Improved Convolutive and Under-Determined Blind Audio Source Separation with MRF Smoothing

Convolutive and under-determined blind audio source separation from noisy recordings is a challenging problem. Several computational strategies have been proposed to address this problem. This study is concerned with several modifications to the expectation-minimization-based algorithm, which iteratively estimates the mixing and source parameters. This strategy assumes that any entry in each source spectrogram is modeled using superimposed Gaussian components, which are mutually and individually independent across frequency and time bins. In our approach, we resolve this issue by considering a locally smooth temporal and frequency structure in the power source spectrograms. Local smoothness is enforced by incorporating a Gibbs prior in the complete data likelihood function, which models the interactions between neighboring spectrogram bins using a Markov random field. Simulations using audio files derived from stereo audio source separation evaluation campaign 2008 demonstrate high efficiency with the proposed improvement

A Novel STAP Algorithm for Airborne MIMO Radar Based on Temporally Correlated Multiple Sparse Bayesian Learning

In a heterogeneous environment, to efficiently suppress clutter with only one snapshot, a novel STAP algorithm for multiple-input multiple-output (MIMO) radar based on sparse representation, referred to as MIMOSR-STAP in this paper, is presented. By exploiting the waveform diversity of MIMO radar, each snapshot at the tested range cell can be transformed into multisnapshots for the phased array radar, which can estimate the high-resolution space-time spectrum by using multiple measurement vectors (MMV) technique. The proposed approach is effective in estimating the spectrum by utilizing Temporally Correlated Multiple Sparse Bayesian Learning (TMSBL). In the sequel, the clutter covariance matrix (CCM) and the corresponding adaptive weight vector can be efficiently obtained. MIMOSR-STAP enjoys high accuracy and robustness so that it can achieve better performance of output signal-to-clutter-plus-noise ratio (SCNR) and minimum detectable velocity (MDV) than the single measurement vector sparse representation methods in the literature. Thus, MIMOSR-STAP can deal with badly inhomogeneous clutter scenario more effectively, especially suitable for insufficient independent and identically distributed (IID) samples environment

Deconvolution of Serum Cortisol Levels by Using Compressed Sensing

The pulsatile release of cortisol from the adrenal glands is controlled by a hierarchical system that involves corticotropin releasing hormone (CRH) from the hypothalamus, adrenocorticotropin hormone (ACTH) from the pituitary, and cortisol from the adrenal glands. Determining the number, timing, and amplitude of the cortisol secretory events and recovering the infusion and clearance rates from serial measurements of serum cortisol levels is a challenging problem. Despite many years of work on this problem, a complete satisfactory solution has been elusive. We formulate this question as a non-convex optimization problem, and solve it using a coordinate descent algorithm that has a principled combination of (i) compressed sensing for recovering the amplitude and timing of the secretory events, and (ii) generalized cross validation for choosing the regularization parameter. Using only the observed serum cortisol levels, we model cortisol secretion from the adrenal glands using a second-order linear differential equation with pulsatile inputs that represent cortisol pulses released in response to pulses of ACTH. Using our algorithm and the assumption that the number of pulses is between 15 to 22 pulses over 24 hours, we successfully deconvolve both simulated datasets and actual 24-hr serum cortisol datasets sampled every 10 minutes from 10 healthy women. Assuming a one-minute resolution for the secretory events, we obtain physiologically plausible timings and amplitudes of each cortisol secretory event with R[superscript 2] above 0.92. Identification of the amplitude and timing of pulsatile hormone release allows (i) quantifying of normal and abnormal secretion patterns towards the goal of understanding pathological neuroendocrine states, and (ii) potentially designing optimal approaches for treating hormonal disorders.National Science Foundation (U.S.). Graduate Research Fellowship ProgramNational Institutes of Health (U.S.) (NIH DP1 OD003646)National Science Foundation (U.S.) (0836720)National Science Foundation (U.S.). Office of Emerging Frontiers in Research and Innovation (EFRI-0735956

Support Recovery of Sparse Signals

We consider the problem of exact support recovery of sparse signals via noisy measurements. The main focus is the sufficient and necessary conditions on the number of measurements for support recovery to be reliable. By drawing an analogy between the problem of support recovery and the problem of channel coding over the Gaussian multiple access channel, and exploiting mathematical tools developed for the latter problem, we obtain an information theoretic framework for analyzing the performance limits of support recovery. Sharp sufficient and necessary conditions on the number of measurements in terms of the signal sparsity level and the measurement noise level are derived. Specifically, when the number of nonzero entries is held fixed, the exact asymptotics on the number of measurements for support recovery is developed. When the number of nonzero entries increases in certain manners, we obtain sufficient conditions tighter than existing results. In addition, we show that the proposed methodology can deal with a variety of models of sparse signal recovery, hence demonstrating its potential as an effective analytical tool.Comment: 33 page

Translation-Invariant Shrinkage/Thresholding of Group Sparse Signals

This paper addresses signal denoising when large-amplitude coefficients form clusters (groups). The L1-norm and other separable sparsity models do not capture the tendency of coefficients to cluster (group sparsity). This work develops an algorithm, called 'overlapping group shrinkage' (OGS), based on the minimization of a convex cost function involving a group-sparsity promoting penalty function. The groups are fully overlapping so the denoising method is translation-invariant and blocking artifacts are avoided. Based on the principle of majorization-minimization (MM), we derive a simple iterative minimization algorithm that reduces the cost function monotonically. A procedure for setting the regularization parameter, based on attenuating the noise to a specified level, is also described. The proposed approach is illustrated on speech enhancement, wherein the OGS approach is applied in the short-time Fourier transform (STFT) domain. The denoised speech produced by OGS does not suffer from musical noise.Comment: 33 pages, 7 figures, 5 table