In this section, we review some key results on the Wasserstein distance. Wpp Rπ(t,θi),Rρ(t,θi), (4) where the approximation comes from using Monte-Carlo integration by samplingθi uniformly in SD 1 [2]. M,M is the number of points used to approximate the integral. Calculating the Wasserstein distance with the empirical distribution function is computationally attractive. To do that, we first sortxms in an ascending order, such thatxi[m] xi[m+1], where i[m]istheindexofthesortedxms. Hamiltonian Monte Carlo (HMC)[24]isahighly-efficient MarkovChain Monte Carlo (MCMC) method used to generate samples from the posteriorw p(w|y).

Different inner loss and outer loss other than what we used can be instantiated in the subclass.

Baseline Model As a baseline, we use the aforementioned linear Cox proportional hazard model[Cox72].

However, since this proof relies on the existence of a convergent subsequence, their proof does not reveal any rate forglobal convergence.

Motion blur caused by camera shake, particularly under large or rotational movements, remains a major challenge in image restoration. We propose a deep learning framework that jointly estimates the latent sharp image and the underlying camera motion trajectory from a single blurry image. Our method leverages the Projective Motion Blur Model (PMBM), implemented efficiently using a differentiable blur creation module compatible with modern networks. A neural network predicts a full 3D rotation trajectory, which guides a model-based restoration network trained end-to-end. This modular architecture provides interpretability by revealing the camera motion that produced the blur. Moreover, this trajectory enables the reconstruction of the sequence of sharp images that generated the observed blurry image. To further refine results, we optimize the trajectory post-inference via a reblur loss, improving consistency between the blurry input and the restored output. Extensive experiments show that our method achieves state-of-the-art performance on both synthetic and real datasets, particularly in cases with severe or spatially variant blur, where end-to-end deblurring networks struggle. Code and trained models are available at https://github.com/GuillermoCarbajal/Blur2Seq/

We minimize the negative Cox partial log-likelihood by gradient descent w.r.t.

Consider the following system with a generic R.H.S-X We also added the approach of Blackbox [25], which also deals with a combinatorial optimization problem with a linear objective.

Different inner loss and outer loss other than what we used can be instantiated in the subclass.