nils-herrmann/clean_scirepeval huggingface dataset:
FRIDA: FRI-based DOA estimation for arbitrary array layouts

In this paper we present FRIDA—an algorithm for estimating directions of arrival of multiple wideband sound sources. FRIDA combines multi-band information coherently and achieves state-of-the-art resolution at extremely low signal-to-noise ratios. It works for arbitrary array layouts, but unlike the various steered response power and subspace methods, it does not require a grid search. FRIDA leverages recent advances in sampling signals with a finite rate of innovation. It is based on the insight that for any array layout, the entries of the spatial covariance matrix can be linearly transformed into a uniformly sampled sum of sinusoids.
How to take advantage of aliasing in bandlimited signals

In signal processing systems, aliasing is normally treated as a disturbing signal. That motivates the need for effective analog, optical and digital anti-aliasing filters. However, aliasing also conveys valuable information on the signal above the Nyquist frequency. Hence, an effective processing of the samples, based on a model of the input signal, would virtually allow the sampling frequency to be increased using slower and cheaper converters. We present such an algorithm for bandlimited signals that are sampled below twice the maximum signal frequency. Using a subspace method in the frequency domain, we show that these signals can be reconstructed from multiple sets of samples. The offset between the sets is unknown and can have arbitrary values. This approach can be applied to the creation of super-resolution images from sets of low resolution images. In this application, registration parameters have to be computed from aliased images. We show that parameters and high resolution images can be computed precisely, even when high levels of aliasing are present on the low resolution images.
Sampling signals with finite rate of innovation

The authors consider classes of signals that have a finite number of degrees of freedom per unit of time and call this number the rate of innovation. Examples of signals with a finite rate of innovation include streams of Diracs (e.g., the Poisson process), nonuniform splines, and piecewise polynomials. Even though these signals are not bandlimited, we show that they can be sampled uniformly at (or above) the rate of innovation using an appropriate kernel and then be perfectly reconstructed. Thus, we prove sampling theorems for classes of signals and kernels that generalize the classic "bandlimited and sinc kernel" case. In particular, we show how to sample and reconstruct periodic and finite-length streams of Diracs, nonuniform splines, and piecewise polynomials using sinc and Gaussian kernels. For infinite-length signals with finite local rate of innovation, we show local sampling and reconstruction based on spline kernels. The key in all constructions is to identify the innovative part of a signal (e.g., time instants and weights of Diracs) using an annihilating or locator filter: a device well known in spectral analysis and error-correction coding. This leads to standard computational procedures for solving the sampling problem, which we show through experimental results. Applications of these new sampling results can be found in signal processing, communications systems, and biological systems.
Rate-Constrained Beamforming for Collaborating Hearing Aids

Hearing aids are audio capture devices which aim at providing the hearing impaired with better audibility. Most of the state-of-the-art systems involve sensing devices that work independently. However, the availability of a wireless communication link between two hearing aids would allow to perform spatial beamforming such as to provide better rejection of interfering signals. In this paper, we identify and study the above scenario from an information-theoretic viewpoint. We explore the gain provided by collaborating hearing aids as a function of the communication rate. In particular, we derive a closed-form gain-rate formula in the case where a sound source has to be extracted from ambient noise. A similar analysis is provided in the presence of an interfering point source and the corresponding optimal rate allocation is discussed
Efficient image compression using directionlets

Directionlets are built as basis functions of critically sampled perfect-reconstruction transforms with directional vanishing moments imposed along different directions. We combine the directionlets with the space-frequency quantization (SFQ) image compression method, originally based on the standard two-dimensional wavelet transform. We show that our new compression method outperforms the standard SFQ as well as the state-of-the-art image compression methods, such as SPIHT and JPEG-2000, in terms of the quality of compressed images, especially in a low-rate compression regime. We also show that the order of computational complexity remains the same, as compared to the complexity of the standard SFQ algorithm.
Space-Time-Frequency Processing of Acoustic Wave Fields: Theory, Algorithms, and Applications

Consider a nonparametric representation of acoustic wave fields that consists of observing the sound pressure along a straight line or a smooth contour L defined in space. The observed data contains implicit information of the surrounding acoustic scene, both in terms of spatial arrangement of the sources and their respective temporal evolution. We show that such data can be effectively analyzed and processed in what we call the space-time-frequency representation space, consisting of a Gabor representation across the spatio-temporal manifold defined by the spatial axis L and the temporal axis t. In the presence of a source, the spectral patterns generated at L have a characteristic triangular shape that changes according to certain parameters, such as the source distance and direction, the number of sources, the concavity of L, and the analysis window size. Yet, in general, the wave fronts can be expressed as a function of elementary directional components-most notably, plane waves and far-field components. Furthermore, we address the problem of processing the wave field in discrete space and time, i.e., sampled along L and t, where a Gabor representation implies that the wave fronts are processed in a block-wise fashion. The key challenge is how to chose and customize a spatio-temporal filter bank such that it exploits the physical properties of the wave field while satisfying strict requirements such as perfect reconstruction, critical sampling, and computational efficiency. We discuss the architecture of such filter banks, and demonstrate their applicability in the context of real applications, such as spatial filtering, deconvolution, and wave field coding.
The contourlet transform: an efficient directional multiresolution image representation

