A new weighted NMF algorithm for missing data interpolation and its application to speech enhancement

In this paper we present a novel weighted NMF (WNMF) algorithm for interpolating missing data. The proposed approach has a computational cost equivalent to that of standard NMF and, additionally, has the flexibility to control the degree of interpolation in the missing data regions. Existing WNMF methods do not offer this capability and, thereby, tend to overestimate the values in the masked regions. By constraining the estimates of the missing-data regions, the proposed approach allows for a better trade-off in the interpolation. We further demonstrate the applicability of WNMF and missing data estimation to the problem of speech enhancement. In this preliminary work, we consider the improvement obtainable by applying the proposed method to ideal binary mask-based gain functions. The instrumental quality metrics (PESQ and SNR) clearly indicate the added benefit of the missing data interpolation, compared to the output of the ideal binary mask. This preliminary work opens up novel possibilities not only in the field of speech enhancement but also, more generally, in the field of missing data interpolation using NMF

Coherency Matrix Decomposition-Based Polarimetric Persistent Scatterer Interferometry

© 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes,creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.The rationale of polarimetric optimization techniques is to enhance the phase quality of the interferograms by combining adequately the different polarization channels available to produce an improved one. Different approaches have been proposed for polarimetric persistent scatterer interferometry (PolPSI). They range from the simple and computationally efficient BEST, where, for each pixel, the polarimetric channel with the best response in terms of phase quality is selected, to those with high-computational burden like the equal scattering mechanism (ESM) and the suboptimum scattering mechanism (SOM). BEST is fast and simple, but it does not fully exploit the potentials of polarimetry. On the other side, ESM explores all the space of solutions and finds the optimal one but with a very high-computational burden. A new PolPSI algorithm, named coherency matrix decomposition-based PolPSI (CMD-PolPSI), is proposed to achieve a compromise between phase optimization and computational cost. Its core idea is utilizing the polarimetric synthetic aperture radar (PolSAR) coherency matrix decomposition to determine the optimal polarization channel for each pixel. Three different PolSAR image sets of both full- (Barcelona) and dual-polarization (Murcia and Mexico City) are used to evaluate the performance of CMD-PolPSI. The results show that CMD-PolPSI presents better optimization results than the BEST method by using either $D_{\mathrm{ A}}$ or temporal mean coherence as phase quality metrics. Compared with the ESM algorithm, CMD-PolPSI is 255 times faster but its performance is not optimal. The influence of the number of available polarization channels and pixel's resolutions on the CMD-PolPSI performance is also discussed.Peer ReviewedPostprint (author's final draft

Overview of Constrained PARAFAC Models

In this paper, we present an overview of constrained PARAFAC models where the constraints model linear dependencies among columns of the factor matrices of the tensor decomposition, or alternatively, the pattern of interactions between different modes of the tensor which are captured by the equivalent core tensor. Some tensor prerequisites with a particular emphasis on mode combination using Kronecker products of canonical vectors that makes easier matricization operations, are first introduced. This Kronecker product based approach is also formulated in terms of the index notation, which provides an original and concise formalism for both matricizing tensors and writing tensor models. Then, after a brief reminder of PARAFAC and Tucker models, two families of constrained tensor models, the co-called PARALIND/CONFAC and PARATUCK models, are described in a unified framework, for $N^{th}$ order tensors. New tensor models, called nested Tucker models and block PARALIND/CONFAC models, are also introduced. A link between PARATUCK models and constrained PARAFAC models is then established. Finally, new uniqueness properties of PARATUCK models are deduced from sufficient conditions for essential uniqueness of their associated constrained PARAFAC models

Rank-1 Tensor Approximation Methods and Application to Deflation

Because of the attractiveness of the canonical polyadic (CP) tensor decomposition in various applications, several algorithms have been designed to compute it, but efficient ones are still lacking. Iterative deflation algorithms based on successive rank-1 approximations can be used to perform this task, since the latter are rather easy to compute. We first present an algebraic rank-1 approximation method that performs better than the standard higher-order singular value decomposition (HOSVD) for three-way tensors. Second, we propose a new iterative rank-1 approximation algorithm that improves any other rank-1 approximation method. Third, we describe a probabilistic framework allowing to study the convergence of deflation CP decomposition (DCPD) algorithms based on successive rank-1 approximations. A set of computer experiments then validates theoretical results and demonstrates the efficiency of DCPD algorithms compared to other ones

