Spatio-temporal Regularization Research Articles

Multi-dimensional signal approximation with sparse structured priors using split Bregman iterations

This paper addresses the structurally constrained sparse decomposition of multi-dimensional signals onto overcomplete families of vectors, called dictionaries. The contribution of the paper is threefold. Firstly, a generic spatio-temporal regularization term is designed and used together with the standard ℓ1 regularization term to enforce a sparse decomposition preserving the spatio-temporal structure of the signal. Secondly, an optimization algorithm based on the split Bregman approach is proposed to handle the associated optimization problem, and its convergence is analyzed. Our well-founded approach yields same accuracy as the other algorithms at the state of the art, with significant gains in terms of convergence speed. Thirdly, the empirical validation of the approach on artificial and real-world problems demonstrates the generality and effectiveness of the method. On artificial problems, the proposed regularization subsumes the Total Variation minimization and recovers the expected decomposition. On the real-world problem of electro-encephalography brainwave decomposition, the approach outperforms similar approaches in terms of P300 evoked potentials detection, using structured spatial priors to guide the decomposition.

Optimal Curiosity-Driven Modular Incremental Slow Feature Analysis.

Consider a self-motivated artificial agent who is exploring a complex environment. Part of the complexity is due to the raw high-dimensional sensory input streams, which the agent needs to make sense of. Such inputs can be compactly encoded through a variety of means; one of these is slow feature analysis (SFA). Slow features encode spatiotemporal regularities, which are information-rich explanatory factors (latent variables) underlying the high-dimensional input streams. In our previous work, we have shown how slow features can be learned incrementally, while the agent explores its world, and modularly, such that different sets of features are learned for different parts of the environment (since a single set of regularities does not explain everything). In what order should the agent explore the different parts of the environment? Following Schmidhuber's theory of artificial curiosity, the agent should always concentrate on the area where it can learn the easiest-to-learn set of features that it has not already learned. We formalize this learning problem and theoretically show that, using our model, called curiosity-driven modular incremental slow feature analysis, the agent on average will learn slow feature representations in order of increasing learning difficulty, under certain mild conditions. We provide experimental results to support the theoretical analysis.

Spatio‐temporal mean curvature based image sequence restoration

In this study, the authors propose a restoration algorithm for blurred and noisy continuous image sequences. The proposed approach treats an image sequence as a space-time volume and employs a spatio-temporal mean curvature regularisation which is a novel regularisation proposed in the study to enhance the smoothness of the solution. An augmented Lagrangian method with splitting techniques is used to handle the problem, iteratively finding solutions to the subproblems. Experiments show that the proposed approach can produce higher quality results and more natural images comparing with other space-time volume based methods on image sequence denoising and deblurring problems.

Distribution of PGE in Permo-Triassic basalts of the Siberian Large Igneous Province

We have revealed the spatio-temporal regularities of distribution of platinum group elements (PGE) in basaltoids related to the activity of the Siberian mantle plume. As objects of study, we chose rift and flood basalts from the Norilsk district (sampled from the SD-9 borehole), flood basalts from the central part of the Tunguska syneclise (Lower Tunguska), Kuznetsk Basin traps, and subalkalic basalt from the Semeitau volcanoplutonic structure in eastern Kazakhstan. Based on the PGE patterns of basaltoids related to the activity of the Permo-Triassic Siberian plume, we have shown that the rocks that formed in the central part of the Siberian Large Igneous Province (LIP) at the early rift stage have low contents of PGE, whereas picrites and tholeiitic flood basalts have high contents. The rift (Semeitau structure) and flood (Kuznetsk Basin traps) basalts from the peripheral regions are characterized by extremely low PGE contents. The high PGE contents in magmas of the plume head are responsible for the high productivity of ultramafic-mafic trap magmatism. The elevated K contents in magmas and the high PGE contents in the mantle plume head are probably due to the ascent of deep-seated material from the core-lower-mantle boundary, as follows from the thermochemical model of the Siberian plume.

