Sparse Recovery Beyond Compressed Sensing: Separable Nonlinear Inverse Problems.

Extracting information from nonlinear measurements is a fundamental challenge in data analysis. In this work, we consider separable inverse problems, where the data are modeled as a linear combination of functions that depend nonlinearly on certain parameters of interest. These parameters may represent neuronal activity in a human brain, frequencies of electromagnetic waves, fluorescent probes in a cell, or magnetic relaxation times of biological tissues. Separable nonlinear inverse problems can be reformulated as underdetermined sparse-recovery problems, and solved using convex programming. This approach has had empirical success in a variety of domains, from geophysics to medical imaging, but lacks a theoretical justification. In particular, compressed-sensing theory does not apply, because the measurement operators are deterministic and violate incoherence conditions such as the restricted-isometry property. Our main contribution is a theory for sparse recovery adapted to deterministic settings. We show that convex programming succeeds in recovering the parameters of interest, as long as their values are sufficiently distinct with respect to the correlation structure of the measurement operator. The theoretical results are illustrated through numerical experiments for two applications: heat-source localization and estimation of brain activity from electroencephalography data.

Brain source localization of MMN and P300 ERPs in mild cognitive impairment and Alzheimer's disease: a high-density EEG approach.

Alzheimer's disease is the most common neurodegenerative disease of Western societies, suggesting the need for early diagnosis, even in preclinical stages. In this vein, the localization of neuronal generators of event-related potential (ERP) components, that is, the mismatch negativity and the P300, based on high-density electroencephalogram data, was explored as a means to enhance their sensitivity as markers of preclinical Alzheimer's disease (AD). A 2-tone oddball experiment was conducted, involving 21 healthy elderly, 21 mild cognitive impairment, and 21 mild AD patients, while high-density electroencephalogram data were recorded. The results revealed longer latencies of both mismatch negativity and P300 and slower and far less accurate responses as neurodegeneration progressed. Standardized low-resolution electromagnetic tomography revealed that source differences between healthy and mild cognitive impairment and healthy and AD patients for both ERP components were present in the same Brodmann area independently of the ERP and the stage of cognitive decline. This finding indicates an early change of source activation related to cognitive performance and may be used to improve the diagnostic and prognostic value of ERPs.

Age-induced differences in brain neural activation elicited by visual emotional stimuli: A high-density EEG study.

Identifying the brain sources of neural activation during processing of emotional information remains a very challenging task. In this work, we investigated the response to different emotional stimuli and the effect of age on the neuronal activation. Two negative emotion conditions, i.e., 'anger' and 'fear' faces were presented to 22 adult female participants (11 young and 11 elderly) while acquiring high-density electroencephalogram (EEG) data of 256 channels. Brain source localization was utilized to study the modulations in the early N170 event-related-potential component. The results revealed alterations in the amplitude of N170 and the localization of areas with maximum neural activation. Furthermore, age-induced differences are shown in the topographic maps and the neural activation for both emotional stimuli. Overall, aging appeared to affect the limbic area and its implication to emotional processing. These findings can serve as a step toward the understanding of the way the brain functions and evolves with age which is a significant element in the design of assistive environments.

Cognitive MMN and P300 in mild cognitive impairment and Alzheimer's disease: A high density EEG-3D vector field tomography approach.

Precise preclinical detection of dementia for effective treatment and stage monitoring is of great importance. Miscellaneous types of biomarkers, e.g., biochemical, genetic, neuroimaging, and physiological, have been proposed to diagnose Alzheimer's disease (AD), the usual suspect behind manifested cognitive decline, and mild cognitive impairment (MCI), a neuropathology prior to AD that does not affect cognitive functions. Event related potential (ERP) methods constitute a non-invasive, inexpensive means of analysis and have been proposed as sensitive biomarkers of cognitive impairment; besides, various ERP components are strongly linked with working memory, attention, sensory processing and motor responses. In this study, an auditory oddball task is employed, to acquire high density electroencephalograhy recordings from healthy elderly controls, MCI and AD patients. The mismatch negativity (MMN) and P300 ERP components are then extracted and their relationship with neurodegeneration is examined. Then, the neural activation at these components is reconstructed using the 3D vector field tomography (3D-VFT) inverse solution. The results reveal a decline of both ERPs amplitude, and a statistically significant prolongation of their latency as cognitive impairment advances. For the MMN, higher brain activation is usually localized in the inferior frontal and superior temporal gyri in the controls. However, in AD, parietal sites exhibit strong activity. Stronger P300 generators are mostly found in the frontal lobe for the controls, but in AD they often shift to the temporal lobe. Reduction in inferior frontal source strength and the switch of the maximum intensity area to parietal and superior temporal sites suggest that these areas, especially the former, are of particular significance when neurodegenerative disorders are investigated. The modulation of MMN and P300 can serve to produce biomarkers of dementia and its progression, and brain imaging can further contribute to the diagnostic efficiency of ERPs.

An open access database for the evaluation of heart sound algorithms.

