Complex patterns arise through spontaneous symmetry breaking in dense homogeneous networks of neural oscillators

There has been much interest in understanding collective dynamics in networks of brain regions due to their role in behavior and cognitive function. Here we show that a simple, homogeneous system of densely connected oscillators, representing the aggregate activity of local brain regions, can exhibit a rich variety of dynamical patterns emerging via spontaneous breaking of permutation or translational symmetries. Upon removing just a few connections, we observe a striking departure from the mean-field limit in terms of the collective dynamics, which implies that the sparsity of these networks may have very important consequences. Our results suggest that the origins of some of the complicated activity patterns seen in the brain may be understood even with simple connection topologies.

IMAGE DENOISING IN MULTIPLICATIVE NOISE

We address the problem of denoising images corrupted by multiplicative noise. The noise is assumed to follow a Gamma distribution. Compared with additive noise distortion, the effect of multiplicative noise on the visual quality of images is quite severe. We consider the mean-square error (MSE) cost function and derive an expression for an unbiased estimate of the MSE. The resulting multiplicative noise unbiased risk estimator is referred to as MURE. The denoising operation is performed in the wavelet domain by considering the image-domain MURE. The parameters of the denoising function (typically, a shrinkage of wavelet coefficients) are optimized for by minimizing MURE. We show that MURE is accurate and close to the oracle MSE. This makes MURE-based image denoising reliable and on par with oracle-MSE-based estimates. Analogous to the other popular risk estimation approaches developed for additive, Poisson, and chi-squared noise degradations, the proposed approach does not assume any prior on the underlying noise-free image. We report denoising results for various noise levels and show that the quality of denoising obtained is on par with the oracle result and better than that obtained using some state-of-the-art denoisers.