Related papers: On recovery guarantees for angular synchronization
The orthogonal group synchronization problem, which aims to recover a set of $d \times d$ orthogonal matrices from their pairwise noisy products, plays a fundamental role in signal processing, computer vision, and network analysis. In…
A fruitful approach for solving signal deconvolution problems consists of resorting to a frame-based convex variational formulation. In this context, parallel proximal algorithms and related alternating direction methods of multipliers have…
This paper addresses the problem of synchronizing orthogonal matrices over directed graphs. For synchronized transformations (or matrices), composite transformations over loops equal the identity. We formulate the synchronization problem as…
This paper introduces a novel approach for recovering sparse signals using sorted L1/L2 minimization. The proposed method assigns higher weights to indices with smaller absolute values and lower weights to larger values, effectively…
We study the nonconvex optimization landscapes of synchronization problems on spheres. First, we present new results for the statistical problem of synchronization over the two-element group $\mathbf{Z}_2$. We consider the nonconvex…
This note considers the unstructured sparse recovery problems in a general form. Examples include rational approximation, spectral function estimation, Fourier inversion, Laplace inversion, and sparse deconvolution. The main challenges are…
We analyze a new spectral graph matching algorithm, GRAph Matching by Pairwise eigen-Alignments (GRAMPA), for recovering the latent vertex correspondence between two unlabeled, edge-correlated weighted graphs. Extending the exact recovery…
This paper deals with the problem of estimating the delays and amplitudes of a weighted superposition of pulses, called stream of pulses. This problem is motivated by a variety of applications, such as ultrasound and radar. This paper shows…
Optimization problems with norm-bounding constraints arise in a variety of applications, including portfolio optimization, machine learning, and feature selection. A common approach to these problems involves relaxing the norm constraint…
Recovering a low-rank tensor from incomplete information is a recurring problem in signal processing and machine learning. The most popular convex relaxation of this problem minimizes the sum of the nuclear norms of the unfoldings of the…
We consider the problem of matrix completion with graphs as side information depicting the interrelations between variables. The key challenge lies in leveraging the similarity structure of the graph to enhance matrix recovery. Existing…
We propose a novel formulation for phase synchronization -- the statistical problem of jointly estimating alignment angles from noisy pairwise comparisons -- as a nonconvex optimization problem that enforces consistency among the pairwise…
Time-varying graph signal recovery has been widely used in many applications, including climate change, environmental hazard monitoring, and epidemic studies. It is crucial to choose appropriate regularizations to describe the…
We propose a convex-concave programming approach for the labeled weighted graph matching problem. The convex-concave programming formulation is obtained by rewriting the weighted graph matching problem as a least-square problem on the set…
Regularization is a critical technique for ensuring well-posedness in solving inverse problems with incomplete measurement data. Traditionally, the regularization term is designed based on prior knowledge of the unknown signal's…
We present a theoretical and empirical analysis of the SyncRank algorithm for recovering a global ranking from noisy pairwise comparisons. By adopting a complex-valued data model where the true ranking is encoded in the phases of a…
We propose two novel approaches to the recovery of an (approximately) sparse signal from noisy linear measurements in the case that the signal is a priori known to be non-negative and obey given linear equality constraints, such as simplex…
This paper investigates the theoretical guarantees of L1-analysis regularization when solving linear inverse problems. Most of previous works in the literature have mainly focused on the sparse synthesis prior where the sparsity is measured…
This paper proposes a precise signal recovery method with multilayered non-convex regularization, enhancing sparsity/low-rankness for high-dimensional signals including images and videos. In optimization-based signal recovery, multilayered…
We consider the problem of learning a sparse graph under the Laplacian constrained Gaussian graphical models. This problem can be formulated as a penalized maximum likelihood estimation of the Laplacian constrained precision matrix. Like in…