Sparse Solution of Underdetermined Systems of Linear Equations by Stagewise Orthogonal Matching Pursuit
نویسندگان
چکیده
منابع مشابه
Sparse Solution of Underdetermined Linear Equations by Stagewise Orthogonal Matching Pursuit
Finding the sparsest solution to underdetermined systems of linear equations y = Φx is NP-hard in general. We show here that for systems with ‘typical’/‘random’ Φ, a good approximation to the sparsest solution is obtained by applying a fixed number of standard operations from linear algebra. Our proposal, Stagewise Orthogonal Matching Pursuit (StOMP), successively transforms the signal into a n...
متن کاملSparse nonnegative solution of underdetermined linear equations by linear programming.
Consider an underdetermined system of linear equations y = Ax with known y and d x n matrix A. We seek the nonnegative x with the fewest nonzeros satisfying y = Ax. In general, this problem is NP-hard. However, for many matrices A there is a threshold phenomenon: if the sparsest solution is sufficiently sparse, it can be found by linear programming. We explain this by the theory of convex polyt...
متن کاملNeighborly Polytopes and Sparse Solution of Underdetermined Linear Equations
Consider a d × n matrix A, with d < n. The problem of solving for x in y = Ax is underdetermined, and has many possible solutions (if there are any). In several fields it is of interest to find the sparsest solution – the one with fewest nonzeros – but in general this involves combinatorial optimization. Let ai denote the i-th column of A, 1 ≤ i ≤ n. Associate to A the quotient polytope P forme...
متن کاملSparse Solution of Underdetermined Linear Equations via Adaptively Iterative Thresholding
Finding the sparset solution of an underdetermined system of linear equations y = Ax has attracted considerable attention in recent years. Among a large number of algorithms, iterative thresholding algorithms are recognized as one of the most efficient and important classes of algorithms. This is mainly due to their low computational complexities, especially for large scale applications. The ai...
متن کاملSparse Subspace Clustering by Orthogonal Matching Pursuit
Subspace clustering methods based on `1, `2 or nuclear norm regularization have become very popular due to their simplicity, theoretical guarantees and empirical success. However, the choice of the regularizer can greatly impact both theory and practice. For instance, `1 regularization is guaranteed to give a subspace-preserving affinity (i.e., there are no connections between points from diffe...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: IEEE Transactions on Information Theory
سال: 2012
ISSN: 0018-9448,1557-9654
DOI: 10.1109/tit.2011.2173241