Multichannel high resolution NMF for modelling convolutive mixtures of non-stationary signals in the time-frequency domain

Several probabilistic models involving latent components have been proposed for modeling time-frequency (TF) representations of audio signals such as spectrograms, notably in the nonnegative matrix factorization (NMF) literature. Among them, the recent high-resolution NMF (HR-NMF) model is able to take both phases and local correlations in each frequency band into account, and its potential has been illustrated in applications such as source separation and audio inpainting. In this paper, HR-NMF is extended to multichannel signals and to convolutive mixtures. The new model can represent a variety of stationary and non-stationary signals, including autoregressive moving average (ARMA) processes and mixtures of damped sinusoids. A fast variational expectation-maximization (EM) algorithm is proposed to estimate the enhanced model. This algorithm is applied to piano signals, and proves capable of accurately modeling reverberation, restoring missing observations, and separating pure tones with close frequencies

A hybrid approach for stain normalisation in digital histopathological images

Stain in-homogeneity adversely affects segmentation and quantifi-cation of tissues in histology images. Stain normalisation techniques have been used to standardise the appearance of images. However, most the available stain normalisation techniques only work on a particular kind of stain images. In addition, some of these techniques fail to utilise both the spatial and tex-tural information in histology images, leading to image tissue distortion. In this paper, a hybrid approach has been developed, based on an octree colour quantisation algorithm combined with the Beer-Lambert law, a modified blind source separation algorithm, and a modified colour transfer approach. The hybrid method consists of two stages the stain separation stage and colour transfer stage. An octree colour quantisation algorithm combined with Beer-Lambert law, and a modified blind source separation algorithm are used during the stain separation stage to computationally estimate the amount of stain in an histology image based on its chromatic and luminous response. A modified colour transfer algorithm is used during the colour transfer stage to minimise the effect of varying staining and illumination. The hybrid method addresses the colour variation problem in both H&DAB (Haemotoxylin and Diaminoben-zidine) and H&E (Haemotoxylin and Eosin) stain images. The stain normali-sation method is validated against ground truth data. It is widely known that the Beer-Lambert law applies to only stains (such as haematoxylin, eosin) that absorb light. We demonstrate that the Beer-Lambert law applies is applicable to images containing a DAB stain. Better stain normalisation results are obtained in both H&E and H&DAB images

Iterative Separation of Note Events from Single-Channel Polyphonic Recordings

This thesis is concerned with the separation of audio sources from single-channel polyphonic musical recordings using the iterative estimation and separation of note events. Each event is defined as a section of audio containing largely harmonic energy identified as coming from a single sound source. Multiple events can be clustered to form separated sources. This solution is a model-based algorithm that can be applied to a large variety of audio recordings without requiring previous training stages. The proposed system embraces two principal stages. The first one considers the iterative detection and separation of note events from within the input mixture. In every iteration, the pitch trajectory of the predominant note event is automatically selected from an array of fundamental frequency estimates and used to guide the separation of the event's spectral content using two different methods: time-frequency masking and time-domain subtraction. A residual signal is then generated and used as the input mixture for the next iteration. After convergence, the second stage considers the clustering of all detected note events into individual audio sources. Performance evaluation is carried out at three different levels. Firstly, the accuracy of the note-event-based multipitch estimator is compared with that of the baseline algorithm used in every iteration to generate the initial set of pitch estimates. Secondly, the performance of the semi-supervised source separation process is compared with that of another semi-automatic algorithm. Finally, a listening test is conducted to assess the audio quality and naturalness of the separated sources when they are used to create stereo mixes from monaural recordings. Future directions for this research focus on the application of the proposed system to other music-related tasks. Also, a preliminary optimisation-based approach is presented as an alternative method for the separation of overlapping partials, and as a high resolution time-frequency representation for digital signals

The MVGC multivariate Granger causality toolbox: a new approach to Granger-causal inference

Background: Wiener-Granger causality (“G-causality”) is a statistical notion of causality applicable to time series data, whereby cause precedes, and helps predict, effect. It is defined in both time and frequency domains, and allows for the conditioning out of common causal influences. Originally developed in the context of econometric theory, it has since achieved broad application in the neurosciences and beyond. Prediction in the G-causality formalism is based on VAR (Vector AutoRegressive) modelling. New Method: The MVGC Matlab c Toolbox approach to G-causal inference is based on multiple equivalent representations of a VAR model by (i) regression parameters, (ii) the autocovariance sequence and (iii) the cross-power spectral density of the underlying process. It features a variety of algorithms for moving between these representations, enabling selection of the most suitable algorithms with regard to computational efficiency and numerical accuracy. Results: In this paper we explain the theoretical basis, computational strategy and application to empirical G-causal inference of the MVGC Toolbox. We also show via numerical simulations the advantages of our Toolbox over previous methods in terms of computational accuracy and statistical inference. Comparison with Existing Method(s): The standard method of computing G-causality involves estimation of parameters for both a full and a nested (reduced) VAR model. The MVGC approach, by contrast, avoids explicit estimation of the reduced model, thus eliminating a source of estimation error and improving statistical power, and in addition facilitates fast and accurate estimation of the computationally awkward case of conditional G-causality in the frequency domain. Conclusions: The MVGC Toolbox implements a flexible, powerful and efficient approach to G-causal inference. Keywords: Granger causality, vector autoregressive modelling, time series analysi

Stain deconvolution using statistical analysis of multi-resolution stain colour representation

Stain colour estimation is a prominent factor of the analysis pipeline in most of histology image processing algorithms. Providing a reliable and efficient stain colour deconvolution approach is fundamental for robust algorithm. In this paper, we propose a novel method for stain colour deconvolution of histology images. This approach statistically analyses the multi-resolutional representation of the image to separate the independent observations out of the correlated ones. We then estimate the stain mixing matrix using filtered uncorrelated data. We conducted an extensive set of experiments to compare the proposed method to the recent state of the art methods and demonstrate the robustness of this approach using three different datasets of scanned slides, prepared in different labs using different scanners