A Class of Nonconvex Penalties Preserving Overall Convexity in Optimization-Based Mean Filtering

$\ell_1$ mean filtering is a conventional, optimization-based method to estimate the positions of jumps in a piecewise constant signal perturbed by additive noise. In this method, the $\ell_1$ norm penalizes sparsity of the first-order derivative of the signal. Theoretical results, however, show that in some situations, which can occur frequently in practice, even when the jump amplitudes tend to $\infty$, the conventional method identifies false change points. This issue is referred to as stair-casing problem and restricts practical importance of $\ell_1$ mean filtering. In this paper, sparsity is penalized more tightly than the $\ell_1$ norm by exploiting a certain class of nonconvex functions, while the strict convexity of the consequent optimization problem is preserved. This results in a higher performance in detecting change points. To theoretically justify the performance improvements over $\ell_1$ mean filtering, deterministic and stochastic sufficient conditions for exact change point recovery are derived. In particular, theoretical results show that in the stair-casing problem, our approach might be able to exclude the false change points, while $\ell_1$ mean filtering may fail. A number of numerical simulations assist to show superiority of our method over $\ell_1$ mean filtering and another state-of-the-art algorithm that promotes sparsity tighter than the $\ell_1$ norm. Specifically, it is shown that our approach can consistently detect change points when the jump amplitudes become sufficiently large, while the two other competitors cannot.Comment: Submitted to IEEE Transactions on Signal Processin

Laboratory Generation and Physics of Propagation of Solitary Waves and Water Surface Depressions

Solitary waves and water surface depressions are generated using a piston-type wavemaker. Different aspects of their propagation including profile evolution, establishment rate, stability, and celerity are examined experimentally. Traditionally, solitary waves are generated in laboratory set-ups using a methodology developed by Goring (1979) that considers a wave of permanent form during the generation process. A New methodology for generation of solitary waves using piston-type wavemakers is proposed by considering the evolving nature of the wave during generation phase. The capability of the New methodology in generation of solitary waves is assessed by conducting a series of laboratory experiments in water depth, h, of 20 cm and for the dimensionless wave height, H/h, values (H - wave height) ranging from 0.3 to 0.6. Waves generated using the Goring methodology served as a benchmark to evaluate the performance of the New methodology in generating solitary waves. Recorded waveforms are compared with theoretical solutions in terms of various wave characteristics (e.g., wave height, profile shape, wave celerity). These comparisons revealed that the New methodology is capable of generating more accurate and rapidly-established solitary waves with less wave attenuation with distance compared to the Goring methodology. In the second part, water surface depressions are generated using the Goring methodology in water depths of 6, 10 and 30 cm and for the dimensionless trough amplitude, at/h, values (at - trough amplitude) ranging from 0.05 to 0.6. Generated water surface depressions are in good agreement with the aimed theoretical profile in the vicinity of the wave paddle. In all experiments, generated negative solitary wave-like depression wave rapidly deforms into a triangular-like depression wave followed by a series of oscillatory trailing waves. As the depression wave propagates, as a result of nonlinear and dispersive effects its amplitude attenuates, slope of the leading edge of the depression wave becomes gentler while its rear edge slope becomes steeper. The amplitudes of the oscillatory trailing waves increase initially as the depression propagates; then the amplitudes of the oscillatory trailing waves start attenuating with distance due to viscous and dispersive effects. Celerity of the depression wave increases with distance as the depression amplitude attenuates with distance, but it never reaches the celerity of long waves in deep waters. Based on the experimental data of the present study and those reported by Hammack and Segur (1978), three empirical equations are proposed to predict the profile shape of a depression (i.e. trough amplitude, frequency of the leading half, and slope of the rear edge) for a given propagation distance

Assessment of knowledge and practice of pharmacists regarding oral health in Kerman, Iran

BACKGROUND AND AIM: Oral health is an integral part of general health. Between the different medical professions, pharmacists are one of the groups who encounter patients seeking consultation in the oral health field a lot. Therefore, this study aimed to assess the knowledge and practice of pharmacists in Kerman, Iran, toward oral health. METHODS: All pharmacists were invited to participate in the study after being informed about the aims of the study. A validated questionnaire with six sections including demographic data, oral hygiene behavior of the participants, the pharmacies’ specifications and products related to oral health, questions related to knowledge, questions related to practice, and questions related to the participants’ assessment were filled out by the participants. The collected data were analyzed using SPSS software, and descriptive results were presented in tables and charts. The chi-square statistical tests were used to explore any association between variables. RESULTS: Data were analyzed for 81 participants. Most of the participants were male and the mean age was 38 ± 10. The pharmacists’ mean knowledge of oral health was 6.5 out of 10 which places them in the medium knowledge range. The performance of pharmacists when encountering oral problems was prescribing analgesics in 79% of cases for tooth aches. There was no statistically significant difference in the knowledge score between different age and gender groups (P = 0.500). CONCLUSION: The results show a medium knowledge of pharmacists on oral health topics. Considering their own desire plans to train and educate in oral health fields to promote oral health seem necessary. KEYWORDS: Knowledge and Practice; Pharmacists; Oral Healt

Recovery of Low-Rank Matrices under Affine Constraints via a Smoothed Rank Function

