Rasmus Kongsgaard Olsson

Linear Regression on Sparse Features for Single-Channel Speech Separation

In this work we address the problem of separating multiple speakers from a single microphone recording. We formulate a linear regression model for estimating each speaker based on features derived from the mixture. The employed feature representation is a sparse, non-negative encoding of the speech mixture in terms of pre-learned speaker-dependent dictionaries. Previous work has shown that this feature representation by itself provides some degree of separation. We show that the performance is significantly improved when regression analysis is performed on the sparse, non-negative features, both compared to linear regression on spectral features and compared to separation based directly on the non-negative sparse features.

State-Space Models: From the EM Algorithm to a Gradient Approach

Slow convergence is observed in the EM algorithm for linear state-space models. We propose to circumvent the problem by applying any off-the-shelf quasi-Newton-type optimizer, which operates on the gradient of the log-likelihood function. Such an algorithm is a practical alternative due to the fact that the exact gradient of the log-likelihood function can be computed by recycling components of the expectation-maximization (EM) algorithm. We demonstrate the efficiency of the proposed method in three relevant instances of the linear state-space model. In high signal-to-noise ratios, where EM is particularly prone to converge slowly, we show that gradient-based learning results in a sizable reduction of computation time.

Blind Separation of More Sources than Sensors in Convolutive Mixtures

We demonstrate that blind separation of more sources than sensors can be performed based solely on the second order statistics of the observed mixtures. This generalization of well-known robust algorithms are suited for equal number of sources and sensors. It is assumed that the sources are non-stationary and sparsely distributed in the time-frequency plane. The mixture model is convolutive, i.e. acoustic setups such as the cocktail party problem are contained. The limits of identifiability are determined in the framework of the PARAFAC model. In the experimental section, it is demonstrated that real room recordings of 3 speakers by 2 microphones can be separated using the method

Linear Program Differentiation for Single-Channel Speech Separation

Many apparently difficult problems can be solved by reduction to linear programming. Such problems are often subproblems within larger systems. When gradient optimisation of the entire larger system is desired, it is necessary to propagate gradients through the internally-invoked LP solver. For instance, when an intermediate quantity z is the solution to a linear program involving constraint matrix A, a vector of sensitivities dE/dz will induce sensitivities dE/dA. Here we show how these can be efficiently calculated, when they exist. This allows algorithmic differentiation to be applied to algorithms that invoke linear programming solvers as subroutines, as is common when using sparse representations in signal processing. Here we apply it to gradient optimisation of over complete dictionaries for maximally sparse representations of a speech corpus. The dictionaries are employed in a single-channel speech separation task, leading to 5 dB and 8 dB target-to-interference ratio improvements for same-gender and opposite-gender mixtures, respectively. Furthermore, the dictionaries are successfully applied to a speaker identification task.

Estimating the Number of Sources in a Noisy Convolutive Mixture Using BIC

The number of source signals in a noisy convolutive mixture is determined based on the exact log-likelihoods of the candidate models. In (Olsson and Hansen, 2004), a novel probabilistic blind source separator was introduced that is based solely on the time-varying second-order statistics of the sources. The algorithm, known as ‘KaBSS’, employs a Gaussian linear model for the mixture, i.e. AR models for the sources, linear mixing filters and a white Gaussian noise model. Using an EM algorithm, which invokes the Kalman smoother in the E-step, all model parameters are estimated and the exact posterior probability of the sources conditioned on the observations is obtained. The log-likelihood of the parameters is computed exactly in the process, which allows for model evidence comparison assisted by the BIC approximation. This is used to determine the activity pattern of two speakers in a convolutive mixture of speech signals.

Femtosecond all-polarization-maintaining fiber laser operating at 1028 nm

We present an effective solution for an all-polarization-maintaining modelocked femtosecond fiber laser operating at the central wavelength of 1028 nm. The laser is based on an Yb-doped active fiber. Modelocking is enabled by a semiconductor saturable absorber mirror, and the central wavelength is enforced by a fiber Bragg grating. The laser is self-starting and demonstrates excellent stability against Q-switching. Pulse energies reach 13 nJ at 34 MHz repetition rate. External compression leads to near transform-limited pulses of 140 fs.