High-Dimensional Data Analysis with Low-Dimensional Models Principles, Computation, and Applications

In human perception, the role of sparse representation has been studied extensively. As we have alluded to in the Introduction, Chapter 1, investigators in neuroscience have revealed that in both low-level and mid-level human vision, many neurons in the visual pathway are selective for recognizing a variety of specific stimuli, such as color, texture, orientation, scale, and even view-tuned object images [OF97, Ser06]. Considering these neurons to form an overcomplete dictionary of base signal elements at each visual stage, the firing of the neurons with respect to a given input image is typically highly sparse.