"We present a novel angular fingerprinting algorithm for detecting changes in the direction of rotation of a target with a monostatic, stationary sonar platform. Unlike other approaches, we assume that the target's centroid is stationary, and exploit doppler multipath signals to resolve the otherwise unavoidable ambiguities that arise. Since the algorithm is based on an underlying differential topological theory, it is highly robust to distortions in the collected data. We demonstrate performance of this algorithm experimentally, by exhibiting a pulsed doppler sonar collection system that runs on a smartphone. The performance of this system is sufficiently good to both detect changes in target rotation direction using angular fingerprints, and also to form high-resolution inverse synthetic aperature images of the target."

We consider a situation where the state of a system is represented by a real-valued vector. Under normal circumstances, the vector is zero, while an event manifests as non-zero entries in this vector, possibly few. Our interest is in the design of algorithms that can reliably detect events (i.e., test whether the vector is zero or not) with the least amount of information. We place ourselves in a situation, now common in the signal processing literature, where information about the vector comes in the form of noisy linear measurements. We derive information bounds in an active learning setup and exhibit some simple near-optimal algorithms. In particular, our results show that the task of detection within this setting is at once much easier, simpler and different than the tasks of estimation and support recovery.

In many data acquisition systems it is common to observe signals whose amplitudes have been clipped. We present two new algorithms for recovering a clipped signal by leveraging the model assumption that the underlying signal is sparse in the frequency domain. Both algorithms employ ideas commonly used in the field of Compressive Sensing; the first is a modified version of Reweighted $ell_1$ minimization, and the second is a modification of a simple greedy algorithm known as Trivial Pursuit. An empirical investigation shows that both approaches can recover signals with significant levels of clipping

Nowadays we are often faced with huge databases resulting from the rapid growth of data storage technologies. This is particularly true when dealing with music databases. In this context, it is essential to have techniques and tools able to discriminate properties from these massive sets. In this work, we report on a statistical analysis of more than ten thousand songs aiming to obtain a complexity hierarchy. Our approach is based on the estimation of the permutation entropy combined with an intensive complexity measure, building up the complexity-entropy causality plane. The results obtained indicate that this representation space is very promising to discriminate songs as well as to allow a relative quantitative comparison among songs. Additionally, we believe that the here-reported method may be applied in practical situations since it is simple, robust and has a fast numerical implementation.

We consider the problem of online audio source separation. Existing algorithms adopt either a sliding block approach or a stochastic gradient approach, which is faster but less accurate. Also, they rely either on spatial cues or on spectral cues and cannot separate certain mixtures. In this paper, we design a general online audio source separation framework that combines both approaches and both types of cues. The model parameters are estimated in the Maximum Likelihood (ML) sense using a Generalised Expectation Maximisation (GEM) algorithm with multiplicative updates. The separation performance is evaluated as a function of the block size and the step size and compared to that of an offline algorithm.

Many natural processes occur over characteristic spatial and temporal scales. This paper presents tools for (i) flexibly and scalably coarse-graining cellular automata and (ii) identifying which coarse-grainings express an automaton's dynamics well, and which express its dynamics badly. We apply the tools to investigate a range of examples in Conway's Game of Life and Hopfield networks and demonstrate that they capture some basic intuitions about emergent processes. Finally, we formalize the notion that a process is emergent if it is better expressed at a coarser granularity.

"This paper considers the fundamental problem of recovering a general signal, an image for example, from the magnitude of its Fourier transform. This problem, also known as phase retrieval, arises in many applications and has challenged engineers, physicists, and mathematicians for decades. Its origin comes from the fact that detectors can often times only record the squared modulus of the Fresnel or Fraunhofer diffraction pattern of the radiation that is scattered from an object. In such settings, one cannot measure the phase of the optical wave reaching the detector and, therefore, much information about the scattered object or the optical field is lost since, as is well known, the phase encodes a lot of the structural content of the image we wish to form."

"Even when the numbers of non-zero entries per column/row in the measurement matrices are limited to $O(1)$, numerical experiments indicate that the algorithm can still typically recover the original signal perfectly with an $O(N)$ computational cost per update as well if the density $\rho$ of non-zero entries of the signal is lower than a certain critical value $\rho_{\rm th}(\alpha)$ as $N,M \to \infty$."

"We survey and show our earlier results about three different ways of fluctuation-enhanced sensing of bio agent, the phage-based method for bacterium detection published earlier; sensing and evaluating the odors of microbes; and spectral and amplitude distribution analysis of noise in light scattering to identify spores based on their diffusion coefficient."