Three essays on decomposition analysis of the territorial CO 2 emissions and the emissions embodiment in trade attributable to consumption of service-oriented economies

With the pace of globalization, the rapid growth in international trade has led to a widespread perception of increasing CO2 embodied emissions. As the fragmentation of international production has become a dominant feature of modern international trade, there is a vibrant debate over how embodied emissions should be attributed and allocated among economies. To contribute to the debate on emission allocations and mitigation effort comparisons, it is important to consistently investigate the structures of carbon transfers across global economies. The role of carbon transfer structures in affecting mitigation efforts can be explored as part of the consequences of various emission allocations. Thus, it becomes a fundamental theme of all three essays. Due to the leading economies in international trade in terms of volume and CO2, extensive attention of this dissertation has been paid to the United States (U.S.), China, and European Union (EU) economies.;Emissions due to U.S. imports grew increasingly and contributed 31% of the worldwide imported emissions in 2012. Undoubtedly, taking emission responsibility for U.S. imports is important to gear up for a low carbon future. To integrate U.S. imports into the responsibility of global emissions, it is important to investigate the U.S. import effects and identify contributing factors behind imported emission changes. Two aspects are of interest for an understanding of imported emissions and the structure of carbon transfers: (1) the U.S. import demand can affect not only embodied emissions but also emissions at home; and (2) the sector coverage can determine the results of contributing factors. In this respect, the first essay entitled Two-Stage Index Decomposition Analyses of Domestic and Import Related CO2 Emission Changes for the U.S. Economy utilizes a modification of multi-period logarithmic mean divisia index (LMDI II) to perform decomposition analyses of the import effects on both emissions for the U.S. economy during the period 1991-2012. It further employs an attribution technique of LMDI II in order to explore emission contributions of four industrial sectors (the utility, primary, secondary, and tertiary sectors). Dynamic changes in imported emissions are decomposed into five consumption factors: emission coefficient; energy intensity; structure of imports; final import composition; and final import scale. Dynamic changes in production emissions are generated based on three production factors of aggregate and disaggregated (real) carbon intensities: emission coefficient; energy intensity; and structure. The main findings of this essay are presented in page 9. Analysis of the interplay of the contributing factors behind changes in emissions stimulated due to both import demand and domestic production become more critical for having a better understanding of the structure of carbon transfers. Also, it becomes important for seeking policy recommendations on emission responsibilities across economies as part of a transition to a low carbon future.;Global production fragmentation significantly affects the allocation of emissions embodied in international trade. Thus, differences between production-based emissions (PBE) and consumption-based emissions (CBE) increasingly produce uneven policy actions for targeting emission reductions between exporting and importing economies. These differences may impact mitigation efforts across economies given the current level of carbon transfers. As an alternative, a sharing-based emissions (SE) allocation is an approach that assigns exporters and importers responsibility for emissions based upon benefits linked to their production and consumption. The challenge facing the application of SE allocation is how to define a weighing procedure. In light of embodied emissions in international trade, Peters (2008) suggested that value-added should be used to define a weighting framework. However, no defined weighting procedure has been addressed so far in the literature. The second essay entitled Sharing-Based CO 2 Emission Allocation with a Perspective on a Multilateral Border Tax Adjustment-the U.S. Economy first aims to design a weighting procedure for establishing shares of the emission allocation.;Due to uneven distributions between emission and global trade intensities across economies, a change in emission allocations from the current PBE approach to an alternative approach that considers both production and consumption can result in a significant emission responsibility burden for specific industries. Thus, an impact evaluation is important to explore mitigation efforts and define the consequences of alternative emission allocations. To identify allocations, the applications of alternative allocations are empirically applied to the U.S. economy for the years 2005 and 2011. These alternative allocation are the SE and the consumption allocation with the application of a unilateral border tax adjustment. The main findings of this essay are presented in page 57. (Abstract shortened by ProQuest.)