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In this paper we consider estimating the system parameters and designing stable observer for unknown noisy linear time-invariant (LTI) systems. We propose a Support Vector Regression (SVR) based estimator to provide adjustable asymmetric…
The success of the compressed sensing paradigm has shown that a substantial reduction in sampling and storage complexity can be achieved in certain linear and non-adaptive estimation problems. It is therefore an advisable strategy for…
Offline Signature Verification (OSV) is a fundamental biometric task across various forensic, commercial and legal applications. The underlying task at hand is to carefully model fine-grained features of the signatures to distinguish…
Singular value decomposition (SVD) is one of the most popular compression methods that approximate a target matrix with smaller matrices. However, standard SVD treats the parameters within the matrix with equal importance, which is a simple…
Block coordinate descent (BCD) methods approach optimization problems by performing gradient steps along alternating subgroups of coordinates. This is in contrast to full gradient descent, where a gradient step updates all coordinates…
Convolution and transposed convolution are fundamental operators widely used in neural networks. However, transposed convolution (a.k.a. deconvolution) does not serve as a true inverse of convolution due to inherent differences in their…
Convexity properties of error rates of a class of decoders, including the ML/min-distance one as a special case, are studied for arbitrary constellations, bit mapping and coding. Earlier results obtained for the AWGN channel are extended to…
Inverse problems are key issues in several scientific areas, including signal processing and medical imaging. Since inverse problems typically suffer from instability with respect to data perturbations, a variety of regularization…
We study the question of extracting a sequence of functions $\{\boldsymbol{f}_i, \boldsymbol{g}_i\}_{i=1}^s$ from observing only the sum of their convolutions, i.e., from $\boldsymbol{y} = \sum_{i=1}^s \boldsymbol{f}_i\ast…
Blind deconvolution has made significant progress in the past decade. Most successful algorithms are classified either as Variational or Maximum a-Posteriori ($MAP$). In spite of the superior theoretical justification of variational…
This paper considers the linear inverse problem where we wish to estimate a structured signal $x$ from its corrupted observations. When the problem is ill-posed, it is natural to make use of a convex function $f(\cdot)$ that exploits the…
In this paper, we examine the convergence of mirror descent in a class of stochastic optimization problems that are not necessarily convex (or even quasi-convex), and which we call variationally coherent. Since the standard technique of…
This study introduces a novel formulation to enhance Support Vector Machines (SVMs) in handling class imbalance and noise. Unlike the conventional Soft Margin SVM, which penalizes the magnitude of constraint violations, the proposed model…
Kitaev's toric code is one of the most prominent models for fault-tolerant quantum computation, currently regarded as the leading solution for connectivity constrained quantum technologies. Significant effort has been recently devoted to…
Learning representation from relative similarity comparisons, often called ordinal embedding, gains rising attention in recent years. Most of the existing methods are batch methods designed mainly based on the convex optimization, say, the…
Statistical dependencies among wavelet coefficients are commonly represented by graphical models such as hidden Markov trees(HMTs). However, in linear inverse problems such as deconvolution, tomography, and compressed sensing, the presence…
A block decomposition method is proposed for minimizing a (possibly non-convex) continuously differentiable function subject to one linear equality constraint and simple bounds on the variables. The proposed method iteratively selects a…
Inverse problems are fundamental in fields like medical imaging, geophysics, and computerized tomography, aiming to recover unknown quantities from observed data. However, these problems often lack stability due to noise and…
Low-rank regularization-based deep unrolling networks have achieved remarkable success in various inverse imaging problems (IIPs). However, the singular value decomposition (SVD) is non-differentiable when duplicated singular values occur,…
Many problems in machine learning can be formulated as optimizing a convex functional over a vector space of measures. This paper studies the convergence of the mirror descent algorithm in this infinite-dimensional setting. Defining Bregman…