Analysis of A Nonsmooth Optimization Approach to Robust Estimation

In this paper, we consider the problem of identifying a linear map from measurements which are subject to intermittent and arbitarily large errors. This is a fundamental problem in many estimation-related applications such as fault detection, state estimation in lossy networks, hybrid system identification, robust estimation, etc. The problem is hard because it exhibits some intrinsic combinatorial features. Therefore, obtaining an effective solution necessitates relaxations that are both solvable at a reasonable cost and effective in the sense that they can return the true parameter vector. The current paper discusses a nonsmooth convex optimization approach and provides a new analysis of its behavior. In particular, it is shown that under appropriate conditions on the data, an exact estimate can be recovered from data corrupted by a large (even infinite) number of gross errors.Comment: 17 pages, 9 figure

Sparse phase retrieval via group-sparse optimization

This paper deals with sparse phase retrieval, i.e., the problem of estimating a vector from quadratic measurements under the assumption that few components are nonzero. In particular, we consider the problem of finding the sparsest vector consistent with the measurements and reformulate it as a group-sparse optimization problem with linear constraints. Then, we analyze the convex relaxation of the latter based on the minimization of a block l1-norm and show various exact recovery and stability results in the real and complex cases. Invariance to circular shifts and reflections are also discussed for real vectors measured via complex matrices

Finding sparse solutions of systems of polynomial equations via group-sparsity optimization

The paper deals with the problem of finding sparse solutions to systems of polynomial equations possibly perturbed by noise. In particular, we show how these solutions can be recovered from group-sparse solutions of a derived system of linear equations. Then, two approaches are considered to find these group-sparse solutions. The first one is based on a convex relaxation resulting in a second-order cone programming formulation which can benefit from efficient reweighting techniques for sparsity enhancement. For this approach, sufficient conditions for the exact recovery of the sparsest solution to the polynomial system are derived in the noiseless setting, while stable recovery results are obtained for the noisy case. Though lacking a similar analysis, the second approach provides a more computationally efficient algorithm based on a greedy strategy adding the groups one-by-one. With respect to previous work, the proposed methods recover the sparsest solution in a very short computing time while remaining at least as accurate in terms of the probability of success. This probability is empirically analyzed to emphasize the relationship between the ability of the methods to solve the polynomial system and the sparsity of the solution.Comment: Journal of Global Optimization (2014) to appea

On Conditions for Uniqueness in Sparse Phase Retrieval

The phase retrieval problem has a long history and is an important problem in many areas of optics. Theoretical understanding of phase retrieval is still limited and fundamental questions such as uniqueness and stability of the recovered solution are not yet fully understood. This paper provides several additions to the theoretical understanding of sparse phase retrieval. In particular we show that if the measurement ensemble can be chosen freely, as few as 4k-1 phaseless measurements suffice to guarantee uniqueness of a k-sparse M-dimensional real solution. We also prove that 2(k^2-k+1) Fourier magnitude measurements are sufficient under rather general conditions

Nonlinear Compressive Particle Filtering

Many systems for which compressive sensing is used today are dynamical. The common approach is to neglect the dynamics and see the problem as a sequence of independent problems. This approach has two disadvantages. Firstly, the temporal dependency in the state could be used to improve the accuracy of the state estimates. Secondly, having an estimate for the state and its support could be used to reduce the computational load of the subsequent step. In the linear Gaussian setting, compressive sensing was recently combined with the Kalman filter to mitigate above disadvantages. In the nonlinear dynamical case, compressive sensing can not be used and, if the state dimension is high, the particle filter would perform poorly. In this paper we combine one of the most novel developments in compressive sensing, nonlinear compressive sensing, with the particle filter. We show that the marriage of the two is essential and that neither the particle filter or nonlinear compressive sensing alone gives a satisfying solution.Comment: Accepted to CDC 201

The Self-Employment of Immigrants and Natives in Sweden

Earlier studies on entrepreneurship and self-employment among immigrants call attention to the fact that also the "market" for self-employment or entrepreneurs consists of a supply and demand side as well as the interaction between these two. More recent research suggests that a mix of personal resources, the surrounding structural context of markets, competition and the current political and economic environment, all acting together are seen as determining factors affecting self-employment by immigrants. However, few studies have been able to quantify the importance of these different aspects that determine ethnic self-employment. The central aim of this paper is therefore, by using multilevel regression, to quantify the role the country of birth respectively labour market area plays for understanding individual differences in self-employment. Using register data on individuals for the year of 2007 for the entire Swedish population we have in this study a unique opportunity to quantify the relative importance of the self-employers embeddedness in the social and ethnic networks (country of birth) and the regional business and public regulatory framework (labour market areas) measured. Our results suggest that of the total variation in individual differences in self-employment can 14 % (men) respectively 16 % (women) be attributed to the ethnic group and the labour market area. Furthermore, the ethnical groups accounted for 70 % (men) and 78 % (women) of this higher level variance. These results show that the social and ethnical context (measured by country of birth) and the economic environment (measured by local labour market areas) played a minor role for understanding individual differences in self-employment. These results can have important implications when planning interventions or other actions focusing on self-employment. Focusing only on ethnical groups/labour market areas might be inefficient as approximately 85 % of the variation is not explained by ethnical groups/labour market areas. Instead more general approaches or interventions focusing on other groups that capture a larger part of the variation might be more efficient.immigrants, self-employment, integration, entrepreneurship, multilevel logistic regression

Studies on Implementation of . . . High Throughput and Low Power Consumption

In this thesis we discuss design and implementation of frequency selective digital filters with high throughput and low power consumption. The thesis includes proposed arithmetic transformations of lattice wave digital filters that aim at increasing the throughput and reduce the power consumption of the filter implementation. The thesis also includes two case studies where digital filters with high throughput and low power consumption are required. A method for obtaining high throughput as well as reduced power consumption of digital filters is arithmetic transformation of the filter structure. In this thesis arithmetic transformations of first- and second-order Richards’ allpass sections composed by symmetric two-port adaptors and implemented using carry-save arithmetic are proposed. Such filter sections can be used for implementation of lattice wave digital filters and bireciprocal lattice wave digital filters. The latter structures are efficient for implementation of interpolators and decimators by factors of two. Th

Monoenergetic Gamma-Rays from Non-Minimal Kaluza-Klein Dark Matter Annihilations

We investigate monoenergetic gamma-ray signatures from annihilations of dark matter comprised of Z^1, the first Kaluza-Klein excitation of the Z boson, in a non-minimal Universal Extra Dimensions model. The self-interactions of the non-Abelian Z^1 gauge boson give rise to a large number of contributing Feynman diagrams that do not exist for annihilations of the Abelian gauge boson B^1, which is the standard Kaluza-Klein dark matter candidate. We find that the annihilation rate is indeed considerably larger for the Z^1 than for the B^1. Even though relic density calculations indicate that the mass of the Z^1 should be larger than the mass of the B^1, the predicted monoenergetic gamma fluxes are of the same order of magnitude. We compare our results to existing experimental limits, as well as to future sensitivities, for image air Cherenkov telescopes, and we find that the limits are reached already with a moderately large boost factor. The realistic prospects for detection depend on the experimental energy resolution.Comment: 21 pages, 6 figures, REVTeX4. Minor misprints correcte

Privileged Communications-Attorney and Client

A high-dimensional regression space usually causes problems in nonlinear system identification.However, if the regression data are contained in (or spread tightly around) some manifold, thedimensionality can be reduced. This paper presents a use of dimension reduction techniques tocompose a two-step identification scheme suitable for high-dimensional identification problems withmanifold-valued regression data. Illustrating examples are also given