2次元NHAを用いた画像処理における再構成法の研究

富山大学・富理工博甲第115号・長谷川昌也・2017/03/23富山大学201

Exploiting Data-Dependent Structure for Improving Sensor Acquisition and Integration

This thesis deals with two approaches to building efficient representations of data. The first is a study of compressive sensing and improved data acquisition. We outline the development of the theory, and proceed into its uses in matrix completion problems via convex optimization. The aim of this research is to prove that a general class of measurement operators, bounded norm Parseval frames, satisfy the necessary conditions for random subsampling and reconstruction. We then demonstrate an example of this theory in solving 2-dimensional Fredholm integrals with partial measurements. This has large ramifications in improved acquisition of nuclear magnetic resonance spectra, for which we give several examples. The second part of this thesis studies the Laplacian Eigenmaps (LE) algorithm and its uses in data fusion. In particular, we build a natural approximate inversion algorithm for LE embeddings using L1 regularization and MDS embedding techniques. We show how this inversion, combined with feature space rotation, leads to a novel form of data reconstruction and inpainting using a priori information. We demonstrate this method on hyperspectral imagery and LIDAR. We also aim to understand and characterize the embeddings the LE algorithm gives. To this end, we characterize the order in which eigenvectors of a disjoint graph emerge and the support of those eigenvectors. We then extend this characterization to weakly connected graphs with clusters of differing sizes, utilizing the theory of invariant subspace perturbations and proving some novel results

Multiscale and Directional Representations of High-Dimensional Information Content in Remotely Sensed Data

This thesis explores the theory and applications of directional representations in the field of anisotropic harmonic analysis. Although wavelets are optimal for decomposing functions in one dimension, they are unable to achieve the same success in two or more dimensions due to the presence of curves and surfaces of discontinuity. In order to optimally capture the behavior of a function at high-dimensional discontinuities, we must be able to incorporate directional information into our analyzing functions, in addition to location and scale. Examples of such representations are contourlets, curvelets, ridgelets, bandelets, wedgelets, and shearlets. Using directional representations, in particular shearlets, we tackle several challenging problems in the processing of remotely sensed data. First, we detect roads and ditches in LIDAR data of rural scenes. Second, we develop an algorithm for superresolution of optical and hyperspectral data. We conclude by presenting a stochastic particle model in which the probability of movement in a particular direction is neighbor-weighted

Anisotropic Harmonic Analysis and Integration of Remotely Sensed Data

This thesis develops the theory of discrete directional Gabor frames and several algorithms for the analysis of remotely sensed image data, based on constructions of harmonic analysis. The problems of image registration, image superresolution, and image fusion are separate but interconnected; a general approach using transform methods is the focus of this thesis. The methods of geometric multiresolution analysis are explored, particularly those related to the shearlet transform. Using shearlets, a novel method of image registration is developed that aligns images based on their shearlet features. Additionally, the anisotropic nature of the shearlet transform is deployed to smoothly superrsolve remotely-sensed image with edge features. Wavelet packets, a generalization of wavelets, are utilized for a flexible image fusion algorithm. The interplay between theoretical guarantees for these mathematical constructions, and their effectiveness for image processing is explored throughout

DISCRETE FRAMES AND TIGHT FRAMES FOR SPARSE IMAGE REPRESENTATION

Ph.DDOCTOR OF PHILOSOPH

Implementasi metode FIRE dan image processing citra mata untuk mendeteksi pola iris pada proses autentikasi smartphone