The limitations of commonly used separable extensions of one-dimensional transforms, such as the Fourier and wavelet transforms, in capturing the geometry of image edges are well known. In this paper, we pursue a "true" two-dimensional transform that can capture the intrinsic geometrical structure that is key in visual information. The main challenge in exploring geometry in images comes from the discrete nature of the data. Thus, unlike other approaches, such as curvelets, that first develop a transform in the continuous domain and then discretize for sampled data, our approach starts with a discrete-domain construction and then studies its convergence to an expansion in the continuous domain. Specifically, we construct a discrete-domain multiresolution and multidirection expansion using nonseparable filter banks, in much the same way that wavelets were derived from filter banks. This construction results in a flexible multiresolution, local, and directional image expansion using contour segments, and, thus, it is named the contourlet transform. The discrete contourlet transform has a fast iterated filter bank algorithm that requires an order N operations for N-pixel images. Furthermore, we establish a precise link between the developed filter bank and the associated continuous-domain contourlet expansion via a directional multiresolution analysis framework. We show that with parabolic scaling and sufficient directional vanishing moments, contourlets achieve the optimal approximation rate for piecewise smooth functions with discontinuities along twice continuously differentiable curves. Finally, we show some numerical experiments demonstrating the potential of contourlets in several image processing applications.
Sampling High-Dimensional Bandlimited Fields on Low-Dimensional Manifolds

Consider the task of sampling and reconstructing a bandlimited spatial field in R2 using moving sensors that take measurements along their path. It is inexpensive to increase the sampling rate along the paths of the sensors but more expensive to increase the total distance traveled by the sensors per unit area, which we call the path density. In this paper, we introduce the problem of designing sensor trajectories that are minimal in path density subject to the condition that the measurements of the field on these trajectories admit perfect reconstruction of bandlimited fields. We study various possible designs of sampling trajectories. Generalizing some ideas from the classical theory of sampling on lattices, we obtain necessary and sufficient conditions on the trajectories for perfect reconstruction. We show that a single set of equispaced parallel lines has the lowest path density from certain restricted classes of trajectories that admit perfect reconstruction. We then generalize some of our results to higher dimensions. We first obtain results on designing sampling trajectories in higher dimensional fields. Further, interpreting trajectories as 1-D manifolds, we extend some of our ideas to higher dimensional sampling manifolds. We formulate the problem of designing κ-dimensional sampling manifolds for d-dimensional spatial fields that are minimal in manifold density, a natural generalization of the path density. We show that our results on sampling trajectories for fields in R2 can be generalized to analogous results on d-dimensional sampling manifolds for d-dimensional spatial fields.
Running FIR and IIR filtering using multirate filter banks

The computational complexity of running FIR (finite-impulse response) and IIR (infinite-impulse response) filtering using multirate filter banks is considered. No restrictions are put on signal, filter, or block lengths. It is shown how to map long running convolutions into smaller ones by using filter banks based on aperiodic convolution algorithms and short-time Fourier transforms. With the proposed approach, good tradeoffs among computational complexity, system architecture, and input-output delay are achieved.
Nonseparable Multidimensional Perfect Reconstruction Filter Banks And Wavelet Bases For R/sup n/

