Role of homeostasis in learning sparse representations

Neurons in the input layer of primary visual cortex in primates develop edge-like receptive fields. One approach to understanding the emergence of this response is to state that neural activity has to efficiently represent sensory data with respect to the statistics of natural scenes. Furthermore, it is believed that such an efficient coding is achieved using a competition across neurons so as to generate a sparse representation, that is, where a relatively small number of neurons are simultaneously active. Indeed, different models of sparse coding, coupled with Hebbian learning and homeostasis, have been proposed that successfully match the observed emergent response. However, the specific role of homeostasis in learning such sparse representations is still largely unknown. By quantitatively assessing the efficiency of the neural representation during learning, we derive a cooperative homeostasis mechanism that optimally tunes the competition between neurons within the sparse coding algorithm. We apply this homeostasis while learning small patches taken from natural images and compare its efficiency with state-of-the-art algorithms. Results show that while different sparse coding algorithms give similar coding results, the homeostasis provides an optimal balance for the representation of natural images within the population of neurons. Competition in sparse coding is optimized when it is fair. By contributing to optimizing statistical competition across neurons, homeostasis is crucial in providing a more efficient solution to the emergence of independent components

4D Seismic History Matching Incorporating Unsupervised Learning

The work discussed and presented in this paper focuses on the history matching of reservoirs by integrating 4D seismic data into the inversion process using machine learning techniques. A new integrated scheme for the reconstruction of petrophysical properties with a modified Ensemble Smoother with Multiple Data Assimilation (ES-MDA) in a synthetic reservoir is proposed. The permeability field inside the reservoir is parametrised with an unsupervised learning approach, namely K-means with Singular Value Decomposition (K-SVD). This is combined with the Orthogonal Matching Pursuit (OMP) technique which is very typical for sparsity promoting regularisation schemes. Moreover, seismic attributes, in particular, acoustic impedance, are parametrised with the Discrete Cosine Transform (DCT). This novel combination of techniques from machine learning, sparsity regularisation, seismic imaging and history matching aims to address the ill-posedness of the inversion of historical production data efficiently using ES-MDA. In the numerical experiments provided, I demonstrate that these sparse representations of the petrophysical properties and the seismic attributes enables to obtain better production data matches to the true production data and to quantify the propagating waterfront better compared to more traditional methods that do not use comparable parametrisation techniques

Mismatch and resolution in compressive imaging

Highly coherent sensing matrices arise in discretization of continuum problems such as radar and medical imaging when the grid spacing is below the Rayleigh threshold as well as in using highly coherent, redundant dictionaries as sparsifying operators. Algorithms (BOMP, BLOOMP) based on techniques of band exclusion and local optimization are proposed to enhance Orthogonal Matching Pursuit (OMP) and deal with such coherent sensing matrices. BOMP and BLOOMP have provably performance guarantee of reconstructing sparse, widely separated objects {\em independent} of the redundancy and have a sparsity constraint and computational cost similar to OMP's. Numerical study demonstrates the effectiveness of BLOOMP for compressed sensing with highly coherent, redundant sensing matrices.Comment: Figure 5 revise