Conjugate mixture models for clustering multimodal data

The problem of multimodal clustering arises whenever the data are gathered with several physically different sensors. Observations from different modalities are not necessarily aligned in the sense there there is no obvious way to associate or compare them in some common space. A solution may consist in considering multiple clustering tasks independently for each modality. The main difficulty with such an approach is to guarantee that the unimodal clusterings are mutually consistent. In this letter, we show that multimodal clustering can be addressed within a novel framework: conjugate mixture models. These models exploit the explicit transformations that are often available between an unobserved parameter space (objects) and each of the observation spaces (sensors). We formulate the problem as a likelihood maximization task and derive the associated conjugate expectation-maximization algorithm. The convergence properties of the proposed algorithm are thoroughly investigated. Several local and global optimization techniques are proposed in order to increase its convergence speed. Two initialization strategies are proposed and compared. A consistent model selection criterion is proposed. The algorithm and its variants are tested and evaluated within the task of 3D localization of several speakers using both auditory and visual data.     

BSLIM: Spectral Localization by Imaging With Explicit B0 Field Inhomogeneity Compensation

Magnetic resonance spectroscopy imaging (MRSI) is an attractive tool for medical imaging. However, its practical use is often limited by the intrinsic low spatial resolution and long acquisition time. Spectral localization by imaging (SLIM) has been proposed as a non-Fourier reconstruction algorithm that incorporates spatial a priori information about spectroscopically uniform compartments. Unfortunately, the influence of the magnetic field inhomogeneity - in particular, the susceptibility effects at tissues' boundaries - undermines the validity of the compartmental model. Therefore, we propose BSLIM as an extension of SLIM with field inhomogeneity compensation. A B₀-field inhomogeneity map, which can be acquired rapidly and at high resolution, is used by the new algorithm as additional a priori information. We show that the proposed method is distinct from the generalized SLIM (GSLIM) framework. Experimental results of a two-compartment phantom demonstrate the feasibility of the method and the importance of inhomogeneity compensation.     

BSLIM: spectral localization by imaging with explicit B0 field inhomogeneity compensation.

Magnetic resonance spectroscopy imaging (MRSI) is an attractive tool for medical imaging. However, its practical use is often limited by the intrinsic low spatial resolution and long acquisition time. Spectral localization by imaging (SLIM) has been proposed as a non-Fourier reconstruction algorithm that incorporates spatial a priori information about spectroscopically uniform compartments. Unfortunately, the influence of the magnetic field inhomogeneity--in particular, the susceptibility effects at tissues' boundaries--undermines the validity of the compartmental model. Therefore, we propose BSLIM as an extension of SLIM with field inhomogeneity compensation. A B0-field inhomogeneity map, which can be acquired rapidly and at high resolution, is used by the new algorithm as additional a priori information. We show that the proposed method is distinct from the generalized SLIM (GSLIM) framework. Experimental results of a two-compartment phantom demonstrate the feasibility of the method and the importance of inhomogeneity compensation.     

Scaled equation for the isochoric heat capacity of methane-ethane mixtures in the critical region

Results of an experimental study of the isochotic heat capacity of methaneethane mixtures in a wide region around the liquid-gas critical line are presented. The data are represented by a universal scaled equation for critical mixtures.     

From differential equations to the construction of new wavelet-like bases

In this paper, an approach is introduced based on differential operators to construct wavelet-like basis functions. Given a differential operator L with rational transfer function, elementary building blocks are obtained that are shifted replicates of the Green's function of L. It is shown that these can be used to specify a sequence of embedded spline spaces that admit a hierarchical exponential B-spline representation. The corresponding B-splines are entirely specified by their poles and zeros; they are compactly supported, have an explicit analytical form, and generate multiresolution Riesz bases. Moreover, they satisfy generalized refinement equations with a scale-dependent filter and lead to a representation that is dense in L/sub 2/. This allows us to specify a corresponding family of semi-orthogonal exponential spline wavelets, which provides a major extension of earlier polynomial spline constructions. These wavelets are completely characterized, and it is proven that they satisfy the following remarkable properties: 1) they are orthogonal across scales and generate Riesz bases at each resolution level; 2) they yield unconditional bases of L/sub 2/-either compactly supported (B-spline-type) or with exponential decay (orthogonal or dual-type); 3) they have N vanishing exponential moments, where N is the order of the differential operator; 4) they behave like multiresolution versions of the operator L from which they are derived; and 5) their order of approximation is (N-M), where N and M give the number of poles and zeros, respectively. Last but not least, the new wavelet-like decompositions are as computationally efficient as the classical ones. They are computed using an adapted version of Mallat's filter bank algorithm, where the filters depend on the decomposition level.     

Isochoric specific heat in the methane-ethane system around the liquid-gas critical line

Experimental and theoretical studies have been made on the behavior of the isochoric specific heat for binary methane-ethane mixtures in the critical region.