Hybrid Compressed Sensing of images

We consider the problem of recovering a signal/image (x) with a k-sparse representation, from hybrid (complex and real), noiseless linear samples (y) using a mixture of complex-valued sparse and real-valued dense projections within a single matrix. The proposed Hybrid Compressed Sensing (HCS) employ...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:2010 IEEE International Workshop on Multimedia Signal Processing S. 99 - 104
Hauptverfasser: Moghadam, Abdolreza Abdolhosseini, Radha, Hayder
Format: Tagungsbericht
Sprache:Englisch
Veröffentlicht: IEEE 01.10.2010
Schlagworte:
Complexity theory
Compressed sensing
Decoding
Equations
Image coding
Indexes
iterative decoding algorithms
Sparse matrices
sparse projections
ISBN:1424481104, 9781424481101
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:We consider the problem of recovering a signal/image (x) with a k-sparse representation, from hybrid (complex and real), noiseless linear samples (y) using a mixture of complex-valued sparse and real-valued dense projections within a single matrix. The proposed Hybrid Compressed Sensing (HCS) employs the complex-sparse part of the projection matrix to divide the n-dimensional signal (x) into subsets. In turn, each subset of the signal (coefficients) is mapped onto a complex sample of the measurement vector (y). Under a worst-case scenario of such sparsity-induced mapping, when the number of complex sparse measurements is sufficiently large then this mapping leads to the isolation of a significant fraction of the k non-zero coefficients into different complex measurement samples from y. Using a simple property of complex numbers (namely complex phases) one can identify the isolated non-zeros of x. After reducing the effect of the identified non-zero coefficients from the compressive samples, we utilize the real-valued dense submatrix to form a full rank system of equations to recover the signal values in the remaining indices (that are not recovered by the sparse complex projection part). We show that the proposed hybrid approach can recover a k-sparse signal (with high probability) while requiring only m ≈ 3k 3 √(n/2k) real measurements (where each complex sample is counted as two real measurements). We also derive expressions for the optimal mix of complex-sparse and real-dense rows within an HCS projection matrix. Further, in a practical range of sparsity ratio (k/n) suitable for images, the hybrid approach outperforms even the most complex compressed sensing frameworks (namely basis pursuit with dense Gaussian matrices). The theoretical complexity of HCS is less than the complexity of solving a full-rank system of m linear equations. In practice, the complexity can be lower than this bound.
ISBN:1424481104
9781424481101
DOI:10.1109/MMSP.2010.5662001