INDONESIA: Perkembangan teknologi sensor gambar pada smartphone yang terus meningkat menyebabkan penyebaran sistem pengenalan biometrik pada perangkat baru semakin cepat. Smartphone memiliki keunggulan utama yaitu portabel, proses komputasi yang canggih, dan dilengkapi dengan kamera resolusi tinggi. Hal tersebut membuat smartphone dapat memiliki fasilitas autentikasi dengan aman dan akurat yang dapat dilakukan kapan saja dan di mana saja. Pandemi COVID-19 mengharuskan seluruh masyarakat menggunakan masker, sehingga sistem pengenalan wajah atau Face Id dianggap dapat membahayakan pengguna smartphone karena mengharuskan membuka masker. Dengan adanya kendala tersebut, pada penelitian ini mengembangkan sistem biometrik Iris Recognition dengan menggunakan metode Image Processing dan dikombinasikan dengan metode Fast Iris Recognition (FIRE). Alasan penggunaan dua metode tersebut yaitu adanya hasil yang lebih baik dalam aspek akurasi dan kecepatan pada proses komputasi dengan perangkat hardware yang memiliki speksifikasi rendah. Uji coba dilakukan menggunakan dataset CASIA V1 yang berjumlah 756 citra iris. Hasil evaluasi dengan menggunakan k-fold cross validation menghasilkan nilai akurasi 97,33% dan rata-rata waktu 0,67 detik. ENGLISH: The development of image sensor technology on smartphone that increases continuously cause the spread of biometric authentication system on new devices faster. Smartphone has the main excellence, it is portable which means an advanced computation process, and equipped with high resolution camera. That matters made smartphone able to have a safe and accurate authentication facility that can be used everywhere and every time. The Covid-19 pandemic has obliged every people to use mask, so that the facial recognition system of Face ID is considered to be dangerous for the smartphone’s user because they have to open the mask before using smartphone. Due to that obstacle, this research is developing biometric system for Iris Recognition by using Image Processing method and combined with another method called Fast Iris Recognition (FIRE). The background of using those two method is the better the result on accuracy and velocity on computation process with hardware that has low specifications. The test has done by using dataset CASIA V1 that has 756 amounts of iris images. The evaluation using k-fold cross validation was resulting accuracy value on 97.33% and the average times on 0.67 seconds. ARABIC: تطور التكنولوجيا مستشعر الصرة على الهاتف الذكي بتطور وسيع يسبب إلى انتشار نظام التعرف على المقياس الحيوي على الجهاز الجديد بشكل أسرع. والهاتف الذكي بالمزايا الرئيسية لكونها محمولة والحوسبة المتقدمة ومجهزة بكاميرة عالية الدقة. ويجعل الهاتف الذكي الحصول على تسهيل مصادقة آمنة ودقيقة يمكن إجراؤها في أي وقت وفي أي مكان. ويتطلب وباء كوفيد-19 من جميع الأشخاص ارتداء القناع، لذلك يعتبر نظام التعرف على الوجه أو Face ID مخطرًا على الهاتف الذكي لأنه يتطلب فتح قناع. بالنظر إلى هذه المشكلة، سيطور الباحث نظام القياسة الحيوية للتعرف على قزحية العين بطريقة معالجة الصورة، ودمجه بالتعرف السريع على القزحية (FIRE). وسبب استخدام هاتين الطريقتين هو أن هناك حاصل أفضل من حيث الدقة والسرعة في عملية الحوسبة بالجهاز ذو المواصفات المنخفضة. وإجراء التجربة باستخدام مجموعة بيانات CASIA V1 ، والتي تتكون من 756 صورة قزحية. ونتيجة التقييم باستخدام التحقق المتقاطع k-fold بقيمة الدقة 97.33% ومتوسط وقت 0.67 دقيقة

Spectral Frame Analysis and Learning through Graph Structure

This dissertation investigates the connection between spectral analysis and frame theory. When considering the spectral properties of a frame, we present a few novel results relating to the spectral decomposition. We first show that scalable frames have the property that the inner product of the scaling coefficients and the eigenvectors must equal the inverse eigenvalues. From this, we prove a similar result when an approximate scaling is obtained. We then focus on the optimization problems inherent to the scalable frames by first showing that there is an equivalence between scaling a frame and optimization problems with a non-restrictive objective function. Various objective functions are considered, and an analysis of the solution type is presented. For linear objectives, we can encourage sparse scalings, and with barrier objective functions, we force dense solutions. We further consider frames in high dimensions, and derive various solution techniques. From here, we restrict ourselves to various frame classes, to add more specificity to the results. Using frames generated from distributions allows for the placement of probabilistic bounds on scalability. For discrete distributions (Bernoulli and Rademacher), we bound the probability of encountering an ONB, and for continuous symmetric distributions (Uniform and Gaussian), we show that symmetry is retained in the transformed domain. We also prove several hyperplane-separation results. With the theory developed, we discuss graph applications of the scalability framework. We make a connection with graph conditioning, and show the in-feasibility of the problem in the general case. After a modification, we show that any complete graph can be conditioned. We then present a modification of standard PCA (robust PCA) developed by Cand\`es, and give some background into Electron Energy-Loss Spectroscopy (EELS). We design a novel scheme for the processing of EELS through robust PCA and least-squares regression, and test this scheme on biological samples. Finally, we take the idea of robust PCA and apply the technique of kernel PCA to perform robust manifold learning. We derive the problem and present an algorithm for its solution. There is also discussion of the differences with RPCA that make theoretical guarantees difficult