Tobias Lindstrøm Jensen

Algorithms and software for total variation image reconstruction via first-order methods

This paper describes new algorithms and related software for total variation (TV) image reconstruction, more specifically: denoising, inpainting, and deblurring. The algorithms are based on one of Nesterov’s first-order methods, tailored to the image processing applications in such a way that, except for the mandatory regularization parameter, the user needs not specify any parameters in the algorithms. The software is written in C with interface to Matlab (version 7.5 or later), and we demonstrate its performance and use with examples.

Fast Link Adaptation for MIMO OFDM

We investigate link-quality metrics (LQMs) based on raw bit-error-rate, effective signal-to-interference-plus-noise ratio, and mutual information (MI) for the purpose of fast link adaptation (LA) in communication systems employing orthogonal frequency-division multiplexing and multiple-input-multiple-output (MIMO) antenna technology. From these LQMs, the packet error rate (PER) can be estimated and exploited to select the modulation and coding scheme (MCS) among a class of candidate MCSs that achieves the maximum throughput for the current channel state under a specified target PER objective. We propose a novel MI-based LQM and compare the PER-estimation accuracy obtained with this LQM with that resulting from using other LQMs by means of comprehensive Monte Carlo simulations. Search methods for the MCS in the class that is most suitable for a given channel state are presented. An algorithm for obtaining a practical upper bound on the throughput of any LA scheme is proposed. The investigated LQMs are applied to the IEEE 802.11n standard with a 2 × 2 MIMO configuration and practical channel estimation. The proposed MI-based LQM yields the highest PER estimation accuracy, and its throughput shows only 1.7 dB signal-to-noise-ratio (SNR) loss with respect to the upper bound but up to 9.5 dB SNR gain, compared to the MCS maximizing the throughput for the current noise variance.

Mutual Information Metrics for Fast Link Adaptation in IEEE 802.11n

We investigate link quality metrics (LQMs) based on mutual information (MI) for fast link adaptation (FLA) in IEEE 802.11n wireless local area network (WLAN) with convolutional coding and higher order modulations. The LQMs are scalar quantities that map the receivers post-decoding behaviour in a frequency-selective channel into an equivalent behaviour in an AWGN channel. From this metric the expected packet error rate (PER) can be predicted. Two LQMs are presented that are derived from the SINRs of all sub-carriers and streams: the effective SNR and the effective mutual information. The effective mutual information is the mean mutual information including a correction factor which improves the PER estimation accuracy in various highly frequency-selective channels. The FLA algorithm dynamically selects a modulation and coding scheme (MCS) that maximizes the throughput (TP), while keeping the average PER over time below a target value. Furthermore, we present methods of searching for the most suitable MCS. Practical performance bounds are obtained by means of simulations. We show that both investigated LQMs yield accurate PER estimates and that the resulting TP of the FLA algorithm used in a 2 x 2 MIMO bit-interleaved coded modulation (BICM) OFDM system that performs channel estimation is only 1.7 dB from the performance bound of the TP.

Compressive Sensing for Spread Spectrum Receivers

With the advent of ubiquitous computing there are two design parameters of wireless communication devices that become very important: power efficiency and production cost. Compressive sensing enables the receiver in such devices to sample below the Shannon-Nyquist sampling rate, which may lead to a decrease in the two design parameters. This paper investigates the use of Compressive Sensing (CS) in a general Code Division Multiple Access (CDMA) receiver. We show that when using spread spectrum codes in the signal domain, the CS measurement matrix may be simplified. This measurement scheme, named Compressive Spread Spectrum (CSS), allows for a simple, effective receiver design. Furthermore, we numerically evaluate the proposed receiver in terms of bit error rate under different signal to noise ratio conditions and compare it with other receiver structures. These numerical experiments show that though the bit error rate performance is degraded by the subsampling in the CS-enabled receivers, this may be remedied by including quantization in the receiver model. We also study the computational complexity of the proposed receiver design under different sparsity and measurement ratios. Our work shows that it is possible to subsample a CDMA signal using CSS and that in one example the CSS receiver outperforms the classical receiver.

Robust Computation of Error Vector Magnitude for Wireless Standards

The modulation accuracy described by an error vector magnitude is a critical parameter in modern communication systems - defined originally as a performance metric for transmitters but now also used in receiver design and for more general signal analysis. The modulation accuracy is a measure of how far a test signal is from a reference signal at the symbol values when some parameters in a reconstruction model are optimized for best agreement. This paper provides an approach to computation of error vector magnitude as described in several standards from measured or simulated data. It is shown that the error vector magnitude optimization problem is generally non-convex. Robust estimation of the initial conditions for the optimizer is suggested, which is particularly important for a non-convex problem. A Bender decomposition approach is used to separate convex and non-convex parts of the problem to make the optimization procedure simpler and robust. A two step global optimization method is suggested where the global step is the grid method and the local method is the Newton method. A number of test cases are shown to illustrate the concepts.

