Related papers: Algebraic Optimization of Binary Spatially Coupled…
An efficient computational approach for optimal reconstruction of binary-type images suitable for models in various applications including biomedical imaging is developed and validated. The methodology includes derivative-free optimization…
We present an analytic approximation model for non-rigid point set registration, grounded in the multivariate Taylor expansion of vector-valued functions. By exploiting the algebraic structure of Taylor expansions, we construct a structured…
In Compressive Sensing, the Restricted Isometry Property (RIP) ensures that robust recovery of sparse vectors is possible from noisy, undersampled measurements via computationally tractable algorithms. It is by now well-known that Gaussian…
We present a simple, general technique for reducing the sample complexity of matrix and tensor decomposition algorithms applied to distributions. We use the technique to give a polynomial-time algorithm for standard ICA with sample…
Compressed sensing was proposed by E. J. Cand\'es, J. Romberg, T. Tao, and D. Donoho for efficient sampling of sparse signals in 2006 and has vast applications in signal processing. The expicit restricted isometry property (RIP) measurement…
Compressed sensing is a promising technique that attempts to faithfully recover sparse signal with as few linear and nonadaptive measurements as possible. Its performance is largely determined by the characteristic of sensing matrix.…
We study the compressed sensing reconstruction problem for a broad class of random, band-diagonal sensing matrices. This construction is inspired by the idea of spatial coupling in coding theory. As demonstrated heuristically and…
We consider a discrete optimization formulation for learning sparse classifiers, where the outcome depends upon a linear combination of a small subset of features. Recent work has shown that mixed integer programming (MIP) can be used to…
The expicit restricted isometry property (RIP) measurement matrices are needed in practical application of compressed sensing in signal processing. RIP matrices from Reed-Solomon codes, BCH codes, orthogonal codes, expander graphs have been…
In this paper, we propose to enhance the performance of the sum-product algorithm (SPA) by interleaving SPA iterations with a random local graph update rule. This rule is known as edge local complementation (ELC), and has the effect of…
In this paper, we study the problem of compressed sensing using binary measurement matrices and $\ell_1$-norm minimization (basis pursuit) as the recovery algorithm. We derive new upper and lower bounds on the number of measurements to…
The choice of the sensing matrix is crucial in compressed sensing. Random Gaussian sensing matrices satisfy the restricted isometry property, which is crucial for solving the sparse recovery problem using convex optimization techniques.…
In this paper, we propose a method of structured construction of the optimal measurement matrix for noiseless compressed sensing (CS), which achieves the minimum number of measurements which only needs to be as large as the sparsity of the…
Compressed Sensing aims to capture attributes of a sparse signal using very few measurements. Cand\`{e}s and Tao showed that sparse reconstruction is possible if the sensing matrix acts as a near isometry on all $\boldsymbol{k}$-sparse…
We propose a novel approach to iterated sparse matrix dense matrix multiplication, a fundamental computational kernel in scientific computing and graph neural network training. In cases where matrix sizes exceed the memory of a single…
Hierarchically sparse signals and Kronecker product structured measurements arise naturally in a variety of applications. The simplest example of a hierarchical sparsity structure is two-level $(s,\sigma)$-hierarchical sparsity which…
Many emerging applications involve sparse signals, and their processing is a subject of active research. We desire a large class of sensing matrices which allow the user to discern important properties of the measured sparse signal. Of…
Magnetic Resonance Imaging (MRI) is a powerful technique employed for non-invasive in vivo visualization of internal structures. Sparsity is often deployed to accelerate the signal acquisition or overcome the presence of motion artifacts,…
Important workloads, such as machine learning and graph analytics applications, heavily involve sparse linear algebra operations. These operations use sparse matrix compression as an effective means to avoid storing zeros and performing…
There are two main algorithmic approaches to sparse signal recovery: geometric and combinatorial. The geometric approach starts with a geometric constraint on the measurement matrix and then uses linear programming to decode information…