In the past few decades, analysis of heart sound signals (i.e. the phonocardiogram or PCG), especially for automated heart sound segmentation and classification, has been widely studied and has been reported to have the potential value to detect pathology accurately in clinical applications. However, comparative analyses of algorithms in the literature have been hindered by the lack of high-quality, rigorously validated, and standardized open databases of heart sound recordings. This paper describes a public heart sound database, assembled for an international competition, the PhysioNet/Computing in Cardiology (CinC) Challenge 2016. The archive comprises nine different heart sound databases sourced from multiple research groups around the world. It includes 2435 heart sound recordings in total collected from 1297 healthy subjects and patients with a variety of conditions, including heart valve disease and coronary artery disease. The recordings were collected from a variety of clinical or nonclinical (such as in-home visits) environments and equipment. The length of recording varied from several seconds to several minutes. This article reports detailed information about the subjects/patients including demographics (number, age, gender), recordings (number, location, state and time length), associated synchronously recorded signals, sampling frequency and sensor type used. We also provide a brief summary of the commonly used heart sound segmentation and classification methods, including open source code provided concurrently for the Challenge. A description of the PhysioNet/CinC Challenge 2016, including the main aims, the training and test sets, the hand corrected annotations for different heart sound states, the scoring mechanism, and associated open source code are provided. In addition, several potential benefits from the public heart sound database are discussed.

Gender effect in human brain responses to bottom-up and top-down attention using the EEG 3D-Vector Field Tomography.

The effect of gender in rapidly allocating attention to objects, features or locations, as reflected in brain activity, is examined in this study. A visual-attention task, consisting of bottom-up (visual pop-out) and top-down (visual search) conditions during stimuli of four triangles, i.e., a target and three distractors, was engaged. In pop-out condition, both color and orientation of the distractors differed from target, while in search condition they differed only in orientation. During the task, high-density EEG (256 channels) data were recorded and analyzed by means of behavioral, event-related potentials, i.e., the P300 component and brain source localization analysis using 3D-Vector Field Tomography (3D-VFT). Twenty subjects (half female; 32±4.7 years old) participated in the experiments, performing 60 trials for each condition. Behavioral analysis revealed that both female and male outperformed in the pop-out condition compared to the search one, with respect to accuracy and reaction time, whereas no gender-related statistical significant differences were found. Nevertheless, in the search condition, higher P300 amplitudes were detected for females compared to males (p <; 7 · 10(-3)). Moreover, the findings suggested that the maximum activation in females was located mainly in the left inferior frontal and superior temporal gyri, whereas in males it was found in the right inferior frontal and superior temporal gyri. Overall, the experimental results show that visual attention depends on contributions from different brain lateralization linked to gender, posing important implications in studying developmental disorders, characterized by gender differences.

Phase-amplitude cross-frequency coupling in EEG-derived cortical time series upon an auditory perception task.

Recent evidence suggests that cross-frequency coupling (CFC) plays an essential role in multi-scale communication across the brain. The amplitude of the high frequency oscillations, responsible for local activity, is modulated by the phase of the lower frequency activity, in a task and region-relevant way. In this paper, we examine this phase-amplitude coupling in a two-tone oddball paradigm for the low frequency bands (delta, theta, alpha, and beta) and determine the most prominent CFCs. Data consisted of cortical time series, extracted by applying three-dimensional vector field tomography (3D-VFT) to high density (256 channels) electroencephalography (HD-EEG), and CFC analysis was based on the phase-amplitude coupling metric, namely PAC. Our findings suggest CFC spanning across all brain regions and low frequencies. Stronger coupling was observed in the delta band, that is closely linked to sensory processing. However, theta coupling was reinforced in the target tone response, revealing a task-dependent CFC and its role in brain networks communication.

Efficient heart sound segmentation and extraction using ensemble empirical mode decomposition and kurtosis features.

An efficient heart sound segmentation (HSS) method that automatically detects the location of first ( S1) and second ( S2) heart sound and extracts them from heart auscultatory raw data is presented here. The heart phonocardiogram is analyzed by employing ensemble empirical mode decomposition (EEMD) combined with kurtosis features to locate the presence of S1, S2, and extract them from the recorded data, forming the proposed HSS scheme, namely HSS-EEMD/K. Its performance is evaluated on an experimental dataset of 43 heart sound recordings performed in a real clinical environment, drawn from 11 normal subjects, 16 patients with aortic stenosis, and 16 ones with mitral regurgitation of different degrees of severity, producing 2608 S1 and S2 sequences without and with murmurs, respectively. Experimental results have shown that, overall, the HSS-EEMD/K approach determines the heart sound locations in a percentage of 94.56% and segments heart cycles correctly for the 83.05% of the cases. Moreover, results from a noise stress test with additive Gaussian noise and respiratory noises justify the noise robustness of the HSS-EEMD/K. When compared with four other efficient methods that mainly employ wavelet transform, energy, simplicity, and frequency measures, respectively, using the same experimental database, the HSS-EEMD/K scheme exhibits increased accuracy and prediction power over all others at the level of 7-19% and 4-9%, respectively, both in controls and pathological cases. The promising performance of the HSS-EEMD/K paves the way for further exploitation of the diagnostic value of heart sounds in everyday clinical practice.