Atomic norm denoising with applications to line spectral estimation

Motivated by recent work on atomic norms in inverse problems, we propose a new approach to line spectral estimation that provides theoretical guarantees for the mean-squared-error (MSE) performance in the presence of noise and without knowledge of the model order. We propose an abstract theory of denoising with atomic norms and specialize this theory to provide a convex optimization problem for estimating the frequencies and phases of a mixture of complex exponentials. We show that the associated convex optimization problem can be solved in polynomial time via semidefinite programming (SDP). We also show that the SDP can be approximated by an l1-regularized least-squares problem that achieves nearly the same error rate as the SDP but can scale to much larger problems. We compare both SDP and l1-based approaches with classical line spectral analysis methods and demonstrate that the SDP outperforms the l1 optimization which outperforms MUSIC, Cadzow's, and Matrix Pencil approaches in terms of MSE over a wide range of signal-to-noise ratios.Comment: 27 pages, 10 figures. A preliminary version of this work appeared in the Proceedings of the 49th Annual Allerton Conference in September 2011. Numerous numerical experiments added to this version in accordance with suggestions by anonymous reviewer

Sequential Complexity as a Descriptor for Musical Similarity

We propose string compressibility as a descriptor of temporal structure in audio, for the purpose of determining musical similarity. Our descriptors are based on computing track-wise compression rates of quantised audio features, using multiple temporal resolutions and quantisation granularities. To verify that our descriptors capture musically relevant information, we incorporate our descriptors into similarity rating prediction and song year prediction tasks. We base our evaluation on a dataset of 15500 track excerpts of Western popular music, for which we obtain 7800 web-sourced pairwise similarity ratings. To assess the agreement among similarity ratings, we perform an evaluation under controlled conditions, obtaining a rank correlation of 0.33 between intersected sets of ratings. Combined with bag-of-features descriptors, we obtain performance gains of 31.1% and 10.9% for similarity rating prediction and song year prediction. For both tasks, analysis of selected descriptors reveals that representing features at multiple time scales benefits prediction accuracy.Comment: 13 pages, 9 figures, 8 tables. Accepted versio

IDENTIFICATION OF COVER SONGS USING INFORMATION THEORETIC MEASURES OF SIMILARITY

13 pages, 5 figures, 4 tables. v3: Accepted version13 pages, 5 figures, 4 tables. v3: Accepted version13 pages, 5 figures, 4 tables. v3: Accepted versio

Evaluating the Correlation Characteristics of Arbitrary AM and FM Radio Signals for the Purpose of Navigation

The Global Positioning System (GPS) provides position estimates on the Earth at anytime, anywhere and in any weather. However, to provide robust positioning, GPS requires an unobstructed path to satellite signals. As such, GPS performance generally degrades or becomes non-existent in environments such as large urban areas. This research investigates and analyzes the correlation characteristics of arbitrary AM and FM radio signals for the purpose of navigation. Simulations are conducted with different combinations of correlation methods (`fixed\u27 or `varying\u27), modulation types (AM or FM), and signal types (song or voice). Out of the eight different variations considered, only two provided promising results for the purpose of navigation. Both the FM voice and FM song signals exhibit distinct autocorrelation peaks (i.e., 5.0 dB peak-to-sidelobe ratios) using the `fixed\u27 reference correlation method. However, results for both FM signal types revealed limited potential for navigation when using the `varying\u27 reference correlation method. All the AM signals considered yielded relatively limited potential for navigation using either correlation method

REITERATIVE MINIMUM MEAN SQUARE ERROR ESTIMATOR FOR DIRECTION OF ARRIVAL ESTIMATION AND BIOMEDICAL FUNCTIONAL BRAIN IMAGING

Two novel approaches are developed for direction-of-arrival (DOA) estimation and functional brain imaging estimation, which are denoted as ReIterative Super-Resolution (RISR) and Source AFFine Image REconstruction (SAFFIRE), respectively. Both recursive approaches are based on a minimum mean-square error (MMSE) framework. The RISR estimator recursively determines an optimal filter bank by updating an estimate of the spatial power distribution at each successive stage. Unlike previous non-parametric covariance-based approaches, which require numerous time snapshots of data, RISR is a parametric approach thus enabling operation on as few as one time snapshot, thereby yielding very high temporal resolution and robustness to the deleterious effects of temporal correlation. RISR has been found to resolve distinct spatial sources several times better than that afforded by the nominal array resolution even under conditions of temporally correlated sources and spatially colored noise. The SAFFIRE algorithm localizes the underlying neural activity in the brain based on the response of a patient under sensory stimuli, such as an auditory tone. The estimator processes electroencephalography (EEG) or magnetoencephalography (MEG) data simulated for sensors outside the patient's head in a recursive manner converging closer to the true solution at each consecutive stage. The algorithm requires a minimal number of time samples to localize active neural sources, thereby enabling the observation of the neural activity as it progresses over time. SAFFIRE has been applied to simulated MEG data and has shown to achieve unprecedented spatial and temporal resolution. The estimation approach has also demonstrated the capability to precisely isolate the primary and secondary auditory cortex responses, a challenging problem in the brain MEG imaging community

Automatic Music Transcription with Convolutional Neural Networks using Intuitive Filter Shapes

This thesis explores the challenge of automatic music transcription with a combination of digital signal processing and machine learning methods. Automatic music transcription is important for musicians who can\u27t do it themselves or find it tedious. We start with an existing model, designed by Sigtia, Benetos and Dixon, and develop it in a number of original ways. We find that by using convolutional neural networks with filter shapes more tailored for spectrogram data, we see better and faster transcription results when evaluating the new model on a dataset of classical piano music. We also find that employing better practices shows improved results. Finally, we open-source our test bed for pre-processing, training, and testing the models to assist in future research