  Event cameras are novel bio-inspired sensors that measure per-pixel
brightness differences asynchronously. Recovering brightness from events is
appealing since the reconstructed images inherit the high dynamic range (HDR)
and high-speed properties of events; hence they can be used in many robotic
vision applications and to generate slow-motion HDR videos. However,
state-of-the-art methods tackle this problem by training an event-to-image
Recurrent Neural Network (RNN), which lacks explainability and is difficult to
tune. In this work we show, for the first time, how tackling the combined
problem of motion and brightness estimation leads us to formulate event-based
image reconstruction as a linear inverse problem that can be solved without
training an image reconstruction RNN. Instead, classical and learning-based
regularizers are used to solve the problem and remove artifacts from the
reconstructed images. The experiments show that the proposed approach generates
images with visual quality on par with state-of-the-art methods despite only
using data from a short time interval. State-of-the-art results are achieved
using an image denoising Convolutional Neural Network (CNN) as the
regularization function. The proposed regularized formulation and solvers have
a unifying character because they can be applied also to reconstruct brightness
from the second derivative. Additionally, the formulation is attractive because
it can be naturally combined with super-resolution, motion-segmentation and
color demosaicing. Code is available at
https://github.com/tub-rip/event_based_image_rec_inverse_problem
