Inverse problems arise in many fields of engineering and science. In this dissertation, we explore various aspects of model uncertainties encountered in computational imaging applications. We will discuss some of the developments in combining convex/nonconvex optimization methods, com- pressive sensing theory, dictionary learning and data-driven hybrid methods, with domain-specific knowledge contained in physical-analytical models, in a coherent way, in solving some of the chal- lenging ill-posed inverse problems.In Chapter 1, we provide a brief introduction to inverse problems, sparsity, and compressive sensing. We introduce how imperfect sensing, dictionary learning, and prior knowledge of the signal can be incorporated into the modeling to address ill-posedness problems, paving the way for subsequent discussions on specific challenges encountered in di↵erent imaging applications. In Chapter 2, we study a form of model uncertainty that arises from uncalibrated sensing coils. We study an auto-calibration problem in which a transform-sparse signal is compressive-sensed by multiple sensors in parallel with unknown sensing parameters. The problem has an important application in parallel Magnetic Resonance Imaging (pMRI) reconstruction, where explicit coil cal- ibrations are often dicult and costly to achieve in practice. We show how ideas from convex optimization, compressive sensing and probabilistic theory can be combined together to solve the auto-calibration problem. Robust and stable recovery guarantees are derived in the presence of noise and sparsity deficiencies in the signals. For the pMRI application, our method provides a theoretically guaranteed approach to self-calibrated parallel imaging to accelerate MRI acquisitions under appropriate assumptions. We also discuss potential deep learning approaches that can serve as a future direction. The main materials presented in this chapter are based on [1] submitted to Inverse Problems. In Chapter 3, we move on to a distinct challenge that arises in Fluorescence Lifetime Imaging (FLIM). FLIM measures a convolution y = i * h + eps, where h represents the signal of inter- est. Conventional methods often involve constraining h to a low dimensional subspace B(h) (i.e. h = B(h)z). Due to the implicit dependence of B on the underlying signal, choosing a proper for- ward matrix that fits well to signals with various decaying physics is nontrivial. We propose learning the best sparse representation from fluorescence impulse response function (fIRFs) through joint deconvolution and sparse non-negative matrix factorization, and comparing the performance with traditional fitting methods that use a fixed basis. As a second step, we explore the application of utilizing the reconstructed h in cancer classification from biological tissue samples. In Chapter 4, we introduce some of the model uncertainty problems in Ptychography that are accounted for by poor calibration using multiplexing illumination. The material presented in this chapter revolves around computational considerations and the design of ecient and distributional algorithms for practical uses. We empirically demonstrate an acceleration in convergence rate if the uncertainties are solved by a separate optimization problem within common phase retrieval algorithms. And it is the first to apply such scheme to large scale problems due to our utilization of ecient coding practices and parallel computing techniques. Moreover, we propose and develop a patch-based scheme to further enhance computation.