UWB Wind Turbine Blade Deflection Sensing for Wind Energy Cost Reduction.

A new application of utilizing ultra-wideband (UWB) technology to sense wind turbine blade deflections is introduced in this paper for wind energy cost reduction. The lower UWB band of 3.1–5.3 GHz is applied. On each blade, there will be one UWB blade deflection sensing system, which consists of two UWB antennas at the blade root and one UWB antenna at the blade tip. The detailed topology and challenges of this deflection sensing system are addressed. Due to the complexity of the problem, this paper will first realize the on-blade UWB radio link in the simplest case, where the tip antenna is situated outside (and on the surface of) a blade tip. To investigate this case, full-blade time-domain measurements are designed and conducted under different deflections. The detailed measurement setups and results are provided. If the root and tip antenna locations are properly selected, the first pulse is always of sufficient quality for accurate estimations under different deflections. The measured results reveal that the blade tip-root distance and blade deflection can be accurately estimated in the complicated and lossy wireless channels around a wind turbine blade. Some future research topics on this application are listed finally.

Stable 1-norm error minimization based linear predictors for speech modeling

In linear prediction of speech, the 1-norm error minimization criterion has been shown to provide a valid alternative to the 2-norm minimization criterion. However, unlike 2-norm minimization, 1-norm minimization does not guarantee the stability of the corresponding all-pole filter and can generate saturations when this is used to synthesize speech. In this paper, we introduce two new methods to obtain intrinsically stable predictors with the 1-norm minimization. The first method is based on constraining the roots of the predictor to lie within the unit circle by reducing the numerical range of the shift operator associated with the particular prediction problem considered. The second method uses the alternative Cauchy bound to impose a convex constraint on the predictor in the 1-norm error minimization. These methods are compared with two existing methods: the Burg method, based on the 1-norm minimization of the forward and backward prediction error, and the iteratively reweighted 2-norm minimization known to converge to the 1-norm minimization with an appropriate selection of weights. The evaluation gives proof of the effectiveness of the new methods, performing as well as unconstrained 1-norm based linear prediction for modeling and coding of speech.

Reconstruction of Undersampled Atomic Force Microscopy Images: Interpolation versus Basis Pursuit

Atomic force microscopy (AFM) is one of the most advanced tools for high-resolution imaging and manipulation of nanoscale matter. Unfortunately, standard AFM imaging requires a timescale on the order of seconds to minutes to acquire an image which makes it complicated to observe dynamic processes. Moreover, it is often required to take several images before a relevant observation region is identified. In this paper we show how to significantly reduce the image acquisition time by under sampling. The reconstruction of an under sampled AFM image can be viewed as an in painting, interpolating problem, or a special case of compressed sensing. We argue that the preferred approach depends upon the type of image. Of the methods proposed for AFM, images containing high frequencies should be reconstructed using basis pursuit from data collected in a spiral pattern. Images without too much high frequency content should be reconstructed using interpolation.

Fast algorithms for high-order sparse linear prediction with applications to speech processing

Propose fast algorithms for sparse linear prediction.Usage of N log N algorithms for repeated solve of symmetric Toeplitz systems.Can handle even quite large dimensions and high-sampling rate.The fast algorithms shows possibilities for implementation in real-time systems.Experiments shows that high and low accuracy solutions performs almost equally well. In speech processing applications, imposing sparsity constraints on high-order linear prediction coefficients and prediction residuals has proven successful in overcoming some of the limitation of conventional linear predictive modeling. However, this modeling scheme, named sparse linear prediction, is generally formulated as a linear programming problem that comes at the expenses of a much higher computational burden compared to the conventional approach. In this paper, we propose to solve the optimization problem by combining splitting methods with two approaches: the Douglas-Rachford method and the alternating direction method of multipliers. These methods allow to obtain solutions with a higher computational efficiency, orders of magnitude faster than with general purpose software based on interior-point methods. Furthermore, computational savings are achieved by solving the sparse linear prediction problem with lower accuracy than in previous work. In the experimental analysis, we clearly show that a solution with lower accuracy can achieve approximately the same performance as a high accuracy solution both objectively, in terms of prediction gain, as well as with perceptually relevant measures, when evaluated in a speech reconstruction application.

Real-time implementations of sparse linear prediction for speech processing

Employing sparsity criteria in linear prediction of speech has been proven successful for several analysis and coding purposes. However, sparse linear prediction comes at the expenses of a much higher computational burden and numerical sensitivity compared to the traditional minimum variance approach. This makes sparse linear prediction difficult to deploy in real-time systems. In this paper, we present a step towards real-time implementation of the sparse linear prediction problem using hand-tailored interior-point methods. Using compiled implementations the sparse linear prediction problems corresponding to a frame size of 20ms can be solved on a standard PC in approximately 2ms and orders faster than with general purpose software.