Image interpolation using Shearlet based iterative refinement

This paper proposes an image interpolation algorithm exploiting sparse representation for natural images. It involves three main steps: (a) obtaining an initial estimate of the high resolution image using linear methods like FIR filtering, (b) promoting sparsity in a selected dictionary through iterative thresholding, and (c) extracting high frequency information from the approximation to refine the initial estimate. For the sparse modeling, a shearlet dictionary is chosen to yield a multiscale directional representation. The proposed algorithm is compared to several state-of-the-art methods to assess its objective as well as subjective performance. Compared to the cubic spline interpolation method, an average PSNR gain of around 0.8 dB is observed over a dataset of 200 images

Sparse and Redundant Representations for Inverse Problems and Recognition

Sparse and redundant representation of data enables the description of signals as linear combinations of a few atoms from a dictionary. In this dissertation, we study applications of sparse and redundant representations in inverse problems and object recognition. Furthermore, we propose two novel imaging modalities based on the recently introduced theory of Compressed Sensing (CS). This dissertation consists of four major parts. In the first part of the dissertation, we study a new type of deconvolution algorithm that is based on estimating the image from a shearlet decomposition. Shearlets provide a multi-directional and multi-scale decomposition that has been mathematically shown to represent distributed discontinuities such as edges better than traditional wavelets. We develop a deconvolution algorithm that allows for the approximation inversion operator to be controlled on a multi-scale and multi-directional basis. Furthermore, we develop a method for the automatic determination of the threshold values for the noise shrinkage for each scale and direction without explicit knowledge of the noise variance using a generalized cross validation method. In the second part of the dissertation, we study a reconstruction method that recovers highly undersampled images assumed to have a sparse representation in a gradient domain by using partial measurement samples that are collected in the Fourier domain. Our method makes use of a robust generalized Poisson solver that greatly aids in achieving a significantly improved performance over similar proposed methods. We will demonstrate by experiments that this new technique is more flexible to work with either random or restricted sampling scenarios better than its competitors. In the third part of the dissertation, we introduce a novel Synthetic Aperture Radar (SAR) imaging modality which can provide a high resolution map of the spatial distribution of targets and terrain using a significantly reduced number of needed transmitted and/or received electromagnetic waveforms. We demonstrate that this new imaging scheme, requires no new hardware components and allows the aperture to be compressed. Also, it presents many new applications and advantages which include strong resistance to countermesasures and interception, imaging much wider swaths and reduced on-board storage requirements. The last part of the dissertation deals with object recognition based on learning dictionaries for simultaneous sparse signal approximations and feature extraction. A dictionary is learned for each object class based on given training examples which minimize the representation error with a sparseness constraint. A novel test image is then projected onto the span of the atoms in each learned dictionary. The residual vectors along with the coefficients are then used for recognition. Applications to illumination robust face recognition and automatic target recognition are presented

Smart Nanoscopy: A Review of Computational Approaches to Achieve Super-Resolved Optical Microscopy

The field of optical nanoscopy , a paradigm referring to the recent cutting-edge developments aimed at surpassing the widely acknowledged 200nm-diffraction limit in traditional optical microscopy, has gained recent prominence & traction in the 21st century. Numerous optical implementations allowing for a new frontier in traditional confocal laser scanning fluorescence microscopy to be explored (termed super-resolution fluorescence microscopy ) have been realized through the development of techniques such as stimulated emission and depletion (STED) microscopy, photoactivated localization microscopy (PALM) and stochastic optical reconstruction microscopy (STORM), amongst others. Nonetheless, it would be apt to mention at this juncture that optical nanoscopy has been explored since the mid-late 20th century, through several computational techniques such as deblurring and deconvolution algorithms. In this review, we take a step back in the field, evaluating the various in silico methods used to achieve optical nanoscopy today, ranging from traditional deconvolution algorithms (such as the Nearest Neighbors algorithm) to the latest developments in the field of computational nanoscopy, founded on artificial intelligence (AI). An insight is provided into some of the commercial applications of AI-based super-resolution imaging, prior to delving into the potentially promising future implications of computational nanoscopy. This is facilitated by recent advancements in the field of AI, deep learning (DL) and convolutional neural network (CNN) architectures, coupled with the growing size of data sources and rapid improvements in computing hardware, such as multi-core CPUs & GPUs, low-latency RAM and hard-drive capacitie