Although filter banks have been in use for more than a decade, only recently have some results emerged setting up the theory of general nonseparable multidimensional filter banks. At the same time, wavelet theory emerged as a useful tool in many different fields of pure and applied mathematics as well as in signal analysis. Recently, it has been shown that the two theories were closely related. Not only does the filter bank perform a discrete wavelet transform but also under certain conditions it can be used to construct continuous bases of compactly supported wavelets. We start by examining filter banks in polyphase and modulation domains and we give conditions for perfect reconstruction. The orthogonal case is analyzed showing the orthogonality relations between the filters in the bank and their shifts with respect to the sampling lattice. A linear phase condition, valid for the whole filter bank, follows, as a tool for testing or building banks containing linear phase (symmetric) filters. We then discuss the possibility of obtaining any of the combinations separable/nonseparable lat tice/filters/polyphase components leading to the observation that a nonseparable filter can sometimes be implemented using separable polyphase components. Due to its importance the two-channel case in multiple dimensions is studied in detail and the form of the general orthogonal polyphase matrix is given. An analysis of the structure of possible linear phase solutions for the multidimensional two-channel case is presented and at tractive cascade structures yielding perfect reconstruction filter banks with specific properties (orthogonality and linear phase) are proposed. Next, we make the connection to nonseparable wavelets through the concept of iterated filter banks. We show the orthogonality relations between the scaling function and wavelets. An iterated filter leading to an interesting "dragon", which by construction tiles the space, is shown. For the quincunx case that is used as a case study, we prove that the wavelet obtained previously together with its shifts on the quincunx lattice and scales by a particular, well-behaved matrix D, constitute a basis for L 2 ( R 2 ) and give design examples.
Near-optimal source placement for linear physical fields

In real-word applications, signal processing is often used to measure and control a physical field by means of sensors and sources, respectively. An aspect that has been often neglected is the optimization of the sources' locations. In this work, we discuss the source placement problem as the dual of the sensor placement problem and propose two polynomial-time algorithms, for scenarios with or without noise. Both algorithms are near-optimal and indicate the possibility to make the control of such physical fields easier, more efficient and more stable to noise.
Discrete- and continuous-time local cosine bases with multiple overlapping

Cosine-modulated filter banks (CMFBs) are filter banks whose impulse responses are obtained by modulating a window with cosines. Among their applications are video and audio compression and multitone modulation. Their continuous-time counterpart is known as local cosine bases. Even though there is an extended literature on the discrete-time case both for single and multiple overlapping, the continuous-time case has received less attention, and only the single overlapping case has been solved. This work gives a solution to the problem of continuous-time local cosine bases with multiple overlapping via a general theory that emphasizes the deep connection between discrete and continuous time. A sampling theorem for local cosine basis and an efficient algorithm to compute the expansion of a signal are also given.
Wireless Sensor Networks for Environmental Monitoring: The SensorScope Experience

While wireless sensor networks have been extensively studied in the past few years, most results are of theoretical nature and were obtained outside of a practical context. This can be problematic for real applications, especially in the area of environmental monitoring where many factors, such as harsh weather conditions, can greatly influence the performance of such a network, while reliable delivery and high-quality measurements are required. SensorScope is an interdisciplinary project, elaborated by environmental and networking researchers, that aims at narrowing the gap between theory and practice. Several successful real-world deployments have already been undertaken in rugged environments. In this paper, we analyze the particular requirements of environmental monitoring and how these requirements have been met in the SensorScope project. We also present an application example of a deployment, undertaken in a harsh mountain environment.
Universal transform coding based on backward adaptation

The method for universal transform coding based on backward adaptation introduced by Goyal et al. ) is reviewed and further analyzed. This algorithm uses a linear transform which is periodically updated based on a local Karhunen-Loeve transform (KLT) estimate. The KLT estimate is derived purely from quantized data, so the decoder can track the encoder state without any side information. The effect of estimating only from quantized data is quantitatively analyzed. Two convergence results which hold in the absence of estimation noise are presented. The first applies for any vector dimension but does not preclude the necessity of a sequence of quantization step sizes that goes to zero. The second applies only in the two-dimensional case, but shows local convergence for a fixed, sufficiently small quantization step size. Refinements which reduce the storage and computational requirements of the algorithm are suggested.
Compressed sensing of streaming data

We introduce a recursive scheme for performing Compressed Sensing (CS) on streaming data and analyze, both analytically and experimentally, the computational complexity and estimation error. The approach consists of sampling the input stream recursively via overlapping windowing and making use of the previous measurement in obtaining the next one. The signal estimate from the previous window is utilized in order to achieve faster convergence in an iterative optimization algorithm to decode the new window. To remove the bias of the estimator a two-step estimation procedure is proposed comprising support set detection and signal amplitude estimation. Estimation accuracy is enhanced by averaging estimates obtained from overlapping windows. The proposed method is shown to have asymptotic computational complexity O(nm3/2), where n is the window length, and m is the number of samples. The variance of normalized estimation error is shown to asymptotically go to 0 if k = O(n1-∈) as n increases. The simulation results show speed up of at least ten times with respect to applying traditional CS on a stream of data while obtaining significantly lower reconstruction error under mild conditions on the signal magnitudes and the noise level.
On the Multiterminal Rate-Distortion Function for Acoustic Sensing

