Lightness illusion: A new look from Compressive Sensing perspective

Lightness illusions, such as the seemingly opposing effects of brightness contrast and assimilation, are characterized by visually perceived intensity images that differ from physical reality. Traditional hypotheses from signal processing community primarily use filtering to explain these phenomena. However, these methods may fail due to the change in geometry (e.g., homography transform). In this paper, we attempt to explain lightness illusion from a novel Compressive Sensing perspective. The underlying mathematics is based on the new theory of compressive sensing, which provides an efficient method for sampling and reconstructing a signal that is sparse in Fourier domain. The sampling amounts to a random sampling of locally averaged values. Reconstruction amounts to solving an underdetermined linear equation system using L₁ norm minimization. The Accelerated Proximal Gradient (APG) method is used to reconstruct the compressed signal. We demonstrate that the reconstruction error can be used for robustly explaining well known lightness illusions.