Abstract-We consider the problem of estimating sparse communication channels in the MIMO context. In small to medium bandwidth communications, as in the current standards for OFDM and CDMA communication systems (with bandwidth up to 20 MHz), such channels are individually sparse and at the same time share a common support set. Since the underlying physical channels are inherently continuous-time, we propose a parametric sparse estimation technique based on finite rate of innovation (FRI) principles. Parametric estimation is especially relevant to MIMO communications as it allows for a robust estimation and concise description of the channels.The core of the algorithm is a generalization of conventional spectral estimation methods to multiple input signals with common support. We show the application of our technique for channel estimation in OFDM (uniformly/contiguous DFT pilots) and CDMA downlink (Walsh-Hadamard coded schemes). In the presence of additive white Gaussian noise, theoretical lower bounds on the estimation of SCS channel parameters in Rayleigh fading conditions are derived. Finally, an analytical spatial channel model is derived, and simulations on this model in the OFDM setting show the symbol error rate (SER) is reduced by a factor 2 (0 dB of SNR) to 5 (high SNR) compared to standard non-parametric methods -e.g. lowpass interpolation.

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.

A central problem in signal processing and communications is to design signals that are compact both in time and frequency. Heisenberg's uncertainty principle states that a given function cannot be arbitrarily compact both in time and frequency, defining an "uncertainty" lower bound. Taking the variance as a measure of localization in time and frequency, Gaussian functions reach this bound for continuous-time signals. For sequences, however, this is not true; it is known that Heisenberg's bound is generally unachievable. For a chosen frequency variance, we formulate the search for "maximally compact sequences" as an exactly and efficiently solved convex optimization problem, thus providing a sharp uncertainty principle for sequences. Interestingly, the optimization formulation also reveals that maximally compact sequences are derived from Mathieu's harmonic cosine function of order zero. We further provide rational asymptotic expansions of this sharp uncertainty bound. We use the derived bounds as a benchmark to compare the compactness of well-known window functions with that of the optimal Mathieu's functions.

If P antennas measure a K-multipath channel with N uniformly sampled measurements per channel, the algorithm possesses an OpKP N log N q complexity and an OpKP N q memory footprint instead of OpP N 3 q and OpP N 2 q for the direct implementation, making it suitable for K ! N . The sparsity is estimated online based on the PER, and the algorithm therefore has a sense of introspection being able to relinquish sparsity if it is lacking.The estimation performances are tested on field measurements with synthetic AWGN, and the proposed algorithm outperforms non-sparse reconstruction in the medium to low SNR range (ď 0dB), increasing the rate of successful symbol decodings by 1{10 th in average, and 1{3 rd in the best case. The experiments also show that the algorithm does not perform worse than a nonsparse estimation algorithm in non-sparse operating conditions, since it may fall-back to it if the PER criterion does not detect a sufficient level of sparsity.The algorithm is also tested against a method assuming a "discrete" sparsity model as in Compressed Sensing (CS). The conducted test indicates a trade-off between speed and accuracy.

We propose an algorithm (SCS-FRI) to estimate multipath channels with Sparse Common Support (SCS) based on Finite Rate of Innovation (FRI) sampling. In this setup, theoretical lower-bounds are derived, and simulation in a Rayleigh fading environment shows that SCS-FRI gets very close to these bounds. We show how to apply SCS-FRI to OFDM and CDMA downlinks. Recovery of a sparse common support is, among other, especially relevant for channel estimation in a multiple output system or beam-forming from multiple input. The present algorithm is based on a multi-output extension of the Cadzow denoising/annihilating filter method [1,2].

Abstract-A fast computational method is given for the Fourier transform of the polyharmonic B-spline autocorrelation sequence in dimensions. The approximation error is exponentially decaying with the number of terms taken into account. The algorithm improves speed upon a simple truncated-sum approach. Moreover, it is virtually independent of the spline's order. The autocorrelation filter directly serves for various tasks related to polyharmonic splines, such as interpolation, orthonormalization, and wavelet basis design.

For a given time or frequency spread, one can always find continuoustime signals, which achieve the Heisenberg uncertainty principle bound. This is known, however, not to be the case for discrete-time sequences; only widely spread sequences asymptotically achieve this bound. We provide a constructive method for designing sequences that are maximally compact in time for a given frequency spread. By formulating the problem as a semidefinite program, we show that maximally compact sequences do not achieve the classic Heisenberg bound. We further provide analytic lower bounds on the time-frequency spread of such signals.

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