On list decoding of wavelet codes over finite fields of characteristic two

Доказывается, что вейвлет-код над полем GF(2m) c длиной кодовых и информационных слов n = 2m — 1 и (n — 1)/2 соответственно, у которого среди коэффициентов спектрального представления порождающего многочлена имеется d + 1 последовательных нулей, 0 < d < (n — 3)/2, допускает списочное декодирование за полиномиальное время. Шаги алгоритма, осуществляющего списочное декодирование с исправлением до e < n — д/n(n — d — 2) ошибок, реализованы в виде программы. Приведены примеры её применения для списочного декодирования зашумленных кодовых слов. Отмечено, что неравенство Варшамова — Гилберта при достаточно больших n не позволяет судить о существовании вейвлет-кодов c максимальным кодовым расстоянием (n — 1) /2

Списочное декодирование вейвлет-кодов

В работе обсуждается возможность списочного декодирования вейвлет-кодов и приводится утверждение, согласно которому вейвлет-коды над полем $GF(q)$ нечетной характеристики с длиной кодовых и информационных слов $n=q-1$ и $n/2$ соответственно, а также над полем четной характеристики с длиной кодовых и информационных слов $n=q-1$ и $(n-1)/2$ соответственно допускают списочное декодирование, если среди коэффициентов спектрального представления их порождающих многочленов имеется $d+1$ последовательных нулей, $0$ &lt; $d$ &lt; $n/2$ для полей нечетной характеристики и $0$ &lt; $d$ &lt; $(n-3)/2$ для полей четной характеристики. Также описывается алгоритм, позволяющий выполнять списочное декодирование вейвлет-кодов при соблюдении перечисленных условий. В качестве демонстрации его работы приводятся пошаговые решения модельных задач списочного декодирования зашумленных кодовых слов вейвлет-кодов над полями четной и нечетной характеристики. Помимо этого, в работе построена вейвлет-версия квазисовершенного троичного кода Голея, длины его кодовых и информационных слов равны 8 и 4 соответственно, кодовое расстояние равно 4, минимальный радиус шаров с центрами в кодовых словах, покрывающих пространство слов длины 8, равен 3

Pyramid scheme for constructing biorthogonal wavelet codes over finite fields

Конструктивным образом доказывается существование биортогонального разбиения векторного пространства V размерности n над полем GF(q), а именно двух его представлений в виде прямых сумм подпространств V = W0 ®W1 ф.. .®Wj®Vj и V = Wо ф W1 ф ... ф Wj ф Vj, таких, что на j-м уровне разложения (0 < j J) Vj-1 = Vj ф Wj, Vj-1 = Vj ф Wj, подпространство Vj ортогонально Wj, а подпространство Wj ортогонально Vj. Для этого используются пары биортогональных фильтров (h,g) и (h,g). Разбиение пространства на j-м уровне разложения осуществляется при помощи пар уровневых фильтров (hj ,gj) и (hj ,gj), для построения которых разработаны и теоретически обоснованы соответствующие алгоритмы. На основе многоуровневой схемы вейвлет-разложения строится новое семейство биортогональных вейвлет-кодов со скоростью кодирования 2-L, где L — количество использованных уровней разложения, и приводятся примеры таких кодов

Fast embedding for image classification & retrieval and its application to the hostel industry

This thesis was submitted for the award of Doctor of Philosophy and was awarded by Brunel University LondonContent-based image classification and retrieval are the automatic processes of taking an unseen image input and extracting its features representing the input image. Then, for the classification task, this mathematically measured input is categorized according to established criteria in the server and consequently shows the output as a result. On the other hand, for the retrieval task, the extracted features of an unseen query image are sent to the server to search for the most visually similar images to a given image and retrieve these images as a result. Despite image features could be represented by classical features, artificial intelligence-based features, Convolutional Neural Networks (CNN) to be precise, have become powerful tools in the field. Nonetheless, the high dimensional CNN features have been a challenge in particular for applications on mobile or Internet of Things devices. Therefore, in this thesis, several fast embeddings are explored and proposed to overcome the constraints of low memory, bandwidth, and power. Furthermore, the first hostel image database is created with three datasets, hostel image dataset containing 13,908 interior and exterior images of hostels across the world, and Hostels-900 dataset and Hostels-2K dataset containing 972 images and 2,380 images, respectively, of 20 London hostel buildings. The results demonstrate that the proposed fast embeddings such as the application of GHM-Rand operator, GHM-Fix operator, and binary feature vectors are able to outperform or give competitive results to those state-of-the-art methods with a lot less computational resource. Additionally, the findings from a ten-year literature review of CBIR study in the tourism industry could picturize the relevant research activities in the past decade which are not only beneficial to the hostel industry or tourism sector but also to the computer science and engineering research communities for the potential real-life applications of the existing and developing technologies in the field

Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)

The implicit objective of the biennial "international - Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST) is to foster collaboration between international scientific teams by disseminating ideas through both specific oral/poster presentations and free discussions. For its second edition, the iTWIST workshop took place in the medieval and picturesque town of Namur in Belgium, from Wednesday August 27th till Friday August 29th, 2014. The workshop was conveniently located in "The Arsenal" building within walking distance of both hotels and town center. iTWIST'14 has gathered about 70 international participants and has featured 9 invited talks, 10 oral presentations, and 14 posters on the following themes, all related to the theory, application and generalization of the "sparsity paradigm": Sparsity-driven data sensing and processing; Union of low dimensional subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph sensing/processing; Blind inverse problems and dictionary learning; Sparsity and computational neuroscience; Information theory, geometry and randomness; Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?; Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website: http://sites.google.com/site/itwist1

Design and Optimization of Graph Transform for Image and Video Compression

The main contribution of this thesis is the introduction of new methods for designing adaptive transforms for image and video compression. Exploiting graph signal processing techniques, we develop new graph construction methods targeted for image and video compression applications. In this way, we obtain a graph that is, at the same time, a good representation of the image and easy to transmit to the decoder. To do so, we investigate different research directions. First, we propose a new method for graph construction that employs innovative edge metrics, quantization and edge prediction techniques. Then, we propose to use a graph learning approach and we introduce a new graph learning algorithm targeted for image compression that defines the connectivities between pixels by taking into consideration the coding of the image signal and the graph topology in rate-distortion term. Moreover, we also present a new superpixel-driven graph transform that uses clusters of superpixel as coding blocks and then computes the graph transform inside each region. In the second part of this work, we exploit graphs to design directional transforms. In fact, an efficient representation of the image directional information is extremely important in order to obtain high performance image and video coding. In this thesis, we present a new directional transform, called Steerable Discrete Cosine Transform (SDCT). This new transform can be obtained by steering the 2D-DCT basis in any chosen direction. Moreover, we can also use more complex steering patterns than a single pure rotation. In order to show the advantages of the SDCT, we present a few image and video compression methods based on this new directional transform. The obtained results show that the SDCT can be efficiently applied to image and video compression and it outperforms the classical DCT and other directional transforms. Along the same lines, we present also a new generalization of the DFT, called Steerable DFT (SDFT). Differently from the SDCT, the SDFT can be defined in one or two dimensions. The 1D-SDFT represents a rotation in the complex plane, instead the 2D-SDFT performs a rotation in the 2D Euclidean space

Efficient compression of motion compensated residuals

EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Hyper-Spectral Image Processing Using High Performance Reconfigurable Computers

The purpose of this thesis is to investigate the methods of implementing a section of a Matlab hyper-spectral image processing software application into a digital system that operates on a High Performance Reconfigurable Computer. The work presented is concerned with the architecture, the design techniques, and the models of digital systems that are necessary to achieve the best overall performance on HPRC platforms. The application is an image-processing tool that detects the tumors in a chicken using analysis of a hyper-spectral image. Analysis of the original Matlab code has shown that it gives low performance in achieving the result. The implementation is performed using a three-stage approach. In the first stage, the Matlab code is converted into C++ code in order to identify the bottlenecks that require the most resources. During the second stage, the digital system is designed to optimize the performance on a single reconfigurable computer. In the final stage of the implementation, this work explores the HPRC architecture by deploying and testing the digital design on multiple machines. The research shows that HPRC platforms grant a noticeable performance boost. Furthermore, the more hyper-spectral bands exist in the input image data, the better of the speedup can be expected from the HPRC design work