Despite significant recent progress, dense, time-resolved imaging of complex, non-stationary 3D flow velocities remains an elusive goal. In this work we tackle this problem by extending an established 2D method, Particle Imaging Velocimetry, to three dimensions by encoding depth into color. The encoding is achieved by illuminating the flow volume with a continuum of light planes (a “rainbow”), such that each depth corresponds to a specific wavelength of light. A diffractive component in the camera optics ensures that all planes are in focus simultaneously. For reconstruction, we derive an image formation model for recovering stationary 3D particle positions. 3D velocity estimation is achieved with a variant of 3D optical flow that accounts for both physical constraints as well as the rainbow image formation model. We evaluate our method with both simulations and an experimental prototype setup.

Convolutional sparse coding (CSC) is a promising direction for unsupervised learning in computer vision. In contrast to recent supervised methods, CSC allows for convolutional image representations to be learned that are equally useful for high-level vision tasks and low-level image reconstruction and can be applied to a wide range of tasks without problem-specific retraining. Due to their extreme memory requirements, however, existing CSC solvers have so far been limited to low-dimensional problems and datasets using a handful of low-resolution example images at a time. In this paper, we propose a new approach to solving CSC as a consensus optimization problem, which lifts these limitations. By learning CSC features from large-scale image datasets for the first time, we achieve significant quality improvements in a number of imaging tasks. Moreover, the proposed method enables new applications in high dimensional feature learning that has been intractable using existing CSC methods. This is demonstrated for a variety of reconstruction problems across diverse problem domains, including 3D multispectral demosaickingand 4D light field view synthesis.