動的学習による辞書を用いたMatching Pursuits符号化

金沢大学理工研究域電子情報学系Recently, an efficient video coding method at low bit rate using Matching Pursuits (MP) has been proposed. The MP coding method represents a signal in an approximate form using a dictionary. Therefore, coding performance depends greatly on the dictionary. In this paper, we introduce a video coding method that employs motion compensation and MP using a dynamic learning dictionary. The dictionary of the proposed method is renewed at each frame by using encoded information. Simulation results show that the coding performance of MP can be improved by applying the dynamic learning dictionary

Which Regular Expression Patterns are Hard to Match?

Regular expressions constitute a fundamental notion in formal language theory and are frequently used in computer science to define search patterns. A classic algorithm for these problems constructs and simulates a non-deterministic finite automaton corresponding to the expression, resulting in an $O(mn)$ running time (where $m$ is the length of the pattern and $n$ is the length of the text). This running time can be improved slightly (by a polylogarithmic factor), but no significantly faster solutions are known. At the same time, much faster algorithms exist for various special cases of regular expressions, including dictionary matching, wildcard matching, subset matching, word break problem etc. In this paper, we show that the complexity of regular expression matching can be characterized based on its {\em depth} (when interpreted as a formula). Our results hold for expressions involving concatenation, OR, Kleene star and Kleene plus. For regular expressions of depth two (involving any combination of the above operators), we show the following dichotomy: matching and membership testing can be solved in near-linear time, except for "concatenations of stars", which cannot be solved in strongly sub-quadratic time assuming the Strong Exponential Time Hypothesis (SETH). For regular expressions of depth three the picture is more complex. Nevertheless, we show that all problems can either be solved in strongly sub-quadratic time, or cannot be solved in strongly sub-quadratic time assuming SETH. An intriguing special case of membership testing involves regular expressions of the form "a star of an OR of concatenations", e.g., $[a|ab|bc]^*$. This corresponds to the so-called {\em word break} problem, for which a dynamic programming algorithm with a runtime of (roughly) $O(n\sqrt{m})$ is known. We show that the latter bound is not tight and improve the runtime to $O(nm^{0.44\ldots})$

4D Seismic History Matching Incorporating Unsupervised Learning

The work discussed and presented in this paper focuses on the history matching of reservoirs by integrating 4D seismic data into the inversion process using machine learning techniques. A new integrated scheme for the reconstruction of petrophysical properties with a modified Ensemble Smoother with Multiple Data Assimilation (ES-MDA) in a synthetic reservoir is proposed. The permeability field inside the reservoir is parametrised with an unsupervised learning approach, namely K-means with Singular Value Decomposition (K-SVD). This is combined with the Orthogonal Matching Pursuit (OMP) technique which is very typical for sparsity promoting regularisation schemes. Moreover, seismic attributes, in particular, acoustic impedance, are parametrised with the Discrete Cosine Transform (DCT). This novel combination of techniques from machine learning, sparsity regularisation, seismic imaging and history matching aims to address the ill-posedness of the inversion of historical production data efficiently using ES-MDA. In the numerical experiments provided, I demonstrate that these sparse representations of the petrophysical properties and the seismic attributes enables to obtain better production data matches to the true production data and to quantify the propagating waterfront better compared to more traditional methods that do not use comparable parametrisation techniques

Improved Approximate String Matching and Regular Expression Matching on Ziv-Lempel Compressed Texts

We study the approximate string matching and regular expression matching problem for the case when the text to be searched is compressed with the Ziv-Lempel adaptive dictionary compression schemes. We present a time-space trade-off that leads to algorithms improving the previously known complexities for both problems. In particular, we significantly improve the space bounds, which in practical applications are likely to be a bottleneck

Application of Time-Fractional Order Bloch Equation in Magnetic Resonance Fingerprinting

Magnetic resonance fingerprinting (MRF) is one novel fast quantitative imaging framework for simultaneous quantification of multiple parameters with pseudo-randomized acquisition patterns. The accuracy of the resulting multi-parameters is very important for clinical applications. In this paper, we derived signal evolutions from the anomalous relaxation using a fractional calculus. More specifically, we utilized time-fractional order extension of the Bloch equations to generate dictionary to provide more complex system descriptions for MRF applications. The representative results of phantom experiments demonstrated the good accuracy performance when applying the time-fractional order Bloch equations to generate dictionary entries in the MRF framework. The utility of the proposed method is also validated by in-vivo study.Comment: Accepted at 2019 IEEE 16th International Symposium on Biomedical Imaging (ISBI 2019

A* Orthogonal Matching Pursuit: Best-First Search for Compressed Sensing Signal Recovery

Compressed sensing is a developing field aiming at reconstruction of sparse signals acquired in reduced dimensions, which make the recovery process under-determined. The required solution is the one with minimum $\ell_0$ norm due to sparsity, however it is not practical to solve the $\ell_0$ minimization problem. Commonly used techniques include $\ell_1$ minimization, such as Basis Pursuit (BP) and greedy pursuit algorithms such as Orthogonal Matching Pursuit (OMP) and Subspace Pursuit (SP). This manuscript proposes a novel semi-greedy recovery approach, namely A* Orthogonal Matching Pursuit (A*OMP). A*OMP performs A* search to look for the sparsest solution on a tree whose paths grow similar to the Orthogonal Matching Pursuit (OMP) algorithm. Paths on the tree are evaluated according to a cost function, which should compensate for different path lengths. For this purpose, three different auxiliary structures are defined, including novel dynamic ones. A*OMP also incorporates pruning techniques which enable practical applications of the algorithm. Moreover, the adjustable search parameters provide means for a complexity-accuracy trade-off. We demonstrate the reconstruction ability of the proposed scheme on both synthetically generated data and images using Gaussian and Bernoulli observation matrices, where A*OMP yields less reconstruction error and higher exact recovery frequency than BP, OMP and SP. Results also indicate that novel dynamic cost functions provide improved results as compared to a conventional choice.Comment: accepted for publication in Digital Signal Processin

Automated Top View Registration of Broadcast Football Videos

In this paper, we propose a novel method to register football broadcast video frames on the static top view model of the playing surface. The proposed method is fully automatic in contrast to the current state of the art which requires manual initialization of point correspondences between the image and the static model. Automatic registration using existing approaches has been difficult due to the lack of sufficient point correspondences. We investigate an alternate approach exploiting the edge information from the line markings on the field. We formulate the registration problem as a nearest neighbour search over a synthetically generated dictionary of edge map and homography pairs. The synthetic dictionary generation allows us to exhaustively cover a wide variety of camera angles and positions and reduce this problem to a minimal per-frame edge map matching procedure. We show that the per-frame results can be improved in videos using an optimization framework for temporal camera stabilization. We demonstrate the efficacy of our approach by presenting extensive results on a dataset collected from matches of football World Cup 2014