3 research outputs found
The Linear Model under Mixed Gaussian Inputs: Designing the Transfer Matrix
Suppose a linear model y = Hx + n, where inputs x, n are independent Gaussian
mixtures. The problem is to design the transfer matrix H so as to minimize the
mean square error (MSE) when estimating x from y. This problem has important
applications, but faces at least three hurdles. Firstly, even for a fixed H,
the minimum MSE (MMSE) has no analytical form. Secondly, the MMSE is generally
not convex in H. Thirdly, derivatives of the MMSE w.r.t. H are hard to obtain.
This paper casts the problem as a stochastic program and invokes gradient
methods. The study is motivated by two applications in signal processing. One
concerns the choice of error-reducing precoders; the other deals with selection
of pilot matrices for channel estimation. In either setting, our numerical
results indicate improved estimation accuracy - markedly better than those
obtained by optimal design based on standard linear estimators. Some
implications of the non-convexities of the MMSE are noteworthy, yet, to our
knowledge, not well known. For example, there are cases in which more pilot
power is detrimental for channel estimation. This paper explains why
Speech Enhancement using Intra-frame Dependency in DCT Domain
In this paper, we present a new speech enhancement approach,
that is based on exploiting the intra-frame dependency
of discrete cosine transform (DCT) domain coefficients.
It can be noted that the existing enhancement techniques
treat the transformdomain coefficients independently.
Instead of this traditional approach of independently processing
the scalars, we split the DCT domain noisy speech
vector into sub-vectors and each sub-vector is enhanced independently.
Through this sub-vector based approach, the
higher dimensional enhancement advantage, viz. non-linear
dependency, is exploited. In the developed method, each
clean speech sub-vector is modeled using a Gaussian mixture
(GM) density. We show that the proposed Gaussian
mixture model (GMM) based DCT domain method, using
sub-vector processing approach, provides better performance
than the conventional approach of enhancing the transform
domain scalar components independently. Performance improvement
over the recently proposed GMM based time domain
approach is also shown