Convolutional Deblurring for Natural Imaging

In this paper, we propose a novel design of image deblurring in the form of one-shot convolution filtering that can directly convolve with naturally blurred images for restoration. The problem of optical blurring is a common disadvantage to many imaging applications that suffer from optical imperfections. Despite numerous deconvolution methods that blindly estimate blurring in either inclusive or exclusive forms, they are practically challenging due to high computational cost and low image reconstruction quality. Both conditions of high accuracy and high speed are prerequisites for high-throughput imaging platforms in digital archiving. In such platforms, deblurring is required after image acquisition before being stored, previewed, or processed for high-level interpretation. Therefore, on-the-fly correction of such images is important to avoid possible time delays, mitigate computational expenses, and increase image perception quality. We bridge this gap by synthesizing a deconvolution kernel as a linear combination of Finite Impulse Response (FIR) even-derivative filters that can be directly convolved with blurry input images to boost the frequency fall-off of the Point Spread Function (PSF) associated with the optical blur. We employ a Gaussian low-pass filter to decouple the image denoising problem for image edge deblurring. Furthermore, we propose a blind approach to estimate the PSF statistics for two Gaussian and Laplacian models that are common in many imaging pipelines. Thorough experiments are designed to test and validate the efficiency of the proposed method using 2054 naturally blurred images across six imaging applications and seven state-of-the-art deconvolution methods.Comment: 15 pages, for publication in IEEE Transaction Image Processin

Nonlinear dynamics in multimode optical waveguide arrays

Ziel der vorliegenden Arbeit sind die Untersuchung und das Verständnis von Effekten, welche durch die nichtlineare Propagation geführter Moden höherer Ordnung in evaneszent gekoppelten Wellenleiterarrays ermöglicht werden. Um dies zu erreichen wurde die Lichtausbreitung in mehrmodigen Wellenleiterarrays untersucht. In diesen Wellenleiterarrays koppelt die optische Nichtlinearität zweiter Ordnung ein optisches Feld kleiner Frequenz, die sogenannte Fundamentalwelle, mit dem Feld der zweiten Harmonischen bei der doppelten Frequenz. Die Anregung von höheren Moden der zweiten Harmonischen aus einer in die Wellenleiter eingekoppelten Fundamentalwelle wurde für geringe Leistungen sowohl in Einzelwellenleitern als auch in Wellenleiterarrays untersucht. Dabei wurde gezeigt, dass höhere Moden unter Berücksichtigung der entsprechenden Phasenanpassbedingungen kontrolliert angeregt werden können. Im Allgemeinen kann eine propagierende Fundamentalmode mit mehreren Moden der zweiten Harmonischen nichtlinear wechselwirken. In der vorliegenden Arbeit wurde gezeigt, dass diskrete räumliche Solitonen mit zwei verschiedenen Moden der zweiten Harmonischen existieren. Dabei wurden zwei unterschiedliche Typen räumlicher Solitonen identifiziert, in denen die zwei nichtlinearen Wechselwirkungsprozesse miteinander konkurrieren oder sich gegenseitig verstärken. Weiterhin konnte experimentell gezeigt werden, dass für bestimmte Parameter dynamische räumlich-nichtlineare Effekte durch die konkurrierenden Prozesse unterdrückt werden. Höhere Moden der zweiten Harmonischen in Wellenleiterarrays haben, im Gegensatz zur Grundmode, eine nichtverschwindende lineare Koppelstärke. In der vorliegenden Arbeit konnte gezeigt werden, dass diese lineare Kopplung der zweiten Harmonischen einen leistungsabhängigen Phasenübergang der diskreten räumlichen Solitonen ermöglicht. Dieser Prozess wurde für dynamische Lichtausbreitung experimentell nachgewiesen, sobald räumlich lokalisierte Strahlen erzeugt wurden

Design of coupled mace filters for optical pattern recognition using practical spatial light modulators

Spatial light modulators (SLMs) are being used in correlation-based optical pattern recognition systems to implement the Fourier domain filters. Currently available SLMs have certain limitations with respect to the realizability of these filters. Therefore, it is necessary to incorporate the SLM constraints in the design of the filters. The design of a SLM-constrained minimum average correlation energy (SLM-MACE) filter using the simulated annealing-based optimization technique was investigated. The SLM-MACE filter was synthesized for three different types of constraints. The performance of the filter was evaluated in terms of its recognition (discrimination) capabilities using computer simulations. The correlation plane characteristics of the SLM-MACE filter were found to be reasonably good. The SLM-MACE filter yielded far better results than the analytical MACE filter implemented on practical SLMs using the constrained magnitude technique. Further, the filter performance was evaluated in the presence of noise in the input test images. This work demonstrated the need to include the SLM constraints in the filter design. Finally, a method is suggested to reduce the computation time required for the synthesis of the SLM-MACE filter

Structured Sub-Nyquist Sampling with Applications in Compressive Toeplitz Covariance Estimation, Super-Resolution and Phase Retrieval

Sub-Nyquist sampling has received a huge amount of interest in the past decade. In classical compressed sensing theory, if the measurement procedure satisfies a particular condition known as Restricted Isometry Property (RIP), we can achieve stable recovery of signals of low-dimensional intrinsic structures with an order-wise optimal sample size. Such low-dimensional structures include sparse and low rank for both vector and matrix cases. The main drawback of conventional compressed sensing theory is that random measurements are required to ensure the RIP property. However, in many applications such as imaging and array signal processing, applying independent random measurements may not be practical as the systems are deterministic. Moreover, random measurements based compressed sensing always exploits convex programs for signal recovery even in the noiseless case, and solving those programs is computationally intensive if the ambient dimension is large, especially in the matrix case. The main contribution of this dissertation is that we propose a deterministic sub-Nyquist sampling framework for compressing the structured signal and come up with computationally efficient algorithms. Besides widely studied sparse and low-rank structures, we particularly focus on the cases that the signals of interest are stationary or the measurements are of Fourier type. The key difference between our work from classical compressed sensing theory is that we explicitly exploit the second-order statistics of the signals, and study the equivalent quadratic measurement model in the correlation domain. The essential observation made in this dissertation is that a difference/sum coarray structure will arise from the quadratic model if the measurements are of Fourier type. With these observations, we are able to achieve a better compression rate for covariance estimation, identify more sources in array signal processing or recover the signals of larger sparsity. In this dissertation, we will first study the problem of Toeplitz covariance estimation. In particular, we will show how to achieve an order-wise optimal compression rate using the idea of sparse arrays in both general and low-rank cases. Then, an analysis framework of super-resolution with positivity constraint is established. We will present fundamental robustness guarantees, efficient algorithms and applications in practices. Next, we will study the problem of phase-retrieval for which we successfully apply the sparse array ideas by fully exploiting the quadratic measurement model. We achieve near-optimal sample complexity for both sparse and general cases with practical Fourier measurements and provide efficient and deterministic recovery algorithms. In the end, we will further elaborate on the essential role of non-negative constraint in underdetermined inverse problems. In particular, we will analyze the nonlinear co-array interpolation problem and develop a universal upper bound of the interpolation error. Bilinear problem with non-negative constraint will be considered next and the exact characterization of the ambiguous solutions will be established for the first time in literature. At last, we will show how to apply the nested array idea to solve real problems such as Kriging. Using spatial correlation information, we are able to have a stable estimate of the field of interest with fewer sensors than classic methodologies. Extensive numerical experiments are implemented to demonstrate our theoretical claims