Compressive Image Reconstruction in Reduced Union of Subspaces

• Published in: Computer graphics forum Vol. 34; no. 2; pp. 33 - 44
• Main Authors: Miandji, Ehsan, Kronander, Joel, Unger, Jonas
• Format: Journal Article
• Language: English
• Published: Oxford Blackwell Publishing Ltd 01.05.2015
• Subjects: Algorithms; Analysis; and texture; Animation; Categories and Subject Descriptors (according to ACM CCS); compressed sensing; Computer graphics; I.3.7 [Computer Graphics]: Three-Dimensional Graphics and Realism-Color; I.3.7 [Computer Graphics]: Three‐Dimensional Graphics and Realism—Color, shading, shadowing, and texture; Image processing systems; Image reconstruction; light field imaging; Representations; shading; shadowing; Studies; Subspaces; Two dimensional; Unions
• ISSN: 0167-7055; 1467-8659; 1467-8659
• DOI: 10.1111/cgf.12539

We present a new compressed sensing framework for reconstruction of incomplete and possibly noisy images and their higher dimensional variants, e.g. animations and light‐fields. The algorithm relies on a learning‐based basis representation. We train an ensemble of intrinsically two‐dimensional (2D) dictionaries that operate locally on a set of 2D patches extracted from the input data. We show that one can convert the problem of 2D sparse signal recovery to an equivalent 1D form, enabling us to utilize a large family of sparse solvers. The proposed framework represents the input signals in a reduced union of subspaces model, while allowing sparsity in each subspace. Such a model leads to a much more sparse representation than widely used methods such as K‐SVD. To evaluate our method, we apply it to three different scenarios where the signal dimensionality varies from 2D (images) to 3D (animations) and 4D (light‐fields). We show that our method outperforms state‐of‐the‐art algorithms in computer graphics and image processing literature.