Buffering the savanna: fire regimes and disequilibrium ecology in West Africa

According to contemporary ecological theory, the mechanisms governing tree cover in savannas vary by precipitation level. In tropical areas with mesic rainfall levels, savannas are unstable systems in which disturbances, such as fire, determine the ratio of trees to grasses. Precipitation in these so-called “disturbance-driven savannas” is sufficient to support forest but frequent disturbances prevent transition to a closed canopy state. Building on a savanna buffering model we argue that a consistent fire regime is required to maintain savannas in mesic areas. We hypothesize that the spatiotemporal pattern of fires is highly regular and stable in these areas. Furthermore, because tree growth rates in savannas are a function of precipitation, we hypothesize that savannas with the highest rainfall levels will have the most consistent fire pattern and the most intense fires—thus the strongest buffering mechanisms. We analyzed the spatiotemporal pattern of burning over 11 years for a large subset of the West African savanna using a moderate resolution imaging spectroradiometer active fire product to document the fire regime for three savanna belts with different precipitation levels. We used LISA analysis to quantify the spatiotemporal patterns of fires, coefficient of variance to quantify differences in peak fire dates, and center or gravity pathways to characterize the spatiotemporal patterns of the fires for each area. Our analysis confirms that spatiotemporal regularity of the fire regime is greater for mesic areas that for areas where precipitation is lower and that areas with more precipitation have more regular fire regimes.

Water detection through spatio-temporal invariant descriptors

In this work, we aim to segment and detect water in videos. Water detection is beneficial for appllications such as video search, outdoor surveillance, and systems such as unmanned ground vehicles and unmanned aerial vehicles. The specific problem, however, is less discussed compared to general texture recognition. Here, we analyze several motion properties of water. First, we describe a video pre-processing step, to increase invariance against water reflections and water colours. Second, we investigate the temporal and spatial properties of water and derive corresponding local descriptors. The descriptors are used to locally classify the presence of water and a binary water detection mask is generated through spatio-temporal Markov Random Field regularization of the local classifications. Third, we introduce the Video Water Database, containing several hours of water and non-water videos, to validate our algorithm. Experimental evaluation on the Video Water Database and the DynTex database indicates the effectiveness of the proposed algorithm, outperforming multiple algorithms for dynamic texture recognition and material recognition.

Temporal sparsity exploiting nonlocal regularization for 4D computed tomography reconstruction.

X-ray imaging applications in medical and material sciences are frequently limited by the number of tomographic projections collected. The inversion of the limited projection data is an ill-posed problem and needs regularization. Traditional spatial regularization is not well adapted to the dynamic nature of time-lapse tomography since it discards the redundancy of the temporal information. In this paper, we propose a novel iterative reconstruction algorithm with a nonlocal regularization term to account for time-evolving datasets. The aim of the proposed nonlocal penalty is to collect the maximum relevant information in the spatial and temporal domains. With the proposed sparsity seeking approach in the temporal space, the computational complexity of the classical nonlocal regularizer is substantially reduced (at least by one order of magnitude). The presented reconstruction method can be directly applied to various big data 4D (x, y, z+time) tomographic experiments in many fields. We apply the proposed technique to modelled data and to real dynamic X-ray microtomography (XMT) data of high resolution. Compared to the classical spatio-temporal nonlocal regularization approach, the proposed method delivers reconstructed images of improved resolution and higher contrast while remaining significantly less computationally demanding.

Right-ventricular assessment using a segmented cine acquisition employing iterative SENSE reconstruction with spatio-temporal L1 regularization: Initial clinical experience

Background Cardiac MR (CMR) has emerged as the gold standard for assessing right-ventricular (RV) size and function with cine acquisitions. However, dyspnea often accompanies RV dysfunction, limiting patient ability to breathhold and consequently image quality at CMR. The application of a novel iterative reconstruction technique to segmented CMR cine acquisitions may enable higher acceleration factors, shortening image acquisitions, while maintaining image quality for RV assessment. The purpose of this study is to evaluate the clinical utility of a prototype iterative reconstruction algorithm utilizing spatio-temporal L1-regularization (iteratively reconstructed Sparse-SENSE) in the quantitative assessment of RV systolic function.

Nonlinear myocardial perfusion imaging with motion corrected reconstruction: validation via quantitative flow mapping

Background Myocardial perfusion imaging typically uses saturation recovery to generate T1 contrast during the Gd passage. Imaging protocols lead to a tradeoff between spatial/ temporal resolution, myocardial coverage, and SNR. To improve resolution while maintaining the image quality we propose a nonlinear iterative reconstruction. This method explicitly integrates respiratory motion correction into the reconstruction to permit spatio-temporal regularization in the presence of motion. Unlike most k-t methods, the motion corrected images are directly output. In this way, complete free-breathing acquisition is achieved. Nonlinear iterative reconstruction is difficult to characterize since implicit filtering resulting from regularization is signal dependent. We propose to validate the proposed method by comparing quantitative myocardial blood flow (MBF) against linear reconstruction. Methods

Convolutional Neural Network for Multi-Category Rapid Serial Visual Presentation BCI.

