Unified Theory for Recovery of Sparse Signals in a General Transform Domain

Cited 0 time in webofscience Cited 0 time in scopus
  • Hit : 253
  • Download : 0
Compressed sensing is provided a data-acquisition paradigm for sparse signals. Remarkably, it has been shown that the practical algorithms provide robust recovery from noisy linear measurements acquired at a near optimal sampling rate. In many real-world applications, a signal of interest is typically sparse not in the canonical basis but in a certain transform domain, such as wavelets or the finite difference. The theory of compressed sensing was extended to the analysis sparsity model, but known extensions are limited to the specific choices of sensing matrix and sparsifying transform. In this paper, we propose a unified theory for robust recovery of sparse signals in a general transform domain by convex programming. In particular, our results apply to the general acquisition and sparsity models and show how the number of measurements for recovery depends on properties of measurement and sparsifying transforms. Moreover, we also provide extensions of our results to the scenarios where the atoms in the transform have varying incoherence parameters and the unknown signal exhibits a structured sparsity pattern. In particular, for the partial Fourier recovery of sparse signals over a circulant transform, our main results suggest a uniformly random sampling. Numerical results demonstrate that the variable density random sampling by our main results provides a superior recovery performance over the known sampling strategies.
Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
Issue Date
2018-08
Language
English
Article Type
Article
Keywords

TOTAL VARIATION MINIMIZATION; COSPARSE ANALYSIS MODEL; LINEAR INVERSE PROBLEMS; GAUSSIAN MEASUREMENTS; RECONSTRUCTION; STRATEGIES; ALGORITHMS; PURSUIT

Citation

IEEE TRANSACTIONS ON INFORMATION THEORY, v.64, no.8, pp.5457 - 5477

ISSN
0018-9448
DOI
10.1109/TIT.2018.2846643
URI
http://hdl.handle.net/10203/244814
Appears in Collection
BiS-Journal Papers(저널논문)
Files in This Item
There are no files associated with this item.

qr_code

  • mendeley

    citeulike


rss_1.0 rss_2.0 atom_1.0