An ADMM Approach to Masked Signal Decomposition Using Subspace Representation
This addresses the challenge of separating non-additive components in signals for applications in image and video processing, though it is incremental as it builds on existing subspace representation methods.
The paper tackles the problem of non-additive signal decomposition, where components like foreground and background are overlaid rather than additive, by proposing an algorithm that relaxes binary mask optimization to a continuous problem solved via alternating optimization. It demonstrates significant improvements in applications such as text-background separation in images, moving object separation in videos, and sinusoidal-spike separation in 1D signals.
Signal decomposition is a classical problem in signal processing, which aims to separate an observed signal into two or more components each with its own property. Usually each component is described by its own subspace or dictionary. Extensive research has been done for the case where the components are additive, but in real world applications, the components are often non-additive. For example, an image may consist of a foreground object overlaid on a background, where each pixel either belongs to the foreground or the background. In such a situation, to separate signal components, we need to find a binary mask which shows the location of each component. Therefore it requires to solve a binary optimization problem. Since most of the binary optimization problems are intractable, we relax this problem to the approximated continuous problem, and solve it by alternating optimization technique. We show the application of the proposed algorithm for three applications: separation of text from background in images, separation of moving objects from a background undergoing global camera motion in videos, separation of sinusoidal and spike components in one dimensional signals. We demonstrate in each case that considering the non-additive nature of the problem can lead to significant improvement.