Inexact Proximal Conjugate Subgradient Algorithm for fMRI Data Completion

Abstract

Tensor representations have proven useful for many problems, including data completion. A promising application for tensor completion is functional magnetic resonance imaging (fMRI) data that has an inherent four-dimensional (4D) structure and is prone to missing voxels and regions due to issues in acquisition. A key component of successful tensor completion is a rank estimation. While widely used as a convex relaxation of the tensor rank, tensor nuclear norm (TNN) imposes strong low-rank constraints on all tensor modes to be simultaneously low-rank and often leads to suboptimal solutions. We propose a novel tensor completion model in tensor train (TT) format with a proximal conjugate subgradient (PCS-TT) method for solving the nonconvex rank minimization problem by using properties of Moreau’s decomposition. PCS-TT allows the use of a wide range of robust estimators and can be used for data completion and sparse signal recovery problems. We present experimental results for data completion in fMRI, where PCS-TT demonstrates significant improvements compared with competing methods. In addition, we present results that demonstrate the advantages of considering the 4D structure of the fMRI data. as opposed to using three- and two-dimensional representations that have dominated the work on fMRI analysis.