"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."

"Like the FFT, the new algorithm works on digital signals. A digital signal is just a series of numbers — discrete samples of an analog signal, such as the sound of a musical instrument. The FFT takes a digital signal containing a certain number of samples and expresses it as the weighted sum of an equivalent number of frequencies.

“Weighted” means that some of those frequencies count more toward the total than others. Indeed, many of the frequencies may have such low weights that they can be safely disregarded. That’s why the Fourier transform is useful for compression. An eight-by-eight block of pixels can be thought of as a 64-sample signal, and thus as the sum of 64 different frequencies. But as the researchers point out in their new paper, empirical studies show that on average, 57 of those frequencies can be discarded with minimal loss of image quality."
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"Signals whose Fourier transforms include a relatively small number of heavily weighted frequencies are called “sparse.” The new algorithm determines the weights of a signal’s most heavily weighted frequencies; the sparser the signal, the greater the speedup the algorithm provides. Indeed, if the signal is sparse enough, the algorithm can simply sample it randomly rather than reading it in its entirety.

“In nature, most of the normal signals are sparse,” says Dina Katabi, one of the developers of the new algorithm. Consider, for instance, a recording of a piece of chamber music: The composite signal consists of only a few instruments each playing only one note at a time. A recording, on the other hand, of all possible instruments each playing all possible notes at once wouldn’t be sparse — but neither would it be a signal that anyone cares about."

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.

Compressed sensing deals with efficient recovery of analog signals from linear measurements. This paper presents a statistical study of compressed sensing by modeling the input signal as random processes. Three classes of encoders are considered, namely optimal nonlinear, optimal linear and random linear encoders. Focusing on optimal decoders, we investigate the fundamental tradeoff between measurement rate and reconstruction fidelity gauged by error probability and noise sensitivity in the absence and presence of measurement noise, respectively. Optimal phase transition thresholds are determined as a functional of the input distribution and compared to suboptimal thresholds achieved by various popular reconstruction algorithms. In particular, we show that Gaussian sensing matrices incur no penalty on the phase transition threshold with respect to optimal nonlinear encoding. Our results also provide a rigorous justification of previous results based on replica heuristics in the weak-noise regime.