealed Langevin Dynamics, a type of DDM, to tackle the fundamental challenges in optical imaging of complex-valued objects (and real images) affected by Poisson noise. We apply our algorithm to various optical scenarios, such as Fourier Ptychography, Phase Retrieval, and Poisson denoising. Our algorithm is evaluated on simulations and biological empirical data.

Lior Dvir, Nadav Torem, Yoav Y. Schechner

We derive the likelihood of a raw signal in a single photon avalanche diode (SPAD), given a fixed photon flux. The raw signal comprises timing of detection events, which are nonlinearly related to the flux. Moreover, they are naturally stochastic. We then derive a score function of the signal. This is a key for solving inverse problems based on SPAD signals. We focus on deriving solutions involving a diffusion model, to express image priors. We demonstrate the effect of low or high photon counts, and the consequence of exploiting timing of detection events.

Nadav Torem, Tamar Sde-Chen, Yoav Y. Schechner

Most natural objects have inherent complexity and variability. While some simple objects can be modeled from first principles, many real-world phenomena, such as cloud formation, require computationally expensive simulations that limit scalability. This work focuses on a class of physically meaningful, nonnegative objects that are computationally tractable but costly to simulate. To dramatically reduce computational costs, we propose nonnegative diffusion (NnD). This is a learned generative model using score based diffusion. It adapts annealed Langevin dynamics to enforce, by design, non-negativity throughout iterative scene generation and analysis (inference). NnD trains on high-quality physically simulated objects. Once trained, it can be used for generation and inference. We demonstrate generation of 3D volumetric clouds, comprising inherently nonnegative microphysical fields. Our generated clouds are consistent with cloud physics trends. They are effectively not distinguished as non-physical by expert perception.