Comparison of Matching Pursuit Algorithm with Other Signal Processing Techniques for Computation of the Time-Frequency Power Spectrum of Brain Signals

Signals recorded from the brain often show rhythmic patterns at different frequencies, which are tightly coupled to the external stimuli as well as the internal state of the subject. In addition, these signals have very transient structures related to spiking or sudden onset of a stimulus, which have durations not exceeding tens of milliseconds. Further, brain signals are highly nonstationary because both behavioral state and external stimuli can change on a short time scale. It is therefore essential to study brain signals using techniques that can represent both rhythmic and transient components of the signal, something not always possible using standard signal processing techniques such as short time fourier transform, multitaper method, wavelet transform, or Hilbert transform. In this review, we describe a multiscale decomposition technique based on an over-complete dictionary called matching pursuit (MP), and show that it is able to capture both a sharp stimulus-onset transient and a sustained gamma rhythm in local field potential recorded from the primary visual cortex. We compare the performance of MP with other techniques and discuss its advantages and limitations. Data and codes for generating all time-frequency power spectra are provided.

IMAGE DENOISING USING OPTIMALLY WEIGHTED BILATERAL FILTERS: A SURE AND FAST APPROACH

The bilateral filter is known to be quite effective in denoising images corrupted with small dosages of additive Gaussian noise. The denoising performance of the filter, however, is known to degrade quickly with the increase in noise level. Several adaptations of the filter have been proposed in the literature to address this shortcoming, but often at a substantial computational overhead. In this paper, we report a simple pre-processing step that can substantially improve the denoising performance of the bilateral filter, at almost no additional cost. The modified filter is designed to be robust at large noise levels, and often tends to perform poorly below a certain noise threshold. To get the best of the original and the modified filter, we propose to combine them in a weighted fashion, where the weights are chosen to minimize (a surrogate of) the oracle mean-squared-error (MSE). The optimally-weighted filter is thus guaranteed to perform better than either of the component filters in terms of the MSE, at all noise levels. We also provide a fast algorithm for the weighted filtering. Visual and quantitative denoising results on standard test images are reported which demonstrate that the improvement over the original filter is significant both visually and in terms of PSNR. Moreover, the denoising performance of the optimally-weighted bilateral filter is competitive with the computation-intensive non-local means filter.

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.