Abstract : This dissertation is devoted to novel computational imaging methods with applications in remote sensing. Computational imaging methods are applied to three distinct applications including imaging and detection of buried explosive hazards utilizing array radar, high resolution imaging of satellites in geosynchronous orbit utilizing optical hypertelescope arrays, and characterization of atmospheric turbulence through multi-frame blind deconvolution utilizing conventional optical digital sensors. The first application considered utilizes a radar array employed as a forward looking ground penetrating radar system with applications in explosive hazard detection. A penalized least squares technique with sparsity-inducing regularization is applied to produce imagery, which is consistent with the expectation that objects are sparsely populated but extended with respect to the pixel grid. Additionally, a series of pre-processing steps is demonstrated which result in a greatly reduced data size and computational cost. Demonstrations of the approach are provided using experimental data and results are given in terms of signal to background ratio, image resolution, and relative computation time. The second application involves a sparse-aperture telescope array configured as a hypertelescope with applications in long range imaging. The penalized least squares technique with sparsity-inducing regularization is adapted and applied to this very different imaging modality. A comprehensive study of the algorithm tuning parameters is performed and performance is characterized using the Structure Similarity Metric (SSIM) to maximize image quality. Simulated measurements are used to show that imaging performance achieved using the pro- posed algorithm compares favorably in comparison to conventional Richardson-Lucy deconvolution. The third application involves a multi-frame collection from a conventional digital sensor with the primary objective of characterizing the atmospheric turbulence in the medium of propagation. In this application a joint estimate of the image is obtained along with the Zernike coefficients associated with the atmospheric PSF at each frame, and the Fried parameter r0 of the atmosphere. A pair of constraints are applied to a penalized least squares objective function to enforce the theoretical statistics of the set of PSF estimates as a function of r0. Results of the approach are shown with both simulated and experimental data and demonstrate excellent agreement between the estimated r0 values and the known or measured r0 values respectively.