Fast Methods for Denoising Matrix Completion Formulations, with Applications to Robust Seismic Data Interpolation

Comparison of sparsity-constrained regularization methods for denoising and interpolation

Missing trace reconstruction is an ongoing challenge in seismic processing due to incomplete acquisition schemes and irregular grids. Noise is also a concern because it is naturally present in acquired seismic data through several mechanisms such as natural noise and equipment noise. Both problems need to be adequately addressed, especially because they negatively affect several important proce...

An SVD-free Pareto curve approach to rank minimization

Recent SVD-free matrix factorization formulations have enabled rank optimization for extremely large-scale systems (millions of rows and columns). In this paper, we consider rank-regularized formulations that only require a target data-fitting error level, and propose an algorithm for the corresponding problem. We illustrate the advantages of the new approach using the Netflix problem, and use ...

Seismic data interpolation and denoising using SVD-free low-rank matrix factorization

Putting the curvature back into sparse solvers

Many problems in signal and image processing seek a sparse solution to an underdetermined linear system. A common problem formulation for such applications is the basis pursuit denoising problem. Many of the most used approaches for this problem – such as iterative soft thresholding and SPGL1 – are first-order methods. As a result, these methods can sometimes be slow to converge. In this paper,...

Data denoising and interpolation using synthesis and analysis sparse regularization

Missing trace reconstruction is a challenge in seismic processing due to incomplete and irregular acquisition. Noise is a concern, due to the many sources of noise that occur during seismic acquisition. Most of the recent research on denoising and interpolation focuses on transform domain approaches using L1 norm minimization. A specific kind of constraint, called the synthesis approach, is wid...