In this paper, the problem of matrix rank minimization under affine constraints is addressed. The state-of-the-art algorithms can recover matrices with a rank much less than what is sufficient for the uniqueness of the solution of this optimization problem. We propose an algorithm based on a smooth approximation of the rank function, which practically improves recovery limits on the rank of the solution. This approximation leads to a non-convex program; thus, to avoid getting trapped in local solutions, we use the following scheme. Initially, a rough approximation of the rank function subject to the affine constraints is optimized. As the algorithm proceeds, finer approximations of the rank are optimized and the solver is initialized with the solution of the previous approximation until reaching the desired accuracy. On the theoretical side, benefiting from the spherical section property, we will show that the sequence of the solutions of the approximating function converges to the minimum rank solution. On the experimental side, it will be shown that the proposed algorithm, termed SRF standing for Smoothed Rank Function, can recover matrices which are unique solutions of the rank minimization problem and yet not recoverable by nuclear norm minimization. Furthermore, it will be demonstrated that, in completing partially observed matrices, the accuracy of SRF is considerably and consistently better than some famous algorithms when the number of revealed entries is close to the minimum number of parameters that uniquely represent a low-rank matrix.Comment: Accepted in IEEE TSP on December 4th, 201

DOA Estimation in Partially Correlated Noise Using Low-Rank/Sparse Matrix Decomposition

We consider the problem of direction-of-arrival (DOA) estimation in unknown partially correlated noise environments where the noise covariance matrix is sparse. A sparse noise covariance matrix is a common model for a sparse array of sensors consisted of several widely separated subarrays. Since interelement spacing among sensors in a subarray is small, the noise in the subarray is in general spatially correlated, while, due to large distances between subarrays, the noise between them is uncorrelated. Consequently, the noise covariance matrix of such an array has a block diagonal structure which is indeed sparse. Moreover, in an ordinary nonsparse array, because of small distance between adjacent sensors, there is noise coupling between neighboring sensors, whereas one can assume that nonadjacent sensors have spatially uncorrelated noise which makes again the array noise covariance matrix sparse. Utilizing some recently available tools in low-rank/sparse matrix decomposition, matrix completion, and sparse representation, we propose a novel method which can resolve possibly correlated or even coherent sources in the aforementioned partly correlated noise. In particular, when the sources are uncorrelated, our approach involves solving a second-order cone programming (SOCP), and if they are correlated or coherent, one needs to solve a computationally harder convex program. We demonstrate the effectiveness of the proposed algorithm by numerical simulations and comparison to the Cramer-Rao bound (CRB).Comment: in IEEE Sensor Array and Multichannel signal processing workshop (SAM), 201

Successive Concave Sparsity Approximation for Compressed Sensing

In this paper, based on a successively accuracy-increasing approximation of the $\ell_0$ norm, we propose a new algorithm for recovery of sparse vectors from underdetermined measurements. The approximations are realized with a certain class of concave functions that aggressively induce sparsity and their closeness to the $\ell_0$ norm can be controlled. We prove that the series of the approximations asymptotically coincides with the $\ell_1$ and $\ell_0$ norms when the approximation accuracy changes from the worst fitting to the best fitting. When measurements are noise-free, an optimization scheme is proposed which leads to a number of weighted $\ell_1$ minimization programs, whereas, in the presence of noise, we propose two iterative thresholding methods that are computationally appealing. A convergence guarantee for the iterative thresholding method is provided, and, for a particular function in the class of the approximating functions, we derive the closed-form thresholding operator. We further present some theoretical analyses via the restricted isometry, null space, and spherical section properties. Our extensive numerical simulations indicate that the proposed algorithm closely follows the performance of the oracle estimator for a range of sparsity levels wider than those of the state-of-the-art algorithms.Comment: Submitted to IEEE Trans. on Signal Processin

Isolation of keratinophilic fungi and aerobic actinomycetes from park soils in Gorgan, North of Iran

Background: Keratinophilic fungi are a group of fungi that colonize in various keratinous substrates and degrade them to the components with low molecular weight. This study was conducted to determine the prevalence of keratinophilic fungi and aerobic Actinomycetes in soil of city parks in Gorgan. Objectives: In this study, we surveyed the city park soils of Gorgan (a northern province of Iran) to determine the identities and diversity of soil aerobic Actinomycetes, keratinophilic and non-keratinophilic fungi. Materials and Methods: A total of 244 soil samples were collected from 22 diferent parks of Gorgan, North of Iran. The samples were collected from the superfcial layer with depth not exceeding than 0-10 cm in sterile polyethylene bags. We used hair bait technique for isolation keratinophilic fungi. The colonies identifed by macroscopic and microscopic characterization after slide culturing. Actinomycetes were isolated by antibiotic dilution methods and detected by using physiological tests such as Lysozyme, Casein, Xanthine, Hypoxanthine, Gelatin, Urea Broth, and modifed acid-fast stain. Results: Totally, 75 isolates of aerobic Actinomycetes were detected that Actinomadura madurae and Nocardia asteroides were the most prevalent strains, with 14.66 and 28% prevalence respectively. Microsporum gypseum was more frequent than other keratinophilic fungi (22.96%) and Aspergillus spp. was the most species of saprophyte fungi (15.92%). Conclusions: This study showed that the collected soil from studied areas was rich of keratinophilic fungi and Actinomycetes, therefore hygiene protocol should be taken to prevent the spread of pathogenic and saprophytes fungi in the environment of susceptible person. © 2013, Ahvaz Jundishapur University of Medical Sciences