Related papers: Fast Cadzow's Algorithm and a Gradient Variant
In this paper, we investigate the application of continuous sparse signal reconstruction algorithms for the estimation of the ranges and speeds of multiple moving targets using an FMCW radar. Conventionally, to be reconstructed, continuous…
This paper describes a new efficient conjugate subgradient algorithm which minimizes a convex function containing a least squares fidelity term and an absolute value regularization term. This method is successfully applied to the inversion…
Image denoising is a fundamental problem in image processing whose primary objective is to remove the noise while preserving the original image structure. In this work, we proposed a new architecture for image denoising. We have used…
The stochastic subgradient method is a widely-used algorithm for solving large-scale optimization problems arising in machine learning. Often these problems are neither smooth nor convex. Recently, Davis et al. [1-2] characterized the…
In this paper, we develop a new framework for sensing and recovering structured signals. In contrast to compressive sensing (CS) systems that employ linear measurements, sparse representations, and computationally complex convex/greedy…
We study the problem of recovery of matrices that are simultaneously low rank and row and/or column sparse. Such matrices appear in recent applications in cognitive neuroscience, imaging, computer vision, macroeconomics, and genetics. We…
We consider the problem of estimating a low-rank matrix from a noisy observed matrix. Previous work has shown that the optimal method depends crucially on the choice of loss function. In this paper, we use a family of weighted loss…
Exponential is a basic signal form, and how to fast acquire this signal is one of the fundamental problems and frontiers in signal processing. To achieve this goal, partial data may be acquired but result in the severe artifacts in its…
Often computational models are too expensive to be solved in the entire domain of simulation, and a cheaper model would suffice away from the main zone of interest. We present for the concrete example of an evolution problem of advection…
While popular optimization methods such as SGD, AdamW, and Lion depend on steepest descent updates in either $\ell_2$ or $\ell_\infty$ norms, there remains a critical gap in handling the non-Euclidean structure observed in modern deep…
Stochastic optimization (SO) considers the problem of optimizing an objective function in the presence of noise. Most of the solution techniques in SO estimate gradients from the noise corrupted observations of the objective and adjust…
The aim of sparse phase retrieval is to recover a $k$-sparse signal $\mathbf{x}_0\in \mathbb{C}^{d}$ from quadratic measurements $|\langle \mathbf{a}_i,\mathbf{x}_0\rangle|^2$ where $\mathbf{a}_i\in \mathbb{C}^d, i=1,\ldots,m$. Noting…
Many problems in data science can be treated as estimating a low-rank matrix from highly incomplete, sometimes even corrupted, observations. One popular approach is to resort to matrix factorization, where the low-rank matrix factors are…
Optimization over the Stiefel manifold is a fundamental computational problem in many scientific and engineering applications. Despite considerable research effort, high-dimensional optimization problems over the Stiefel manifold remain…
The dual challenges of prohibitive communication overhead and the impracticality of gradient computation due to data privacy or black-box constraints in distributed systems motivate this work on communication-constrained gradient-free…
This paper introduces a novel computationally efficient method of solving the 3D single image super-resolution (SR) problem, i.e., reconstruction of a high-resolution volume from its low-resolution counterpart. The main contribution lies in…
Compressive Sensing, as an emerging technique in signal processing is reviewed in this paper together with its common applications. As an alternative to the traditional signal sampling, Compressive Sensing allows a new acquisition strategy…
This paper considers reconstructing a spectrally sparse signal from a small number of randomly observed time-domain samples. The signal of interest is a linear combination of complex sinusoids at $R$ distinct frequencies. The frequencies…
In this paper, we present a new algorithm, called MagnitudeCut, for recovering a signal from the phase of its Fourier transform. We casted our recovering problem into a new convex optimization problem, and then solved it by the block…
We propose a novel optimization-based decoding algorithm for LDPC-coded massive MIMO channels. The proposed decoding algorithm is based on a proximal gradient method for solving an approximate maximum a posteriori (MAP) decoding problem.…