Statistical image recovery techniques for optical imaging systems

Statistical techniques are very attractive for image recovery because they can incorporate the physical model of imaging systems, thus improving the quality of recovered images. To overcome the ill-posed nature of image recovery, one often uses penalized-likelihood estimation. Since closed-form solutions for these statistical techniques are unavailable, iterative algorithms are needed. However, existing algorithms lack one or more desirable properties, such as the guarantee of convergence, rapid convergence, and efficient computation.; In the first part of the dissertation, we present a new, fast-converging algorithm called partitioned-separable paraboloidal surrogate coordinate ascent (PPCA). This algorithm captures the fast convergence of iterative coordinate ascent algorithms, while remaining parallelizable to reduce computation time. The PPCA algorithm is based on paraboloidal surrogate functions and a concavity technique. It is most beneficial when applied to space-variant systems for which the fast Fourier transform (FFT) is inapplicable.; Because our primary applications are confocal microscopy and image plane holography, for which space-invariance of the systems is usually assumed, in the second part of the dissertation, we develop another algorithm that can be used with the FFT for fast computation time. We adapt the relaxed ordered-subset separable paraboloidal surrogate (OS-SPS) algorithm, which was originally invented for projection-based tomographic reconstruction, to pixel-based image restoration. The relaxed OS-SPS algorithm provides very fast initial convergence and is guaranteed to converge to the optimal solution. Furthermore, we develop different strategies for choosing subsets and efficient implementation. Both the PPCA and relaxed OS-SPS algorithms can be applied to many imaging problems; here we demonstrate their use for confocal microscopy problems.; In the third and last part of the dissertation, we develop a new statistical image reconstruction technique for digital holography including image plane holography. This approach reconstructs the complex object field from real-valued hologram intensity data. We develop a Poisson statistical model for this problem and derive an optimization transfer algorithm that monotonically decreases the cost function at each iteration and ensures convergence to a local minimum. Our statistical technique is shown to improve image quality in simulated digital holography relative to conventional numerical reconstruction using a filter applied in the frequency domain.