2 research outputs found
Controlling Neural Networks via Energy Dissipation
The last decade has shown a tremendous success in solving various computer
vision problems with the help of deep learning techniques. Lately, many works
have demonstrated that learning-based approaches with suitable network
architectures even exhibit superior performance for the solution of (ill-posed)
image reconstruction problems such as deblurring, super-resolution, or medical
image reconstruction. The drawback of purely learning-based methods, however,
is that they cannot provide provable guarantees for the trained network to
follow a given data formation process during inference. In this work we propose
energy dissipating networks that iteratively compute a descent direction with
respect to a given cost function or energy at the currently estimated
reconstruction. Therefore, an adaptive step size rule such as a line-search,
along with a suitable number of iterations can guarantee the reconstruction to
follow a given data formation model encoded in the energy to arbitrary
precision, and hence control the model's behavior even during test time. We
prove that under standard assumptions, descent using the direction predicted by
the network converges (linearly) to the global minimum of the energy. We
illustrate the effectiveness of the proposed approach in experiments on single
image super resolution and computed tomography (CT) reconstruction, and further
illustrate extensions to convex feasibility problems.Comment: Published as a conference paper at ICCV 2019, Seou
Bilevel Integrative Optimization for Ill-posed Inverse Problems
Classical optimization techniques often formulate the feasibility of the
problems as set, equality or inequality constraints. However, explicitly
designing these constraints is indeed challenging for complex real-world
applications and too strict constraints may even lead to intractable
optimization problems. On the other hand, it is still hard to incorporate
data-dependent information into conventional numerical iterations. To partially
address the above limits and inspired by the leader-follower gaming
perspective, this work first introduces a bilevel-type formulation to jointly
investigate the feasibility and optimality of nonconvex and nonsmooth
optimization problems. Then we develop an algorithmic framework to couple
forward-backward proximal computations to optimize our established bilevel
leader-follower model. We prove its convergence and estimate the convergence
rate. Furthermore, a learning-based extension is developed, in which we
establish an unrolling strategy to incorporate data-dependent network
architectures into our iterations. Fortunately, it can be proved that by
introducing some mild checking conditions, all our original convergence results
can still be preserved for this learnable extension. As a nontrivial byproduct,
we demonstrate how to apply this ensemble-like methodology to address different
low-level vision tasks. Extensive experiments verify the theoretical results
and show the advantages of our method against existing state-of-the-art
approaches.Comment: arXiv admin note: text overlap with arXiv:1706.04008 by other author