Beyond Low Rank + Sparse: Multi-scale Low Rank Matrix Decomposition

We present a natural generalization of the recent low rank + sparse matrix decomposition and consider the decomposition of matrices into components of multiple scales. Such decomposition is well motivated in practice as data matrices often exhibit local correlations in multiple scales. Concretely, we propose a multi-scale low rank modeling that represents a data matrix as a sum of block-wise low rank matrices with increasing scales of block sizes. We then consider the inverse problem of decomposing the data matrix into its multi-scale low rank components and approach the problem via a convex formulation. Theoretically, we show that under various incoherence conditions, the convex program recovers the multi-scale low rank components \revised{either exactly or approximately}. Practically, we provide guidance on selecting the regularization parameters and incorporate cycle spinning to reduce blocking artifacts. Experimentally, we show that the multi-scale low rank decomposition provides a more intuitive decomposition than conventional low rank methods and demonstrate its effectiveness in four applications, including illumination normalization for face images, motion separation for surveillance videos, multi-scale modeling of the dynamic contrast enhanced magnetic resonance imaging and collaborative filtering exploiting age information

Bird abundance and diversity in shade coffee and natural forest Kenya

Coffee, one of the major traded commodities in the world, has captured attention of both the international business class and conservation community due to its value as a beverage and for the habitat it can provide for wildlife. Previous work in Central Kenya has demonstrated that when cultivated with shade trees, coffee farms can host high levels of bird diversity. However, questions of how the bird community in shade coffee farms compares to those in natural forest remained unanswered. Using three visits to each of 160-point count locations in natural forest (80) and shade coffee sites (80) in Central Kenya, I estimated bird abundance and species richness in natural forest and shade coffee. Specifically, I predicted higher abundance and diversity of granivores, forest visitors, forest generalists and no forest association in shade coffee than in natural forest, and higher abundance and diversity of insectivores, frugivores and forest specialists in natural forest than in shade coffee farms. Compared to natural forest, shade coffee had higher bird abundance and species diversity of all feeding guilds except frugivores, which were mostly detected in natural forest. Forest specialists and forest generalists were more abundant and with higher species richness in natural forest than in shade coffee. My study accentuates the value of remnant native trees within coffee plantations for the persistence and conservation of avian communities, while also clarifying that some groups of birds are reliant on natural forests and unlikely to be conserved in shade coffee farms. These findings contribute to a growing understanding of the value and limitations of shade coffee for avian conservation, which land managers can use in their management plans while promoting conservation efforts

BLADE: Filter Learning for General Purpose Computational Photography

The Rapid and Accurate Image Super Resolution (RAISR) method of Romano, Isidoro, and Milanfar is a computationally efficient image upscaling method using a trained set of filters. We describe a generalization of RAISR, which we name Best Linear Adaptive Enhancement (BLADE). This approach is a trainable edge-adaptive filtering framework that is general, simple, computationally efficient, and useful for a wide range of problems in computational photography. We show applications to operations which may appear in a camera pipeline including denoising, demosaicing, and stylization