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Person# Arash Amini

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Minimum mean square error

In statistics and signal processing, a minimum mean square error (MMSE) estimator is an estimation method which minimizes the mean square error (MSE), which is a common measure of estimator quality,

Lévy process

In probability theory, a Lévy process, named after the French mathematician Paul Lévy, is a stochastic process with independent, stationary increments: it represents the motion of a point whose succ

Normal distribution

In statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function

Related publications (16)

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Arash Amini, Mitra Fatemi, Martin Vetterli

We present a sampling theory for a class of binary images with finite rate of innovation (FRI). Every image in our model is the restriction of $\mathds{1}_{\{p\leq0\}}$ to the image plane, where $\mathds{1}$ denotes the indicator function and $p$ is some real bivariate polynomial. This particularly means that the boundaries in the image form a subset of an algebraic curve with the implicit polynomial $p$. We show that the image parameters --i.e., the polynomial coefficients-- satisfy a set of linear annihilation equations with the coefficients being the image moments. The inherent sensitivity of the moments to noise makes the reconstruction process numerically unstable and narrows the choice of the sampling kernels to polynomial reproducing kernels. As a remedy to these problems, we replace conventional moments with more stable \emph{generalized moments} that are adjusted to the given sampling kernel. The benefits are threefold: (1) it relaxes the requirements on the sampling kernels, (2) produces annihilation equations that are robust at numerical precision, and (3) extends the results to images with unbounded boundaries. We further reduce the sensitivity of the reconstruction process to noise by taking into account the sign of the polynomial at certain points, and sequentially enforcing measurement consistency. We consider various numerical experiments to demonstrate the performance of our algorithm in reconstructing binary images, including low to moderate noise levels and a range of realistic sampling kernels.

2016Arash Amini, Julien René Fageot, Zsuzsanna Püspöki, Michaël Unser, John Paul Ward

The detection of landmarks or patterns is of interest for extracting features in biological images. Hence, algorithms for finding these keypoints have been extensively investigated in the literature, and their localization and detection properties are well known. In this paper, we study the complementary topic of local orientation estimation, which has not received similar attention. Simply stated, the problem that we address is the following: estimate the angle of rotation of a pattern with steerable filters centered at the same location, where the image is corrupted by colored isotropic Gaussian noise. For this problem, we propose an estimator formulated as linear combinations of circular harmonics with given radial profiles. We prove that the proposed estimator is unbiased. This property allows us to use a statistical framework based on the Cramer-Rao lower bound (CRLB) to study the limits on the accuracy of the corresponding class of estimators. We aim at evaluating the performance of detection methods based on steerable filters in terms of angular accuracy (as a lower bound), while considering the connection to maximum likelihood estimation. Beyond the general results, we analyze the asymptotic behavior of the lower bound in terms of the order of steerablility and propose an optimal subset of components that minimizes the bound. We define a mechanism for selecting optimal subspaces of the span of the detectors. These are characterized by the most relevant angular frequencies. Finally, we project our template to the span of circular harmonics with given radial profiles and experimentally show that the prediction accuracy achieves the predicted CRLB. As an extension, we also consider steerable wavelet detectors.

Arash Amini, Hatef Otroshi Shahreza

With the emergence of social networks and improvements in the internet speed, the video data has become an ever-increasing portion of the global internet traffic. Besides the content, the quality of a video sequence is an important issue at the user end which is often affected by various factors such as compression. Therefore, monitoring the quality is crucial for the video content and service providers. A simple monitoring approach is to compare the raw video content (uncompressed) with the received data at the receiver. In most practical scenarios, however, the reference video sequence is not available. Consequently, it is desirable to have a general reference-less method for assessing the perceived quality of any given video sequence. In this paper, a no-reference video quality assessment technique based on video features is proposed. In particular, a long list of video features (21 sets of features, each consisting of 1 to 216 features) is considered and all possible combinations (2(21) - 1) for training an Extra Trees regressor is examined. This choice of the regressor is wisely selected and is observed to perform better than other common regressors. The results reveal that the top 20 performing feature subsets all outperformthe existing featurebased assessment methods in terms of the Pearson linear correlation coefficient (PLCC) or the Spearman rank order correlation coefficient (SROCC). Specially, the best performing regressor achieves PLCC = 0.786 on the test data over the KonVid-1k dataset. It is believed that the results of the comprehensive comparison could be potentially useful for other feature-based video-related problems. The source codes of the implementations are publicly available.