A time domain blind source separation algorithm of convolutive sound mixtures is studied based on a compact partial inversion formula in closed form. An L1-constrained minimization problem is formulated to find demixing filter coefficients for source separation while capturing scaling invariance and sparseness of solutions. The minimization aims to reduce (lagged) cross correlations of the mixture signals, which are modeled stochastically. The problem is non-convex, however it is put in a nonlinear least squares form where the robust and convergent Levenberg-Marquardt iterative method is applicable to compute local minimizers. Efficiency is achieved in recovering lower dimensional demixing filter solutions than the physical ones. Computations on recorded and synthetic mixtures show satisfactory performance, and are compared with other iterative methods.

We study sparse blind source separation (BSS) for a class of positive and partially overlapped signals. The signals are only allowed to have nonoverlapping at certain locations, while they could overlap with each other elsewhere. For nonnegative data, a novel approach has been proposed by Naanaa and Nuzillard (NN) assuming that nonoverlapping exists for each source signal at some location of acquisition variable. However, the NN method introduces errors (spurious peaks) in the output when their nonoverlapping condition is not satisfied. To resolve this problem and improve robustness of separation, postprocessing techniques are developed in two aspects. One is to detect coherent and uncertain components from NN outputs by using multiple mixture data, then removing the uncertain portion to enhance signals. The other is to find better estimation of mixing matrix by leveraging reliable source peak

A collaborative convex framework for factoring a data matrix <i>X</i> into a nonnegative product <i>AS</i> , with a sparse coefficient matrix <i>S</i> , is proposed. We restrict the columns of the dictionary matrix <i>A</i> to coincide with certain columns of the data matrix <i>X</i> , thereby guaranteeing a physically meaningful dictionary and dimensionality reduction. We use <i>l</i> _1, regularization to select the dictionary from the data and show that this leads to an exact convex relaxation of <i>l</i> ₀ in the case of distinct noise-free data. We also show how to relax the restriction-to- <i>X</i> constraint by initializing an alternating minimization approach with the solution of the convex model, obtaining a dictionary close to but not necessarily in <i>X</i> . We focus on applications of the proposed framework to hyperspectral endmember and abundance identification and also show an application to blind source separation of nuclear magnetic resonance data.

In geometric modeling and processing, computer graphics and computer vision, smooth surfaces are approximated by discrete triangular meshes reconstructed from sample points on the surfaces. A fundamental problem is to design rigorous algorithms to guarantee the geometric approximation accuracy by controlling the sampling density. This paper gives explicit formulae to the bounds of Hausdorff distance, normal distance and Riemannian metric distortion between the smooth surface and the discrete mesh in terms of principle curvature and the radii of geodesic circum-circle of the triangles. These formulae can be directly applied to design sampling density for data acquisitions and surface reconstructions. Furthermore, we prove that the meshes induced from the Delaunay triangulations of the dense samples on a smooth surface are convergent to the smooth surface under both Hausdorff distance and normal

We describe a high-resolution, real-time 3D absolute coordinate measurement system based on a phase-shifting method. It acquires 3D shape at 30 frames per second (fps), with 266K points per frame. A tiny marker is encoded in the projected fringe pattern, and detected by software from the texture image and the gamma map. Absolute 3D coordinates are obtained from the detected marker position and the calibrated system parameters. To demonstrate the performance of the system, we measure a hand moving over a depth distance of approximately 700 mm, and human faces with expressions. Applications of such a system include manufacturing, inspection, entertainment, security, medical imaging.