Reduced Look Ahead Orthogonal Matching Pursuit

Compressed Sensing (CS) is an elegant technique to acquire signals and reconstruct them efficiently by solving a system of under-determined linear equations. The excitement in this field stems from the fact that we can sample at a rate way below the Nyquist rate and still reconstruct the signal provided some conditions are met. Some of the popular greedy reconstruction algorithms are the Orthogonal Matching Pursuit (OMP), the Subspace Pursuit (SP) and the Look Ahead Orthogonal Matching Pursuit (LAOMP). The LAOMP performs better than the OMP. However, when compared to the SP and the OMP, the computational complexity of LAOMP is higher. We introduce a modified version of the LAOMP termed as Reduced Look Ahead Orthogonal Matching Pursuit (Reduced LAOMP). Reduced LAOMP uses prior information from the results of the OMP and the SP in the quest to speedup the look ahead strategy in the LAOMP. Monte Carlo simulations of this algorithm deliver promising results.

DETERMINISTIC ALGORITHMS FOR MATCHING AND PACKING PROBLEMS BASED ON REPRESENTATIVE SETS

In this work, we study the well-known r-DIMENSIONAL k-MATCHING ((r, k)-DM), and r-SET k-PACKING ((r, k)-SP) problems. Given a universe U := U-1 ... U-r and an r-uniform family F subset of U-1 x ... x U-r, the (r, k)-DM problem asks if F admits a collection of k mutually disjoint sets. Given a universe U and an r-uniform family F subset of 2(U), the (r, k)-SP problem asks if F admits a collection of k mutually disjoint sets. We employ techniques based on dynamic programming and representative families. This leads to a deterministic algorithm with running time O(2.851((r-1)k) .vertical bar F vertical bar. n log(2)n . logW) for the weighted version of (r, k)-DM, where W is the maximum weight in the input, and a deterministic algorithm with running time O(2.851((r-0.5501)k).vertical bar F vertical bar.n log(2) n . logW) for the weighted version of (r, k)-SP. Thus, we significantly improve the previous best known deterministic running times for (r, k)-DM and (r, k)-SP and the previous best known running times for their weighted versions. We rely on structural properties of (r, k)-DM and (r, k)-SP to develop algorithms that are faster than those that can be obtained by a standard use of representative sets. Incorporating the principles of iterative expansion, we obtain a better algorithm for (3, k)-DM, running in time O(2.004(3k).vertical bar F vertical bar . n log(2)n). We believe that this algorithm demonstrates an interesting application of representative families in conjunction with more traditional techniques. Furthermore, we present kernels of size O(e(r)r(k-1)(r) logW) for the weighted versions of (r, k)-DM and (r, k)-SP, improving the previous best known kernels of size O(r!r(k-1)(r) logW) for these problems.

A coupled discriminative dictionary and transformation learning approach with applications to cross domain matching

Cross domain and cross-modal matching has many applications in the field of computer vision and pattern recognition. A few examples are heterogeneous face recognition, cross view action recognition, etc. This is a very challenging task since the data in two domains can differ significantly. In this work, we propose a coupled dictionary and transformation learning approach that models the relationship between the data in both domains. The approach learns a pair of transformation matrices that map the data in the two domains in such a manner that they share common sparse representations with respect to their own dictionaries in the transformed space. The dictionaries for the two domains are learnt in a coupled manner with an additional discriminative term to ensure improved recognition performance. The dictionaries and the transformation matrices are jointly updated in an iterative manner. The applicability of the proposed approach is illustrated by evaluating its performance on different challenging tasks: face recognition across pose, illumination and resolution, heterogeneous face recognition and cross view action recognition. Extensive experiments on five datasets namely, CMU-PIE, Multi-PIE, ChokePoint, HFB and IXMAS datasets and comparisons with several state-of-the-art approaches show the effectiveness of the proposed approach. (C) 2015 Elsevier B.V. All rights reserved.

A coupled discriminative dictionary and transformation learning approach with applications to cross domain matching

Cross domain and cross-modal matching has many applications in the field of computer vision and pattern recognition. A few examples are heterogeneous face recognition, cross view action recognition, etc. This is a very challenging task since the data in two domains can differ significantly. In this work, we propose a coupled dictionary and transformation learning approach that models the relationship between the data in both domains. The approach learns a pair of transformation matrices that map the data in the two domains in such a manner that they share common sparse representations with respect to their own dictionaries in the transformed space. The dictionaries for the two domains are learnt in a coupled manner with an additional discriminative term to ensure improved recognition performance. The dictionaries and the transformation matrices are jointly updated in an iterative manner. The applicability of the proposed approach is illustrated by evaluating its performance on different challenging tasks: face recognition across pose, illumination and resolution, heterogeneous face recognition and cross view action recognition. Extensive experiments on five datasets namely, CMU-PIE, Multi-PIE, ChokePoint, HFB and IXMAS datasets and comparisons with several state-of-the-art approaches show the effectiveness of the proposed approach. (C) 2015 Elsevier B.V. All rights reserved.

