Fast Modular Reduction for Large-Integer Multiplication

The work contained in this thesis is a representation of the successful attempt to speed-up the modular reduction as an independent step of modular multiplication, which is the central operation in public-key cryptosystems. Based on the properties of Mersenne and Quasi-Mersenne primes, four distinct sets of moduli have been described, which are responsible for converting the single-precision multiplication prevalent in many of today\u27s techniques into an addition operation and a few simple shift operations. A novel algorithm has been proposed for modular folding. With the backing of the special moduli sets, the proposed algorithm is shown to outperform (speed-wise) the Modified Barrett algorithm by 80% for operands of length 700 bits, the least speed-up being around 70% for smaller operands, in the range of around 100 bits

Advanced Prior Modeling for Nano-scale Imaging

Many material and biological samples in scientific imaging are characterized by non-local repeating structures. These are studied using scanning/transmission electron microscopy and electron tomography. Sparse sampling of individual pixels in a 2D image acquisition geometry, or sparse sampling of projection images with large tilt increments in a tomography experiment, or low-resolution data acquisition can enable high speed data acquisition and minimize sample damage caused by the electron beam. However, accurate reconstructions from such sparse/low-resolution data is often challenging. In this work, we present algorithms for electron tomographic reconstruction, sparse image interpolation (or inpainting), and super-resolution that exploits the non-local redundancy in images. We adapt a framework, termed plug-and-play priors, to solve these imaging problems in a regularized inversion setting. The power of the plug-and-play approach is that it allows a wide array of modern denoising algorithms to be used as a prior model for a variety of inverse problems. We also present sufficient mathematical conditions that ensure convergence of the plug-and-play approach, and we use these insights to design a new non-local means denoising algorithm. In the end, we look at 4x, 8x, and 16x super-resolution reconstruction using library-based non-local means (LB-NLM) denoiser as a prior model within plug-and-play, to accurately characterize high-resolution textures and edge features, using high-resolution library patches acquired over a small field-of-view of the microscopy sample. Finally, we demonstrate that our algorithms produces higher quality reconstructions on both simulated and real electron microscope data, along with improved convergence properties compared to other methods

Media 2: High frame-rate multichannel beam-scanning microscopy based on Lissajous trajectories

Originally published in Optics Express on 06 October 2014 (oe-22-20-24224

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