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Manifold models for signals and images

By Gabriel Peyré


This article proposes a new class of models for natural signals and images. The set of patches extracted from the data to analyze is constrained to be close to a low dimensional manifold. This manifold structure is detailed for various ensembles suitable for natural signals, images and textures modeling. These manifolds provide a low-dimensional parameterization of the local geometry of these datasets. These manifold models can be used to regularize inverse problems in signal and image processing. The restored signal is represented as a smooth curve or surface traced on the manifold that matches the forward measurements. A manifold pursuit algorithm computes iteratively a solution of the manifold regularization problem. Numerical simulations on inpainting and compressive sensing inversion show that manifolds models bring an improvement for the recovery of data with geometrical features. Key words: signal processing, image modeling, texture, manifold. PACS: code, code Capturing the complex geometry of signals and images is at the core of recent advances in sound and natural image processing. Edges and texture patterns create complex non-local interactions. This paper studies these geometries for several sounds, images and textures models. The set of local patches in the dataset is modeled using smooth manifolds. These local features trace a continuous curve (resp. surface) on the manifold, which is a prior that can be used to solve inverse problems

Year: 2009
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