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The image restoration problem deals with images in which information has been degraded by blur or noise. In this work, we present a new method for image deblurring by solving a regularized linear least-squares problem. In the proposed method, a synthetic perturbation matrix with a bounded norm is forced into the discrete ill-conditioned model matrix. This perturbation is added to enhance the singular-value...
A method for penalized likelihood tomographic reconstruction is presented which is based on a spatially adaptive stochastic image model. The model imposes onto the image a smoothing Gaussian prior whose parameters follow a Gamma distribution. Three variations of the model are examined: (i) a stationary model, where the Gamma distribution has the same constant parameter for the entire image, (ii) a...
We address the problem of selecting, from a given dictionary, a subset of predictors whose linear combination provides the best description for the vector of measurements. To this end, we apply the well-known matching pursuit algorithm (MPA). Even if there are theoretical results on the performance of MPA, there is no widely accepted rule for stopping the algorithm. In this work, we focus on stopping...
In this paper, we apply probability density function (PDF) projection to arrive at an exact closed-form expression for the marginal distribution of the visible data of a restricted Boltzmann machine (RBM) without requiring integrating over the distribution of the hidden variables or needing to know the partition function. We express the visible data marginal as a projected PDF based on a set of sufficient...
We study joint estimation of the channel impulse response (CIR) and of the carrier frequency offset (CFO) for linear channels in which both the CIR and the noise statistics vary periodically in time. This model corresponds to interference-limited communications as well as to power line communication and doubly selective channels. We first consider the joint maximum likelihood estimator (JMLE) for...
In kernel methods, temporal information on the data is commonly included by using time-delayed embeddings as inputs. Recently, an alternative formulation was proposed by defining a γ-filter explicitly in a reproducing kernel Hilbert space, giving rise to a complex model where multiple kernels operate on different temporal combinations of the input signal. In the original formulation, the kernels are...
We propose an online algorithm for supervised learning with strong performance guarantees under the empirical zero-one loss. The proposed method adaptively partitions the feature space in a hierarchical manner and generates a powerful finite combination of basic models. This provides algorithm to obtain a strong classification method which enables it to create a linear piecewise classifier model that...
Segmentation is one of the central problems in image analysis, where the goal is to partition the image domain into regions exhibiting some sort of homogeneity. Most often, the partition is obtained by solving a combinatorial optimization problem, which is, in general, NP-hard. In this paper, we follow an alternative approach, using a Bayesian formulation based on a set of hidden real-valued random...
The autoregressive models (AR) and moving-average models (MA) are regularly used in signal processing. Previous works have been done on dissimilarity measures between AR models by using a Riemannian distance, the Jeffrey's divergence (JD) and the spectral distances such as the Itakura-Saito divergence. In this paper, we compare the Rao distance and the JD for MA models and more particularly in the...
In this paper we consider the problem of learning the genetic-interaction-map, i.e., the topology of a directed acyclic graph (DAG) of genetic interactions from noisy double knockout (DK) data. Based on a set of well established biological interaction models we detect and classify the interactions between genes. Furthermore, we propose a novel linear integer optimization framework called Genetic-Interactions-Detector...
This paper studies the detection of anomalies, or defects, on wheels' surface. The wheel surface is inspected using an imaging system, placed over the conveyor belt. Due to the nature of the wheels, the different elements are analyzed separately. Because many different types of wheels can be manufactured, it is proposed to detect any anomaly using a general and original adaptive linear parametric...
Modern signal processing methods rely strongly on Bayesian statistical models to solve challenging problems. This paper considers the objective comparison of two alternative Bayesian models, for scenarios with no ground truth available, and with a focus on model selection. Existing model selection approaches are generally difficult to apply to signal processing because they are unsuitable for models...
A new method for the blind identification of large-scale finite impulse response (FIR) systems is presented. It exploits the fact that the system coefficients in large-scale problems often depend on much fewer parameters than the total number of entries in the coefficient vectors. We use low-rank models to compactly represent matricized versions of these compressible system coefficients. We show that...
The electrocardiogram (ECG) is one of the most important physiological signals to monitor the health status of a patient. Technological advances allow the size and weight of ECG acquisition devices to be strongly reduced so that wearable systems are now available, even though the computational power and memory capacity is generally limited. An ECG signal is affected by several artifacts, among which...
Learning the underlying low-dimensional subspace from streaming incomplete high-dimensional observations data has attracted considerable attention lately. In this paper, we present a new computationally efficient Bayesian scheme for online low-rank subspace learning and matrix completion. The proposed scheme builds upon a properly defined hierarchical Bayesian model that explicitly imposes low rank...
In this paper we describe two methods to estimate the concentration of polycyclic aromatic hydrocarbons (PAHs) in a methanol solution, from a gas chromatography analysis. We present an innovative stochastic forward model based on a molecular random walk. To infer on PAHs concentration profiles, we use two inversion methods. The first one is a Bayesian estimator using a MCMC algorithm and Gibbs sampling...
Music artist (i.e., singer) recognition is a challenging task in Music Information Retrieval (MIR). The presence of different musical instruments, the diversity of music genres and singing techniques make the retrieval of artist-relevant information from a song difficult. Many authors tried to address this problem by using complex features or hybrid systems. In this paper, we propose new song-level...
The LASSO (Least Absolute Shrinkage and Selection Operator) has been a popular technique for simultaneous linear regression estimation and variable selection. Robust approaches for LASSO are needed in the case of heavy-tailed errors or severe outliers. We propose a novel robust LASSO method that has a non-parametric flavor: it solves a criterion function based on ranks of the residuals with LASSO...
A non-linear active noise control (ANC) scheme, which is based on an even mirror Fourier non-linear filter has been developed in this paper. A new weight update mechanism for the proposed scheme has been suggested and the range of the learning rate which ensures stability has been derived. The noise mitigation achieved using the new scheme has been compared with that obtained using a functional link...
In the literature of machine learning, a class of unsupervised approaches is based on Dirichlet process mixture models. These approaches fall into the category of nonparametric Bayesian methods, and they find a wide range of applications including in biology, computer science, engineering, and finance. An important assumption of the Dirichlet process mixture models is that the data are exchangeable...
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