We consider the rate-distortion problem for recording a Gaussian acoustic field with an array of sensors equipped with microphones. Our analysis is based on the field's spatio-temporal correlation structure, which is induced by the physics of sound propagation. Under certain assumptions about the spectrum of the wave kernel, we determine the rate-distortion functions for various distributed source coding schemes and sampling lattices. Our results also include an answer to the multiterminal rate-distortion problem for the setup considered in the paper
Soft caching: image caching in a rate-distortion framework

This paper presents a novel approach to image caching for image databases, Web browsers, proxies and other similar applications. Current caches employ a hard strategy: either the image is stored in the cache, or it is not. In a soft cache, a variable amount of memory is assigned to each image. This is ideally matched to progressive image file formats. Our strategy for optimal soft caching considers the image download delay as a distortion measure. Then the minimization of the expected delay can be carried out in an operational rate-distortion framework. We present optimal theoretical solutions as well as simulation results.
Quantization of overcomplete expansions

We present a method that represents a signal with respect to an overcomplete set of vectors which we call a dictionary. The use of overcomplete sets of vectors (redundant bases or frames) together with quantization is explored as an alternative to transform coding for signal compression. The goal is to retain the computational simplicity of transform coding while adding flexibility like adaptation to signal statistics. We show results using both fixed quantization in frames and greedy quantization using matching pursuit. An MSE slope of -6 dB/octave of frame redundancy is shown for a particular tight frame and is verified experimentally for another frame.
Support recovery in compressed sensing: An estimation theoretic approach

Compressed sensing (CS) deals with the reconstruction of sparse signals from a small number of linear measurements. One of the main challenges in CS is to find the support of a sparse signal from a set of noisy observations. In the CS literature, several information-theoretic bounds on the scaling law of the required number of measurements for exact support recovery have been derived, where the focus is mainly on random measurement matrices. In this paper, we investigate the support recovery problem from an estimation theory point of view, where no specific assumption is made on the underlying measurement matrix. By using the Hammersley-Chapman-Robbins (HCR) bound, we derive a fundamental lower bound on the performance of any unbiased estimator which provides necessary conditions for reliable l2-norm support recovery. We then analyze the optimal decoder to provide conditions under which the HCR bound is achievable. This leads to a set of sufficient conditions for reliable l2-norm support recovery.
Annihilation-driven localised image edge models

We propose a novel edge detection algorithm with sub-pixel accuracy based on annihilation of signals with finite rate of innovation [1, 2]. We show that the Fourier domain annihilation equations can be interpreted as spatial domain multiplications. From this new perspective, we obtain an accurate estimation of the edge model by assuming a simple parametric form within each localised block. Further, we build a locally adaptive global mask function (i.e, our edge model) for the whole image. The mask function is then used as an edge-preserving constraint in further processing. Numerical experiments on both edge localisations and image up-sampling show the effectiveness of the proposed approach, which out-performs state-of-the-art method.
Simple algorithms for BCH decoding

Proposes some simple algorithms for decoding BCH codes. The authors show that the pruned FFT is an effective method for evaluating syndromes and for finding the roots of error-locator polynomials. They show that a simple variation of the basic Gaussian elimination procedure can be adapted to compute the error-locator polynomial efficiently for codes with small designed distance. Finally, they give a procedure for computing the error values that has half the complexity of the Forney algorithm.
Signal Reconstruction From Multiple Unregistered Sets Of Samples Using Groebner Bases

We present a new method for signal reconstruction from multiple sets of samples with unknown offsets. We rewrite the reconstruction problem as a set of polynomial equations in the unknown signal parameters and the offsets between the sets of samples. Then, we construct a Grobner basis for the corresponding affine variety. The signal parameters can then easily be derived from this Grobner basis. This provides us with an elegant solution method for the initial nonlinear problem. We show two examples for the reconstruction of polynomial signals and Fourier series
A lower bound to the scaling behavior of sensor networks

For a class of sensor networks, the task is to monitor an underlying physical phenomenon over space and time through a noisy observation process. The sensors can communicate back to a data collector over a noisy channel. The key parameters in such a setting are the fidelity at which the underlying physical phenomenon can be estimated by a central data collector, and the cost of operating the communication network. This paper presents a lower bound to the scaling behavior of sensor networks
Theory of two-dimensional multirate filter banks

Results are presented on 2-D FIR (two-dimensional finite-impulse-response) filter banks for multirate applications. The theory is valid for all sampling lattices; conditions for alias-free and perfect signal reconstruction are derived. Synthesis structures for paraunitary and nonparaunitary polynomial matrices are derived, which yield perfect reconstruction filter banks. The degrees of freedom are given for these systems. Linear phase conditions are posed on the polyphase form of filter banks. which is used to derive a design structure for the restricted, but important, case of linear phase filter banks.