Comparison of Matching Pursuit Algorithm with Other Signal Processing Techniques for Computation of the Time-Frequency Power Spectrum of Brain Signals

Signals recorded from the brain often show rhythmic patterns at different frequencies, which are tightly coupled to the external stimuli as well as the internal state of the subject. In addition, these signals have very transient structures related to spiking or sudden onset of a stimulus, which have durations not exceeding tens of milliseconds. Further, brain signals are highly nonstationary because both behavioral state and external stimuli can change on a short time scale. It is therefore essential to study brain signals using techniques that can represent both rhythmic and transient components of the signal, something not always possible using standard signal processing techniques such as short time fourier transform, multitaper method, wavelet transform, or Hilbert transform. In this review, we describe a multiscale decomposition technique based on an over-complete dictionary called matching pursuit (MP), and show that it is able to capture both a sharp stimulus-onset transient and a sustained gamma rhythm in local field potential recorded from the primary visual cortex. We compare the performance of MP with other techniques and discuss its advantages and limitations. Data and codes for generating all time-frequency power spectra are provided.

Hydrogen Bonds Computing Server (HBCS): an online web server to compute hydrogen-bond interactions and their precision

Hydrogen bonds in biological macromolecules play significant structural and functional roles. They are the key contributors to most of the interactions without which no living system exists. In view of this, a web-based computing server, the Hydrogen Bonds Computing Server (HBCS), has been developed to compute hydrogen-bond interactions and their standard deviations for any given macromolecular structure. The computing server is connected to a locally maintained Protein Data Bank (PDB) archive. Thus, the user can calculate the above parameters for any deposited structure, and options have also been provided for the user to upload a structure in PDB format from the client machine. In addition, the server has been interfaced with the molecular viewers Jmol and JSmol to visualize the hydrogen-bond interactions. The proposed server is freely available and accessible via the World Wide Web at http://bioserver1.physics.iisc.ernet.in/hbcs/.

Non-Gravitational Effects with Density-Matching in Evaluating the Influence of Sedimentation on Colloidal Coagulation

The method of density matching between the solid and liquid phases is often adopted to effectively eliminate the effect of sedimentation of suspensions in studies on dynamic behaviour of a colloidal system. However, the associated changes in the solvent composition may bring side effects to the properties investigated and therefore might lead to a faulty conclusion if the relevant correction is not made. To illustrate the importance of this side effect, we present an example of the sedimentation influence on the coagulation rate of suspensions of 2 μm (diameter) polystyrene. The liquid mixtures, in the proper proportions of water (H2O), deuterium oxide (D2O) and methanol (MeOH) as the liquid phase, density-matched and unmatched experiments are performed. Besides the influence of viscosity, the presence of methanol in solvent media, used to enhance the sedimentation effect, causes significant changes (reduction) in rapid coagulation rates compared to that in pure water. Without the relevant corrections for those non-gravitational factors it seems that gravitational sedimentation would retard the coagulation. The magnitude of the contribution from the non-gravitational factor is quantitatively determined, making the relevant correction possible. After necessary corrections for all factors, our experiments show that the influence of the sedimentation on coagulation rates at the initial stage of the coagulation is not observable.

Practical matching of principal stress field geometries in composite components

A simple composite design methodology has been developed from the basic principles of composite component failure. This design approach applies the principles of stress field matching to develop suitable reinforcement patterns around three-dimensional details such as lugs in mechanical components. The resulting patterns are essentially curvilinear orthogonal meshes, adjusted to meet the restrictions imposed by geometric restraints and the intended manufacturing process. Whilst the principles behind the design methodology can be applied to components produced by differing manufacturing processes, the results found from looking at simple generic example problems suggest a realistic and practical generic manufacturing approach. The underlying principles of the design methodology are described and simple analyses are used to help illustrate both the methodology and how such components behave. These analyses suggest it is possible to replace high-strength steel lugs with composite components whose strength-to-weight ratio is some 4-5 times better. © 1998 Elsevier Science Ltd. All rights reserved.