Search results for: ‎isometry‎

Authors: Israa Sh. Tawfic, Sema Koc Kayhan

Abstract:

Given a large sparse signal, great wishes are to reconstruct the signal precisely and accurately from lease number of measurements as possible as it could. Although this seems possible by theory, the difficulty is in built an algorithm to perform the accuracy and efficiency of reconstructing. This paper proposes a new proved method to reconstruct sparse signal depend on using new method called Least Support Matching Pursuit (LS-OMP) merge it with the theory of Partial Knowing Support (PSK) given new method called Partially Knowing of Least Support Orthogonal Matching Pursuit (PKLS-OMP). The new methods depend on the greedy algorithm to compute the support which depends on the number of iterations. So to make it faster, the PKLS-OMP adds the idea of partial knowing support of its algorithm. It shows the efficiency, simplicity, and accuracy to get back the original signal if the sampling matrix satisfies the Restricted Isometry Property (RIP). Simulation results also show that it outperforms many algorithms especially for compressible signals.

Keywords: compressed sensing, lest support orthogonal matching pursuit, partial knowing support, restricted isometry property, signal reconstruction

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Authors: Mohsen Zahraei

Abstract:

‎In this paper, ‎the notion of ‎rank-k numerical range of rectangular complex matrix polynomials‎ ‎are introduced. ‎Some algebraic and geometrical properties are investigated. ‎Moreover, ‎for ε>0 the notion of Birkhoff-James approximate orthogonality sets for ε-higher ‎rank numerical ranges of rectangular matrix polynomials is also introduced and studied. ‎The proposed definitions yield a natural generalization of the standard higher rank numerical ranges.

Keywords: ‎‎Rank-k numerical range‎, ‎isometry‎, ‎numerical range‎, ‎rectangular matrix polynomials

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Authors: Israa Sh. Tawfic, Sema Koc Kayhan

Abstract:

In this paper, first, we propose least support orthogonal matching pursuit (LS-OMP) algorithm to improve the performance, of the OMP (orthogonal matching pursuit) algorithm. LS-OMP algorithm adaptively chooses optimum L (least part of support), at each iteration. This modification helps to reduce the computational complexity significantly and performs better than OMP algorithm. Second, we give the procedure for the invisible image watermarking in the presence of compressive sampling. The image reconstruction based on a set of watermarked measurements is performed using LS-OMP.

Keywords: compressed sensing, orthogonal matching pursuit, restricted isometry property, signal reconstruction, least support orthogonal matching pursuit, watermark

Procedia PDF Downloads 338