"We study, using simulated experiments inspired by thin film magnetic domain patterns, the feasibility of phase retrieval in X-ray diffractive imaging in the presence of intrinsic charge scattering given only photon-shot-noise limited diffraction data. We detail a reconstruction algorithm to recover the sample's magnetization distribution under such conditions, and compare its performance with that of Fourier transform holography. Concerning the design of future experiments, we also chart out the reconstruction limits of diffractive imaging when photon- shot-noise and the intensity of charge scattering noise are independently varied. This work is directly relevant to the time-resolved imaging of magnetic dynamics using coherent and ultrafast radiation from X-ray free electron lasers and also to broader classes of diffractive imaging experiments which suffer noisy data, missing data or both."

"Transient algebra is a multi-valued algebra for hazard detection in gate circuits. Sequences of alternating 0's and 1's, called transients, represent signal values, and gates are modeled by extensions of boolean functions to transients. Formulas for computing the output transient of a gate from the input transients are known for NOT, AND, OR} and XOR gates and their complements, but, in general, even the problem of deciding whether the length of the output transient exceeds a given bound is NP-complete. We propose a method of evaluating extensions of general boolean functions. We introduce and study a class of functions with the following property: Instead of evaluating an extension of a boolean function on a given set of transients, it is possible to get the same value by using transients derived from the given ones, but having length at most 3. We prove that all functions of three variables, as well as certain other functions, have this property, and can be efficiently evaluated."

"This paper presents a new numerical approach to the study of non-periodicity in signals, which can complement the maximal Lyapunov exponent method for determining chaos transitions of a given dynamical system. The proposed technique is based on the continuous wavelet transform and the wavelet multiresolution analysis. A new parameter, the \textit{scale index}, is introduced and interpreted as a measure of the degree of the signal's non-periodicity. This methodology is successfully applied to three classical dynamical systems: the Bonhoeffer-van der Pol oscillator, the logistic map, and the Henon map."

"We study the problem of reconstructing a sparse signal from a limited number of its linear projections when a part of its support is known, although the known part may contain some errors. The ``known" part of the support, denoted T, may be available from prior knowledge. Alternatively, in a problem of recursively reconstructing time sequences of sparse spatial signals, one may use the support estimate from the previous time instant as the ``known" part. The idea of our proposed solution (modified-CS) is to solve a convex relaxation of the following problem: find the signal that satisfies the data constraint and is sparsest outside of T.…"

"Recovery of the sparsity pattern (or support) of a sparse vector from a small number of noisy linear samples is a common problem that arises in signal processing and statistics. In the high dimensional setting, it is known that recovery with a vanishing fraction of errors is impossible if the sampling rate and per-sample signal-to-noise ratio (SNR) are finite constants independent of the length of the vector. In this paper, it is shown that recovery with an arbitrarily small but constant fraction of errors is, however, possible, and that in some cases a computationally simple thresholding estimator is near-optimal.…"

"We introduce the notion of Principal Component Analysis (PCA) of image gradient orientations. As image data is typically noisy, but noise is substantially different from Gaussian, traditional PCA of pixel intensities very often fails to estimate reliably the low-dimensional subspace of a given data population. We show that replacing intensities with gradient orientations and the $\ell_2$ norm with a cosine-based distance measure offers, to some extend, a remedy to this problem.…"

"An exact, one-to-one transform is presented that not only allows digital circular convolutions, but is free from multiplications and quantisation errors for transform lengths of arbitrary powers of two. The transform is analogous to the Discrete Fourier Transform, with the canonical harmonics replaced by a set of cyclic integers computed using only bit-shifts and additions modulo a prime number. The prime number may be selected to occupy contemporary word sizes or to be very large for cryptographic or data hiding applications. The transform is an extension of the Rader Transforms via Carmichael's Theorem. These properties allow for exact convolutions that are impervious to numerical overflow and to utilise Fast Fourier Transform algorithms."

"[Open Questions] Most of the encoding schemes considered in this paper use randomness and therefore are not given explicitly. As a result, the encoding and decoding schemes are not efficient. Finding explicit and efficient encoding and decoding schemes for the scenarios described in the paper remains open."

"Using total variation based energy minimisation we address the recovery of a blurred (convoluted) one dimensional (1D) barcode. We consider functionals defined over all possible barcodes with fidelity to a convoluted signal of a barcode, and regularised by total variation. Our fidelity terms consist of the L^2 distance either directly to the measured signal or preceded by deconvolution. Key length scales and parameters are the X-dimension of the underlying barcode, the size of the supports of the convolution and deconvolution kernels, and the fidelity parameter. For all functionals, we establish regimes (sufficient conditions) wherein the underlying barcode is the unique minimiser. We also present some numerical experiments suggesting that these sufficient conditions are not optimal and the energy methods are quite robust for significant blurring."