Brain computer interfaces rely on machine learning (ML) algorithms to decode the brain's electrical activity into decisions. For example, in rapid serial visual presentation (RSVP) tasks, the subject is presented with a continuous stream of images containing rare target images among standard images, while the algorithm has to detect brain activity associated with target images. Here, we continue our previous work, presenting a deep neural network model for the use of single trial EEG classification in RSVP tasks. Deep neural networks have shown state of the art performance in computer vision and speech recognition and thus have great promise for other learning tasks, like classification of EEG samples. In our model, we introduce a novel spatio-temporal regularization for EEG data to reduce overfitting. We show improved classification performance compared to our earlier work on a five categories RSVP experiment. In addition, we compare performance on data from different sessions and validate the model on a public benchmark data set of a P300 speller task. Finally, we discuss the advantages of using neural network models compared to manually designing feature extraction algorithms.

Evolution of the Barents Sea basin and oil and gas potential of coastal zones in the Kola region

The perspectives of development of the Varanger–Timan petroleum basin are considered. The Varanger–Timan oil-and-gas basin was formed in the Riphean and Vendian on the passive continental margin of the East European Plate. Evolution of the Barents–Kara region in the Mesoproterozoic and Neoproterozoic led to a mosaic junction of the lithospheric plates having different ages and having undergone significant alterations during the Caledonian and Variscan orogenies. The spatiotemporal regularities of the interaction between geodynamic processes and conditions providing for the formation of conventional and unconventional hydrocarbon fields are described.

Perceptual adaptation: Getting ready for the future

Perceptual systems continually adapt to changes in their sensory environment. Adaptation has been mainly thought of as a mechanism to exploit the spatiotemporal regularities of the sensory input in order to efficiently represent sensory information. Thus, most computational explanations for adaptation can be conceptualized as a form of Efficient coding. We propose a novel and more holistic explanation. We argue that perceptual adaptation is a process with which the perceptual system adjusts its operational regime to be best possible prepared for the future, i.e. the next sensory input. Crucially, we assume that these adjustments affect both the way the system represents sensory information (encoding) and how it interprets that information (decoding). We apply this idea in the context of a Bayesian observer model. More specifically, we propose that the perceptual system tries to predict the probability distribution from which the next sensory input is drawn. It does so by exploiting the fact that the recent stimulus history is generally a good predictor of the future and that the overall long-term stimulus distribution is stationary. We assume that this predicted probability distribution reflects the updated prior belief of the Bayesian observer. In addition, we assume that the system is adjusting its sensory representation according to the predicted future stimulus distribution via Efficient coding. Because this sensory representation directly constrains the likelihood function, we can define an optimal Bayesian observer model for any predicted distribution over the next sensory input. We demonstrate that this model framework provides a natural account of the reported adaptation after-effects for visual orientation and spatial frequency, both in terms of discrimination thresholds and biases. It also allows us to predict how these after-effects depend on the specific form of the short- and long-term input histories. Meeting abstract presented at VSS 2015

Spatio-Temporal Regularization for Longitudinal Registration to Subject-Specific 3d Template.

Neurodegenerative diseases such as Alzheimer's disease present subtle anatomical brain changes before the appearance of clinical symptoms. Manual structure segmentation is long and tedious and although automatic methods exist, they are often performed in a cross-sectional manner where each time-point is analyzed independently. With such analysis methods, bias, error and longitudinal noise may be introduced. Noise due to MR scanners and other physiological effects may also introduce variability in the measurement. We propose to use 4D non-linear registration with spatio-temporal regularization to correct for potential longitudinal inconsistencies in the context of structure segmentation. The major contribution of this article is the use of individual template creation with spatio-temporal regularization of the deformation fields for each subject. We validate our method with different sets of real MRI data, compare it to available longitudinal methods such as FreeSurfer, SPM12, QUARC, TBM, and KNBSI, and demonstrate that spatially local temporal regularization yields more consistent rates of change of global structures resulting in better statistical power to detect significant changes over time and between populations.

Spatiotemporal regularity in networks with stochastically varying links

In this work we investigate time varying networks with complex dynamics at the nodes. We consider two scenarios of network change in an interval of time: first, we have the case where each link can change with probability p t , i.e. the network changes occur locally and independently at each node. Secondly we consider the case where the entire connectivity matrix changes with probability p t , i.e. the change is global. We show that network changes, occuring both locally and globally, yield an enhanced range of synchronization. When the connections are changed slowly (i.e. p t is low) the nodes display nearly synchronized intervals interrupted by intermittent unsynchronized chaotic bursts. However when the connections are switched quickly (i.e. p t is large), the intermittent behavior quickly settles down to a steady synchronized state. Furthermore we find that the mean time taken to reach synchronization from generic random initial states is significantly reduced when the underlying links change more rapidly. We also analyse the probabilistic dynamics of the system with changing connectivity and the stable synchronized range thus obtained is in broad agreement with those observed numerically.

