A classic problem is the estimation of a set of parameters from measurements collected by only a few sensors. The number of sensors is often limited by physical or economical constraints and their placement is of fundamental importance to obtain accurate estimates. Unfortunately, the selection of the optimal sensor locations is intrinsically combinatorial and the available approximation algorithms are not guaranteed to generate good solutions in all cases of interest. We propose FrameSense, a greedy algorithm for the selection of optimal sensor locations. The core cost function of the algorithm is the frame potential, a scalar property of matrices that measures the orthogonality of its rows. Notably, FrameSense is the first algorithm that is near-optimal in terms of mean square error, meaning that its solution is always guaranteed to be close to the optimal one. Moreover, we show with an extensive set of numerical experiments that FrameSense achieves state-of-the-art performance while having the lowest computational cost, when compared to other greedy methods.Comment: 13 pages, accepted for publication on IEEE TS

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Background: Fluorescence microscopy is widely used to determine the subcellular location of proteins. Efforts to determine location on a proteome-wide basis create a need for automated methods to analyze the resulting images. Over the past ten years, the feasibility of using machine learning methods to recognize all major subcellular location patterns has been convincingly demonstrated, using diverse feature sets and classifiers. On a well-studied data set of 2D HeLa single-cell images, the best performance to date, 91.5%, was obtained by including a set of multiresolution features. This demonstrates the value of multiresolution approaches to this important problem.

We study the spatiotemporal sampling of a diffusion field generated by K point sources, aiming to fully reconstruct the unknown initial field distribution from the sample measurements. The sampling operator in our problem can be described by a matrix derived from the diffusion model. We analyze the important properties of the sampling matrices, leading to precise bounds on the spatial and temporal sampling densities under which perfect field reconstruction is feasible. Moreover, our analysis indicates that it is possible to compensate linearly for insufficient spatial sampling densities by oversampling in time. Numerical simulations on initial field reconstruction under different spatiotemporal sampling densities confirm our theoretical results.

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This survey gives an introduction to redundant signal representations called frames. These representations have recently emerged as yet another powerful tool in the signal processing toolbox and have become popular through use in numerous applications. Our aim is to familiarize a general audience with the area, while at the same time giving a snapshot of the current state-of-the-art.

Abstract-We consider the problem of reconstructing a diffusion field, such as temperature, from samples collected by a sensor network. Motivated by the fast decay of the eigenvalues of the diffusion equation, we approximate the field by a truncated series. We show that the approximation error decays rapidly with time. On the other hand, the information content in the field also decays with time, suggesting the need for a proper choice of the sampling strategy. We propose two algorithms for sampling and reconstruction of the field. The first one reconstructs the distribution of point sources appearing at known times using the finite rate of innovation (FRI) framework. The second algorithm addresses a more difficult problem of estimating the unknown times at which the point sources appear, in addition to their locations and magnitudes. It relies on the assumption that the sources appear at distinct times. We verify that the algorithms are capable of reconstructing the field accurately through a set of numerical experiments. Specifically, we show that the second algorithm successfully recovers an arbitrary number of sources with unknown release times, satisfying the assumption. For simplicity, we develop the 1-D theory, noting the possibility of extending the framework to more general domains.