A well-known result due to J. T. Stafford asserts that a stably free left module M over the Weyl algebras D = An(k) or Bn(k) − where k is a field of characteristic 0 − with rankD(M) ≥ 2 is free. The purpose of this paper is to present a new constructive proof of this result as well as an effective algorithm for the computation of bases of M . This algorithm, based on the new constructive proofs...

In this paper, we propose a particle filtering approach for tracking applications in image sequences. The system we propose combines a measurement equation and a dynamic equation which both depend on the image sequence. Taking into account several possible observations, the likelihood is modeled as a linear combination of Gaussian laws. Such a model allows inferring an analytic expression of th...

In an M × N interference network, there are M transmitters and N receivers with each transmitter having independent messages for each of the 2 −1 possible non-empty subsets of the receivers. We consider the 2 × 2 interference network with 6 possible messages, of which the 2 × 2 interference channel and X channel are special cases obtained by using only 2 and 4 messages respectively. Starting fr...

Abstract. Let Θ be a smooth compact oriented manifold without boundary, imbedded in a euclidean space E, and let γ be a smooth map of Θ into a Riemannian manifold Λ. An unknown state θ ∈ Θ is observed via X = θ + ǫξ where ǫ > 0 is a small parameter and ξ is a white Gaussian noise. For a given smooth prior λ on Θ and smooth estimators g(X) of the map γ we have derived a second-order asymptotic e...

The problem of extracting the relevant aspects of data was addressed through the information bottleneck (IB) method, by (soft) clustering one variable while preserving information about another relevance variable. An interesting question addressed in the current work is the extension of these ideas to obtain continuous representations that preserve relevant information, rather than discrete clu...

The quality of the RGB color image degrades from the minute it is captured to the time it is displayed to the human observer. The image is subject to many kinds of distortions during the stages that it might pass through such as storing, processing, compressing, and transmitting, thus enhancing the image quality is a major important issue. This paper will introduce the effects of salt&pepper an...

Single-channel late reverberation suppression algorithms need estimates of the late reverberance spectral variance (LRSV) in order to suppress the late reverberance. Often the LRSV estimators are derived from a statistical room impulse response (RIR) model. Usually the late reverberation is modeled as a white Gaussian noise sequence with exponentially decaying variance. The whiteness assumption...

The work is addressed to provide realistic modelling of a generic noise probability density function (pdf), in order to optimize signal detection in non-Gaussian environments. The target is to obtain a model depending on few parameters (quick and easy to estimate), and so general to be able to describe many kinds of noise (e.g., symmetric or asymmetric, with variable sharpness). To this end, a ...

We propose a method which refines the range measurement of range finders by computing correspondences of vertices of multiple range images acquired from various viewpoints. Our method assumes that a range image acquired by a laser range finder has anisotropic error distribution which is parallel to the ray direction. Thus, we find corresponding points of range images along with the ray directio...

Consider the high-dimensional linear regression model y = Xβ∗ +w, where y ∈ R is an observation vector, X ∈ R is a design matrix with d > n, the quantity β∗ ∈ R is an unknown regression vector, and w ∼ N (0, σI) is additive Gaussian noise. This paper studies the minimax rates of convergence for estimating β∗ in either l2-loss and l2-prediction loss, assuming that β∗ belongs to an lq-ball Bq(Rq)...