Studying the spatiotemporal variability of the components of the North Caspian Sea water balance using the water balance model

Considered is the water balance model of the estuarine seaside of the Volga and Ural rivers and the North Caspian Sea as well as of its separate parts. The following computational spatial elements, three parts of the North Caspian Sea, are singled out: the shallow zone of the Volga River estuarine seaside, the deep zone in the western part of the North Caspian Sea, and the eastern part of the North Caspian Sea. The input parameters in this model are evaporation from the water surface computed using the ISPAR technique and precipitation depth corrected using the technique of the correction of the measured amount of precipitation worked out by the Main Geophysical Observatory and Kazakh Research Hydrometeorological Institute. The computations are based on the data of observations at four weather stations: Zelenga (Russia), Peshnoi Island, Kulaly Island, and Fort Shevchenko (Kazakhstan). The water inflow to the Volga River delta top corrected by the value of natural evaporation loss in the delta is used as the water inflow to the North Caspian Sea. The water inflow from the Ural River delta to the North Caspian Sea is estimated from the data of Makhambet hydrological station. Using the water balance model, the water balance components can be computed for the separate parts of the North Caspian Sea and the water balance equation can be solved regarding the water balance outflow from these parts. The volume of the water outflow from the North Caspian Sea to the Middle Caspian Sea is determined as a result of water exchange between them. The variations of basic components of the North Caspian Sea following different typical scenarios (typical years determined from the Volga River runoff) are computed using its water balance model. Analyzed are the spatiotemporal regularities of water redistribution in the North Caspian Sea with account of the river runoff volume, evaporation loss, and amount of precipitation at different background levels of the Caspian Sea.

Joint leaf chlorophyll content and leaf area index retrieval from Landsat data using a regularized model inversion system (REGFLEC)

Leaf area index (LAI) and leaf chlorophyll content (Chll) represent key biophysical and biochemical controls on water, energy and carbon exchange processes in the terrestrial biosphere. In combination, LAI and Chll provide critical information on vegetation density, vitality and photosynthetic potentials. However, simultaneous retrieval of LAI and Chll from space observations is extremely challenging. Regularization strategies are required to increase the robustness and accuracy of retrieved properties and enable more reliable separation of soil, leaf and canopy parameters. To address these challenges, the REGularized canopy reFLECtance model (REGFLEC) inversion system was refined to incorporate enhanced techniques for exploiting ancillary LAI and temporal information derived from multiple satellite scenes. In this current analysis, REGFLEC is applied to a time-series of Landsat data.A novel aspect of the REGFLEC approach is the fact that no site-specific data are required to calibrate the model, which may be run in a largely automated fashion using information extracted entirely from image-based and other widely available datasets. Validation results, based upon in-situ LAI and Chll observations collected over maize and soybean fields in central Nebraska for the period 2001–2005, demonstrate Chll retrieval with a relative root-mean-square-deviation (RMSD) on the order of 19% (RMSD=8.42μgcm−2). While Chll retrievals were clearly influenced by the version of the leaf optical properties model used (PROSPECT), the application of spatio-temporal regularization constraints was shown to be critical for estimating Chll with sufficient accuracy. REGFLEC also reproduced the dynamics of in-situ measured LAI well (r2=0.85), but estimates were biased low, particularly over maize (LAI was underestimated by ~36 %). This disparity may be attributed to differences between effective and true LAI caused by significant foliage clumping not being properly accounted for in the canopy reflectance model (SAIL). Additional advances in the retrieval of canopy biophysical and leaf biochemical constituents will require innovative use of existing remote sensing data within physically realistic canopy reflectance models along with the ability to exploit the enhanced spectral and spatial capabilities of upcoming satellite systems.

Space–time interaction of residential burglaries in Wuhan, China

Borrowing methods from epidemiology, studies of spatiotemporal regularities of crime have been booming in various industrialized countries. However, few such attempts are empirical studies using crime data in developing countries due to a lack of data availability. Utilizing a recent burglary dataset in Wuhan, the fourth largest city in China, current research applied the sequential kernel density estimation and the space–time K-function methods to analyze the spatiotemporal changes of hotspots of residential burglaries. The results show that, both spatial and spatiotemporal clustering exists. The hotspots were relatively stable over time. The space–time clustering, however, shows significant concentrations both in space and over time. In addition, analytic results show significant effects of distance decay in terms of occurrences of burglary incidents along the spatial and temporal dimensions. Moreover, findings from the research provide critical information on the space–time rhythm of crime, and therefore can be utilized in crime prevention practice. Finally, the implications of the findings and limitations are discussed.

