F.4. Probability and Statistics
Z. Shaeiri; M. R. Karami; A. Aghagolzadeh
Abstract
Sufficient number of linear and noisy measurements for exact and approximate sparsity pattern/support set recovery in the high dimensional setting is derived. Although this problem as been addressed in the recent literature, there is still considerable gaps between those results and the exact limits ...
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Sufficient number of linear and noisy measurements for exact and approximate sparsity pattern/support set recovery in the high dimensional setting is derived. Although this problem as been addressed in the recent literature, there is still considerable gaps between those results and the exact limits of the perfect support set recovery. To reduce this gap, in this paper, the sufficient condition is enhanced. A specific form of a Joint Typicality decoder is used for the support recovery task. Two performance metrics are considered for the recovery validation; one, which considers exact support recovery, and the other which seeks partial support recovery. First, an upper bound is obtained on the error probability of the sparsity pattern recovery. Next, using the mentioned upper bound, sufficient number of measurements for reliable support recovery is derived. It is shown that the sufficient condition for reliable support recovery depends on three key parameters of the problem; the noise variance, the minimum nonzero entry of the unknown sparse vector and the sparsity level. Simulations are performed for different sparsity rate, different noise variances, and different distortion levels. The results show that for all the mentioned cases the proposed methodology increases convergence rate of upper bound of the error probability of support recovery significantly which leads to a lower error probability bound compared with previously proposed bounds.
F.2.2. Interpolation
V. Abolghasemi; S. Ferdowsi; S. Sanei
Abstract
The focus of this paper is to consider the compressed sensing problem. It is stated that the compressed sensing theory, under certain conditions, helps relax the Nyquist sampling theory and takes smaller samples. One of the important tasks in this theory is to carefully design measurement matrix (sampling ...
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The focus of this paper is to consider the compressed sensing problem. It is stated that the compressed sensing theory, under certain conditions, helps relax the Nyquist sampling theory and takes smaller samples. One of the important tasks in this theory is to carefully design measurement matrix (sampling operator). Most existing methods in the literature attempt to optimize a randomly initialized matrix with the aim of decreasing the amount of required measurements. However, these approaches mainly lead to sophisticated structure of measurement matrix which makes it very difficult to implement. In this paper we propose an intermediate structure for the measurement matrix based on random sampling. The main advantage of block-based proposed technique is simplicity and yet achieving acceptable performance obtained through using conventional techniques. The experimental results clearly confirm that in spite of simplicity of the proposed approach it can be competitive to the existing methods in terms of reconstruction quality. It also outperforms existing methods in terms of computation time.
