Mixed dictionaries generated by cosine and B-spline functions are considered. It is shown that, by highly nonlinear approaches such as Orthogonal Matching Pursuit, the discrete version of the proposed dictionaries yields a significant gain in the sparsity of an image representation.

We want to use a variety of sparseness measured applied to ‘the minimal `1 norm representation’ of a music signal in an over-complete dictionary as features for automatic classification of music. Unfortunately, the process of computing the optimal `1 norm representation is rather slow, and we therefore investigate the use of matching pursuit, alternating projection, and Moore-Penrose inverse fo...

This paper provides a simple proof of the mutual incoherence condition (μ < 1 2K−1 ) under which K-sparse signal can be accurately reconstructed from a small number of linear measurements using the orthogonal matching pursuit (OMP) algorithm. Our proof, based on mathematical induction, is built on an observation that the general step of the OMP process is in essence same as the initial step sin...

It is shown that Theorem 10 (Non-Nestedness of ERC) in [Plumbley, IEEE Trans. Info. Theory, vol. 53, pp. 3188, Sep. 2007] neglects the derivations of the exact recovery conditions (ERCs) of constrained `1-minimization (BP) and orthogonal matching pursuit (OMP). This means that it does not reflect the recovery properties of these algorithms. Furthermore, an ERC of BP more general than that in [T...

Temperature variations have significant effects on propagation of Lamb wave and therefore can severely limit the damage detection for Lamb wave. In order to mitigate the temperature effect, a temperature compensation method based on baseline signal reconstruction is developed for Lamb wave-based damage detection. The method is a reconstruction of a baseline signal at the temperature of current ...

In many hybrid video compression algorithms there is a clear distinction between motion estimation and compensation (MEMC) on the one hand, and transform coding of the residue on the other hand. By translating MEMC into the framework of Matching Pursuit (MP), we will show that uniication of both steps is possible. Moreover, adapting the MP approach to the small size dictionaries involved in MEM...

We introduce an image coding algorithm in which perceptual pruning is used to select the most perceptually relevant image components. The algorithm uses a new maximum likelihood based image indistinguishability criterion that derives from a cortical snapshot, which is a model of the response of striate cortical simple cells to the image at a given point of fixation. The criterion must be satisf...

In this note, we investigate the theoretical properties of Orthogonal Matching Pursuit (OMP), a class of decoder to recover sparse signal in compressed sensing. In particular, we show that the OMP decoder can give (p, q) instance optimality for a large class of encoders with 1 ≤ p ≤ q ≤ 2 and (p, q) 6= (2, 2). We also show that, if the encoding matrix is drawn from an appropriate distribution, ...

In this paper we present our original methodology, in which Matching Pursuit is used for networks anomaly and intrusion detection. The architecture of anomaly-based IDS based on signal processing is presented. We propose to use mean projection of the reconstructed network signal to determine if the examined trace is normal or attacked. Experimental results confirm the efficiency of our method i...

In this paper, we use the block orthogonal matching pursuit (BOMP) algorithm to recover block sparse signals x from measurements y = Ax+v, where v is a l2 bounded noise vector (i.e., ‖v‖2 ≤ ǫ for some constant ǫ). We investigate some sufficient conditions based on the block restricted isometry property (block-RIP) for exact (when v = 0) and stable (when v 6= 0) recovery of block sparse signals ...