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A broad range of problems in computer graphics rendering, appearance acquisition for graphics and vision, and imaging,
involve sampling, reconstruction, and integration of high-dimensional (4D-8D) signals. For example, precomputation-based
real-time rendering of glossy materials and intricate lighting effects like caustics, can involve (pre)-computing the
response of the scene to different light and viewing directions, which is often a 6D dataset. Similarly, image-based appearance
acquisition of facial details, car paint, or glazed wood, requires us to take images from different light and view
directions. Even offline rendering of visual effects like motion blur from a fast-moving car, or depth of field, involves
high-dimensional sampling across time and lens aperture. The same problems are also common in computational imaging
applications such as light field cameras.
In the past few years, computer graphics and computer vision researchers have made significant progress in subsequent
analysis and compact factored or multiresolution representations for some of these problems. However, the initial full
dataset must almost always still be acquired or computed by brute force. This is often prohibitively expensive, taking hours
to days of computation and acquisition time, as well as being a challenge for memory usage and storage. For example, on
the order of 10,000 megapixel images are needed for a 1 degree sampling of lights and views for high-frequency materials.
We argue that dramatically sparser sampling and reconstruction of these signals is possible, before the full dataset is
acquired or simulated. Our key idea is to exploit the structure of the data that often lies in lower-frequency, sparse, or
low-dimensional spaces. Our framework will apply to a diverse set of problems such as sparse reconstruction of light
transport matrices for relighting, sheared sampling and denoising for offline shadow rendering, time-coherent compressive
sampling for appearance acquisition, and new approaches to computational photography and imaging.
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