Related papers: Safe squeezing for antisparse coding
We investigate the problem of estimating the 3D shape of an object defined by a set of 3D landmarks, given their 2D correspondences in a single image. A successful approach to alleviating the reconstruction ambiguity is the 3D deformable…
The problem of minimizing a polynomial over a set of polynomial inequalities is an NP-hard non-convex problem. Thanks to powerful results from real algebraic geometry, one can convert this problem into a nested sequence of…
We propose a stochastic variance reduced optimization algorithm for solving sparse learning problems with cardinality constraints. Sufficient conditions are provided, under which the proposed algorithm enjoys strong linear convergence…
The ultimate goal of any sparse coding method is to accurately recover from a few noisy linear measurements, an unknown sparse vector. Unfortunately, this estimation problem is NP-hard in general, and it is therefore always approached with…
Approximate Message Passing (AMP) has been shown to be a superior method for inference problems, such as the recovery of signals from sets of noisy, lower-dimensionality measurements, both in terms of reconstruction accuracy and in…
In this paper, we propose a novel sparse coding and counting method under Bayesian framwork for visual tracking. In contrast to existing methods, the proposed method employs the combination of L0 and L1 norm to regularize the linear…
Over the past decade, the celebrated sparse representation model has achieved impressive results in various signal and image processing tasks. A convolutional version of this model, termed convolutional sparse coding (CSC), has been…
Compressed sensing aims to undersample certain high-dimensional signals, yet accurately reconstruct them by exploiting signal characteristics. Accurate reconstruction is possible when the object to be recovered is sufficiently sparse in a…
Correspondence problems are often modelled as quadratic optimization problems over permutations. Common scalable methods for approximating solutions of these NP-hard problems are the spectral relaxation for non-convex energies and the…
We consider the problem of reconstructing an infinite set of sparse, finite-dimensional vectors, that share a common sparsity pattern, from incomplete measurements. This is in contrast to the work [17], where the single vector signal can be…
In this work, we propose an optimization framework for estimating a sparse robust one-dimensional subspace. Our objective is to minimize both the representation error and the penalty, in terms of the l1-norm criterion. Given that the…
Sparse coding algorithms are about finding a linear basis in which signals can be represented by a small number of active (non-zero) coefficients. Such coding has many applications in science and engineering and is believed to play an…
We present the framework of slowly varying regression under sparsity, allowing sparse regression models to exhibit slow and sparse variations. The problem of parameter estimation is formulated as a mixed-integer optimization problem. We…
Recently, sparsity has become a key concept in various areas of applied mathematics, computer science, and electrical engineering. One application of this novel methodology is the separation of data, which is composed of two (or more)…
This paper considers the problem of detecting a high dimensional signal (not necessarily sparse) based on compressed measurements with physical layer secrecy guarantees. First, we propose a collaborative compressive detection (CCD)…
The problem of sparse approximation and the closely related compressed sensing have received tremendous attention in the past decade. Primarily studied from the viewpoint of applied harmonic analysis and signal processing, there have been…
In high dimensional settings, sparse structures are crucial for efficiency, both in term of memory, computation and performance. It is customary to consider $\ell_1$ penalty to enforce sparsity in such scenarios. Sparsity enforcing methods,…
This paper presents a novel convex optimization-based method for finding the globally optimal solutions of a class of mixed-integer non-convex optimal control problems. We consider problems with non-convex constraints that restrict the…
Many classification approaches first represent a test sample using the training samples of all the classes. This collaborative representation is then used to label the test sample. It was a common belief that sparseness of the…
Recently dictionary screening has been proposed as an effective way to improve the computational efficiency of solving the lasso problem, which is one of the most commonly used method for learning sparse representations. To address today's…