Practical ReProCS for separating sparse and low-dimensional signal sequences from their sum — Part 1

This paper designs and evaluates a practical algorithm, called Prac-ReProCS, for recovering a time sequence of sparse vectors S_t and a time sequence of dense vectors L_t from their sum, M_t := S_t + L_t, when any subsequence of the L_t´s lies in a slowly changing low-dimensional subspace. A key application where this problem occurs is in video layering where the goal is to separate a video sequence into a slowly changing background sequence and a sparse foreground sequence that consists of one or more moving regions/objects. Prac-ReProCS is the practical analog of its theoretical counterpart that was studied in our recent work.