Related papers: Quantum matching pursuit: A quantum algorithm for …
Motivated by applications such as sparse PCA, in this paper we present provably-accurate one-pass algorithms for the sparse approximation of the top eigenvectors of extremely massive matrices based on a single compact linear sketch. The…
Compressive sensing is a signal processing technique that enables the reconstruction of sparse signals from a limited number of measurements, leveraging the signal's inherent sparsity to facilitate efficient recovery. Recent works on the…
Sparse coding is a basic task in many fields including signal processing, neuroscience and machine learning where the goal is to learn a basis that enables a sparse representation of a given set of data, if one exists. Its standard…
The Kaczmarz algorithm is popular for iteratively solving an overdetermined system of linear equations. The traditional Kaczmarz algorithm can approximate the solution in few sweeps through the equations but a randomized version of the…
Quantum computing is emerging as a new computing resource that could be superior to conventional computing for certain classes of optimization problems. However, in principle, most existing approaches to quantum optimization are intended to…
We propose a fast greedy algorithm to compute sparse representations of signals from continuous dictionaries that are factorizable, i.e., with atoms that can be separated as a product of sub-atoms. Existing algorithms strongly reduce the…
Fundamental matrix operations and solving linear systems of equations are ubiquitous in scientific investigations. Using the "Sender-Receiver" model, we propose quantum algorithms for matrix operations such as matrix-vector product,…
The ability of having a sparse representation for a certain class of signals has many applications in data analysis, image processing, and other research fields. Among sparse representations, the cosparse analysis model has recently gained…
Quantum computing is a winsome field that concerns with the behaviour and nature of energy at the quantum level to improve the efficiency of computations. In recent years, quantum computation is receiving much attention for its capability…
The representation of images in the brain is known to be sparse. That is, as neural activity is recorded in a visual area ---for instance the primary visual cortex of primates--- only a few neurons are active at a given time with respect to…
As the availability of imagery data continues to swell, so do the demands on transmission, storage and processing power. Processing requirements to handle this plethora of data is quickly outpacing the utility of conventional processing…
Greedy algorithms for minimizing L0-norm of sparse decomposition have profound application impact on many signal processing problems. In the sparse coding setup, given the observations $\mathrm{y}$ and the redundant dictionary…
We consider the change detection problem where the pre-change observation vectors are purely noise and the post-change observation vectors are noise-corrupted compressive measurements of sparse signals with a common support, measured using…
In many compressive sensing problems today, the relationship between the measurements and the unknowns could be nonlinear. Traditional treatment of such nonlinear relationships have been to approximate the nonlinearity via a linear model…
By means of a simple example it is demonstrated that the task of finding and identifying certain patterns in an otherwise (macroscopically) unstructured picture (data set) can be accomplished efficiently by a quantum computer. Employing the…
Quantum computing is a game-changing technology for global academia, research centers and industries including computational science, mathematics, finance, pharmaceutical, materials science, chemistry and cryptography. Although it has seen…
Convolution operations are foundational to classical image processing and modern deep learning architectures, yet their extension into the quantum domain has remained algorithmically and physically costly due to inefficient data encoding…
Quantum computation offers a promising new kind of information processing, where the non-classical features of quantum mechanics can be harnessed and exploited. A number of models of quantum computation exist, including the now well-studied…
The non-negative solution to an underdetermined linear system can be uniquely recovered sometimes, even without imposing any additional sparsity constraints. In this paper, we derive conditions under which a unique non-negative solution for…
The aim of this paper is to develop novel quantum algorithms for Gaussian process quadrature methods. Gaussian process quadratures are numerical integration methods where Gaussian processes are used as functional priors for the integrands…