DOA estimation using multiple measurement vector model with sparse solutions in linear array scenarios

A novel algorithm is presented based on sparse multiple measurement vector (MMV) model for direction of arrival (DOA) estimation of far-field narrowband sources. The algorithm exploits singular value decomposition denoising to enhance the reconstruction process. The proposed multiple nature of MMV model enables the simultaneous processing of several data snapshots to obtain greater accuracy in the DOA estimation. The DOA problem is addressed in both uniform linear array (ULA) and nonuniform linear array (NLA) scenarios. Superior performance is demonstrated in terms of root mean square error and running time of the proposed method when compared with conventional compressed sensing methods such as simultaneous orthogonal matching pursuit (S-OMP), l_2,1 minimization, and root-MUISC

Reconstruction of Demand Shocks in Input-Output Networks

Input-Output analysis describes the dependence of production, demand and trade between sectors and regions and allows to understand the propagation of economic shocks through economic networks. A central challenge in practical applications is the availability of data. Observations may be limited to the impact of the shocks in few sectors, but a complete picture of the origin and impacts would be highly desirable to guide political countermeasures. In this article we demonstrate that a shock in the final demand in few sectors can be fully reconstructed from limited observations of production changes. We adapt three algorithms from sparse signal recovery and evaluate their performance and their robustness to observation uncertainties.Comment: 10 pages, 4 figures, conference proceeding for CompleNet 202

k is the Magic Number -- Inferring the Number of Clusters Through Nonparametric Concentration Inequalities

Most convex and nonconvex clustering algorithms come with one crucial parameter: the $k$ in $k$-means. To this day, there is not one generally accepted way to accurately determine this parameter. Popular methods are simple yet theoretically unfounded, such as searching for an elbow in the curve of a given cost measure. In contrast, statistically founded methods often make strict assumptions over the data distribution or come with their own optimization scheme for the clustering objective. This limits either the set of applicable datasets or clustering algorithms. In this paper, we strive to determine the number of clusters by answering a simple question: given two clusters, is it likely that they jointly stem from a single distribution? To this end, we propose a bound on the probability that two clusters originate from the distribution of the unified cluster, specified only by the sample mean and variance. Our method is applicable as a simple wrapper to the result of any clustering method minimizing the objective of $k$-means, which includes Gaussian mixtures and Spectral Clustering. We focus in our experimental evaluation on an application for nonconvex clustering and demonstrate the suitability of our theoretical results. Our \textsc{SpecialK} clustering algorithm automatically determines the appropriate value for $k$, without requiring any data transformation or projection, and without assumptions on the data distribution. Additionally, it is capable to decide that the data consists of only a single cluster, which many existing algorithms cannot

Necessary and sufficient conditions of solution uniqueness in ℓ1\ell_1 minimization

This paper shows that the solutions to various convex $\ell_1$ minimization problems are \emph{unique} if and only if a common set of conditions are satisfied. This result applies broadly to the basis pursuit model, basis pursuit denoising model, Lasso model, as well as other $\ell_1$ models that either minimize $f(Ax-b)$ or impose the constraint $f(Ax-b)\leq\sigma$, where $f$ is a strictly convex function. For these models, this paper proves that, given a solution $x^*$ and defining I=\supp(x^*) and s=\sign(x^*_I), $x^*$ is the unique solution if and only if $A_I$ has full column rank and there exists $y$ such that $A_I^Ty=s$ and $|a_i^Ty|_\infty<1$ for $i\not\in I$. This condition is previously known to be sufficient for the basis pursuit model to have a unique solution supported on $I$. Indeed, it is also necessary, and applies to a variety of other $\ell_1$ models. The paper also discusses ways to recognize unique solutions and verify the uniqueness conditions numerically.Comment: 6 pages; revised version; submitte

Learning Partially Shared Dictionaries for Domain Adaptation

Abstract. Real world applicability of many computer vision solutions is constrained by the mismatch between the training and test domains. This mismatch might arise because of factors such as change in pose, lighting conditions, quality of imaging devices, intra-class variations in-herent in object categories etc. In this work, we present a dictionary learning based approach to tackle the problem of domain mismatch. In our approach, we jointly learn dictionaries for the source and the target domains. The dictionaries are partially shared, i.e. some elements are common across both the dictionaries. These shared elements can rep-resent the information which is common across both the domains. The dictionaries also have some elements to represent the domain specific information. Using these dictionaries, we separate the domain specific information and the information which is common across the domains. We use the latter for training cross-domain classifiers i.e., we build classi-fiers that work well on a new target domain while using labeled examples only in the source domain. We conduct cross-domain object recognition experiments on popular benchmark datasets and show improvement in results over the existing state of art domain adaptation approaches.

Perceptual Compressive Sensing

Compressive sensing (CS) works to acquire measurements at sub-Nyquist rate and recover the scene images. Existing CS methods always recover the scene images in pixel level. This causes the smoothness of recovered images and lack of structure information, especially at a low measurement rate. To overcome this drawback, in this paper, we propose perceptual CS to obtain high-level structured recovery. Our task no longer focuses on pixel level. Instead, we work to make a better visual effect. In detail, we employ perceptual loss, defined on feature level, to enhance the structure information of the recovered images. Experiments show that our method achieves better visual results with stronger structure information than existing CS methods at the same measurement rate.Comment: Accepted by The First Chinese Conference on Pattern Recognition and Computer Vision (PRCV 2018). This is a pre-print version (not final version

Minimizing Acquisition Maximizing Inference -- A demonstration on print error detection

Is it possible to detect a feature in an image without ever looking at it? Images are known to have sparser representation in Wavelets and other similar transforms. Compressed Sensing is a technique which proposes simultaneous acquisition and compression of any signal by taking very few random linear measurements (M). The quality of reconstruction directly relates with M, which should be above a certain threshold for a reliable recovery. Since these measurements can non-adaptively reconstruct the signal to a faithful extent using purely analytical methods like Basis Pursuit, Matching Pursuit, Iterative thresholding, etc., we can be assured that these compressed samples contain enough information about any relevant macro-level feature contained in the (image) signal. Thus if we choose to deliberately acquire an even lower number of measurements - in order to thwart the possibility of a comprehensible reconstruction, but high enough to infer whether a relevant feature exists in an image - we can achieve accurate image classification while preserving its privacy. Through the print error detection problem, it is demonstrated that such a novel system can be implemented in practise