Non-invasive imaging of propagating cortical rhythms

Event Abstract Back to Event Non-invasive imaging of propagating cortical rhythms Gustavo Deco1* and Rikkert Hindriks1* 1 Universitat Pompeu Fabra, Department of Information and Communication Technologies, Spain Although cortical rhythms are known to play a fundamental role in perception and cognition, their spatiotemporal behavior is not well characterized yet, which hampers understanding of the involved mechanisms. The dominating view is that cortical rhythms are organized as functional networks in which spatially confined rhythms interact through white-matter pathways. In contrast, voltage sensitive dye imaging studies suggest that, at least on small spatial scales, cortical rhythms propagate and are organized as traveling waves. We argue that this view is appropriate also for large-scale rhythms as recorded with EEG and MEG and present data to illustrate this view. We propose improvements on existing methods for reconstructing the cortical currents underlying propagating rhythms as recorded with EEG and MEG, with particular focus on spatiotemporal regularization techniques. We compare the different methods through biophysical simulations. Keywords: EEG, non-invasive imaging, cortical rhythms, neural circuits, computational neuroscience, propagation Conference: B·DEBATE | A Dialogue with the Cerebral Cortex: Cortical Function and Interfacing (Workshop), Barcelona, Spain, 29 Apr - 30 Apr, 2015. Presentation Type: Poster Presentation Topic: SESSION 1: Cortical Function and Computations Citation: Deco G and Hindriks R (2015). Non-invasive imaging of propagating cortical rhythms. Front. Syst. Neurosci. Conference Abstract: B·DEBATE | A Dialogue with the Cerebral Cortex: Cortical Function and Interfacing (Workshop). doi: 10.3389/conf.fnsys.2015.06.00014 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 02 Apr 2015; Published Online: 06 May 2015. * Correspondence: Dr. Gustavo Deco, Universitat Pompeu Fabra, Department of Information and Communication Technologies, Barcelona, Spain, gustavo.deco@upf.edu Dr. Rikkert Hindriks, Universitat Pompeu Fabra, Department of Information and Communication Technologies, Barcelona, Spain, Rikkert.Hindriks@upf.edu Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Gustavo Deco Rikkert Hindriks Google Gustavo Deco Rikkert Hindriks Google Scholar Gustavo Deco Rikkert Hindriks PubMed Gustavo Deco Rikkert Hindriks Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.

Optical Flow on Moving Manifolds

Optical flow is a powerful tool for the study and analysis of motion in a sequence of images. In this paper we study a Horn--Schunck-type spatio-temporal regularization functional for image sequences that have a non-Euclidean, time varying image domain. To that end we construct a Riemannian metric that describes the deformation and structure of this evolving surface. The resulting functional can be seen as a natural geometric generalization of previous work by Weickert and Schnörr in 2001 and Lefèvre and Baillet in 2008 for static image domains. In this paper we show the existence and well-posedness of the corresponding optical flow problem and derive necessary and sufficient optimality conditions. We demonstrate the functionality of our approach in two experiments using both synthetic and real data.

Correlating mobility with social encounters: distributed localization in sparse mobile networks

Most existing connectivity-based localization algorithms require high node density which is unavailable in many large-scale sparse mobile networks. By analyzing large datasets of real user traces from Dartmouth and MIT, we observe that user mobility exhibits high spatiotemporal regularity and, more importantly, that user mobility is strongly correlated with the user's social encounters (including so called Familiar Strangers). Motivated by these important observations, we propose a distributed localization scheme called SOMA that is particularly suitable for sparse mobile networks. To exploit the correlation between mobility and social encounters, we formulate the localization process as an optimization problem with the objective of maximizing the probability of visiting a sequence of locations when the user witnesses the given set of social encounters at different time. Employing the Hidden Markov Model, we design an efficient algorithm based on dynamic programming for solving the optimization problem. SOMA is fully distributed, in which each user only makes use of the connectivity information with other users. Since different users may have varying levels of mobility regularity, one critical challenge with SOMA is that a user with weak mobility regularity may result in poor localization accuracy. We introduce the concept of mobility irregularity to distinguish users. Then, one optimization is made to SOMA that allows a user with weak mobility regularity to leverage the locations from the users encounters. Experimental results based on large-scale real traces demonstrate that SOMA achieves much smaller localization error than many state-of-the-art localization schemes, but requires it minimal running time.