Certifying the Restricted Isometry Property is Hard
نویسندگان
چکیده
منابع مشابه
Approximately certifying the restricted isometry property is hard
Amatrix is said to possess the Restricted Isometry Property (RIP) if it acts as an approximate isometry when restricted to sparse vectors. Previous work has shown it to be np-hard to determine whether a matrix possess this property, but only in a narrow range of parameters. In this work, we show that it is np-hard to make this determination for any accuracy parameter, even when we restrict ours...
متن کاملComputational Complexity of Certifying Restricted Isometry Property
Given a matrix A with n rows, a number k < n, and 0 < δ < 1, A is (k, δ)-RIP (Restricted Isometry Property) if, for any vector x ∈ R, with at most k non-zero co-ordinates, (1− δ)‖x‖2 ≤ ‖Ax‖2 ≤ (1 + δ)‖x‖2 In other words, a matrix A is (k, δ)-RIP if Ax preserves the length of x when x is a k-sparse vector. In many applications, such as compressed sensing and sparse recovery, it is desirable to c...
متن کاملA Generalized Restricted Isometry Property
Compressive Sampling (CS) describes a method for reconstructing high-dimensional sparse signals from a small number of linear measurements. Fundamental to the success of CS is the existence of special measurement matrices which satisfy the so-called Restricted Isometry Property (RIP). In essence, a matrix satisfying RIP is such that the lengths of all sufficiently sparse vectors are approximate...
متن کاملCompressed Sensing: How sharp is the Restricted Isometry Property
Compressed Sensing (CS) seeks to recover an unknown vector with N entries by making far fewer than N measurements; it posits that the number of compressed sensing measurements should be comparable to the information content of the vector, not simply N . CS combines the important task of compression directly with the measurement task. Since its introduction in 2004 there have been hundreds of ma...
متن کاملThe restricted isometry property for random convolutions
We present significantly improved estimates for the restricted isometry constants of partial random circulant matrices as they arise in the matrix formulation of subsampled convolution with a random pulse. We show that the required condition on the number m of rows in terms of the sparsity s and the vector length n is m & s log s log n.
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: 2013
ISSN: 0018-9448,1557-9654
DOI: 10.1109/tit.2013.2248414