Nicolas Papadakis's research while affiliated with University of Bordeaux and other places

... One can partially circumvent this limitation by combining a proximal algorithm with a generic weakly convex regularizer, for which the proximal operator is well-defined. The convergence to stationary points of the objective is established in [24,22] for the forward-backward splitting [5] based on the very general convergence result for functions with the Kurdyka-Lojasiewicz (KL) property given in [3]. When R is differentiable, as will be assumed in our setting, similar results can be obtained for gradient descent applied to the non-convex objective (2), see [3]. ...

... They have nice mathematical properties, since they are the Fréchet means with respect to the Wasserstein distance [3][4][5]. Their applications range from mixing textures [6,7], stippling patterns and bidirectional reflectance distribution functions [8], or color distributions and shapes [9] over averaging of sensor data [10] to Bayesian statistics [11], just to name a few. For further reading, we refer to the surveys [12,13]. ...

... The convergence proof was later provided in [1]. Under the same setting, a nonlinear power method was proposed in [6] with connections to proximal operators and neural networks. For the case when J is the total variation (TV) and H is the L 1 norm, the Rayleigh quotient (6) approximates the Cheeger cut problem [11,5]. ...

... More details of the texture synthesis can be found in [20,21]. Please note that our framework is generic and a variety of different texture synthesis techniques can be applied in our approach, such as [28][29][30]. ...

... where D is a data-fidelity term which depends on the noise model and measures how well the reconstruction fits to the observation and R is a regularizer which copes with the ill-posedness and incorporates prior information. Over the last years, learned regularizers like the total deep variation [46,47] or adversarial regularizers [55,58,63] as well as extensions of plug-andplay and unrolled methods [24,78,84,88] with learned denoisers [32,35,67,91] showed promising results, see [8,59] for an overview. Furthermore, many papers leveraged the tractability of the likelihood of normalizing flows (NFs) to learn a prior [9,30,85,86,90] or use conditional variants to learn the posterior [12,53,79,87] They utilize the invertibility to optimize over the range of the flow together with the Gaussian assumption on the latent space. ...

... For all these results we see that for fixed ε > 0 the empirical EOT cost admits faster rates in n than the empirical unregularized OT cost. Such results are complemented by extensive research on distributional limits for the empirical OT cost at scaling rate n 1/2 which establish the parametric rate to be sharp [5,11,34,35,36,37,44,49,59]. However, as the regularization parameter decreases to zero, the statistical error bound generally deteriorates in high dimensions polynomially or even exponentially in ε −1 . ...

... In preparation for the SWOT mission, the Jet Propulsion Laboratory (JPL) developed the observation error covariance model [2,4] which served as a basis for numerous experiments aimed at assessing both the added value of the mission in monitoring the global ocean (e.g., [5][6][7][8][9]) and at dealing with spatial correlations of the errors contaminating SWOT observations (e.g., [10][11][12]). ...

... The Wasserstein barycenter problem (i.e., Example 1.4) has recently become a highly active research area due to its widespread applications in statistical inference [14,62], pattern recognition [64], image synthesis [49], clustering [73], and various other fields in machine learning. Most studies about the computation of Wasserstein barycenter focus on the case where µ 1 , . . . ...

... The quotient minimization (6) also appears in learning parameterized regularizations [3] and filter functions [2]. In this paper, we propose a novel scheme to minimize the general model (1) based on a gradient descent flow for the Rayleigh quotient minimization [9]. We then apply the proposed algorithm to the three specific examples (L 1 /L 2 , L 1 /S K , and L 1 /L 2 on the gradient). ...

... For other noise types, the data fidelity term is formulated differently. We give three specific signal and image processing examples that fit into our general model (1). ...