In the past decade, camera manufacturers have offered smaller form factors, smaller pixel sizes (leading to higher resolution images), and faster processing chips to increase the performance of consumer cameras. However, these conventional approaches have failed to capitalize on the spatio-temporal redundancy inherent in images, nor have they adequately provided a solution for finding $3$D point correspondences for cameras sampling different bands of the visible spectrum. In this thesis, we pose the following question---given the repetitious nature of image patches, and appropriate camera architectures, can statistical models be used to increase temporal, structural, or spectral resolution? While many techniques have been suggested to tackle individual aspects of this question, the proposed solutions either require prohibitively expensive hardware modifications and/or require overly simplistic assumptions about the geometry of the scene. We propose a two-stage solution to facilitate image reconstruction; 1) design a linear camera system that optically encodes scene information and 2) recover full scene information using prior models learned from statistics of natural images. By leveraging the tendency of small regions to repeat throughout an image or video, we are able to learn prior models from patches pulled from exemplar images. The quality of this approach will be demonstrated for two application domains, using low-speed video cameras for high-speed video acquisition and multi-spectral fusion using an array of cameras. We also investigate a conventional approach for finding 3D correspondence that enables a generalized assorted array of cameras to operate in multiple modalities, including multi-spectral, high dynamic range, and polarization imaging of dynamic scenes.