13 accepted papers
We propose a statistical benchmark for diffusion posterior sampling (DPS) algorithms in linear inverse problems. Our test signals are discretized Lévy processes whose posteriors admit efficient Gibbs methods. These Gibbs methods provide gold-standard posterior samples for direct, distribution-level…
We introduce Flower, a solver for linear inverse problems. It leverages a pre-trained flow model to produce reconstructions that are consistent with the observed measurements. Flower operates through an iterative procedure over three steps: (i) a flow-consistent destination estimation, where the vel…
State-of-the-art image reconstruction often relies on complex, abundantly parameterized deep architectures. We propose an alternative: a data-driven reconstruction method inspired by the classic Tikhonov regularization. Our approach iteratively refines intermediate reconstructions by solving a seque…
Supervised deep learning has become the method of choice for image denoising. It involves the training of neural networks on large datasets composed of pairs of noisy and clean images. However, the necessity of training data that are specific to the targeted application constrains the widespread use…
Phase retrieval, a nonlinear problem prevalent in imaging applications, has been extensively studied using random models, some of which with i.i.d. sensing matrix components. While these models offer robust reconstruction guarantees, they are computationally expensive and impractical for real-world…
We investigate the learning of a convex patch-based synthesis model for the reconstruction of images. In essence, we propose to learn a dictionary via bilevel optimization for denoising. Using implicit differentiation, we find a closed-form formula of the derivative of the minimizer of an objective…
The projection of sample measurements onto a reconstruction space represented by a basis on a regular grid is a powerful and simple approach to estimate a probability density function. In this paper, we focus on Riesz bases and propose a projection operator that, in contrast to previous works, guara…
We study a variant of the interpolation problem where the continuously defined solution is regularized by minimizing the L <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</inf> -norm of its second-order derivative. For this continuous-domain problem,…
The motivation for this work is to improve the performance of deep neural networks through the optimization of the individual activation functions. Since the latter results in an infinite- dimensional optimization problem, we resolve the ambiguity by searching for the sparsest and most regular solut…
We propose a discretization method for continuous-domain linear inverse problems with multiple-order total-variation (TV) regularization. It is based on a recent result that proves that such inverse problems have sparse polynomial-spline solutions. Our method consists in restricting the search space…
We propose a new statistical dictionary learning algorithm for sparse signals that is based on an $\alpha$-stable innovation model. The parameters of the underlying model—that is, the atoms of the dictionary, the sparsity index $\alpha$ and the dispersion of the transform-domain coefficients—are rec…
Learning Tomography (LT) is a nonlinear optimization algorithm for computationally imaging three-dimensional (3D) distribution of the refractive index in semi-transparent samples. Since the energy function in LT is generally non-convex, the solution it obtains is not guaranteed to be globally optima…
We propose two minimum-mean-square-error (MMSE) estimation methods for denoising non-Gaussian first-order autoregressive (AR(1)) processes. The first one is based on the message passing framework and gives the exact theoretic MMSE estimator. The second is an iterative algorithm that combines standar…