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result(s) for
"sparse signal"
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Noise-aware dictionary-learning-based sparse representation framework for detection and removal of single and combined noises from ECG signal
Automatic electrocardiogram (ECG) signal enhancement has become a crucial pre-processing step in most ECG signal analysis applications. In this Letter, the authors propose an automated noise-aware dictionary learning-based generalised ECG signal enhancement framework which can automatically learn the dictionaries based on the ECG noise type for effective representation of ECG signal and noises, and can reduce the computational load of sparse representation-based ECG enhancement system. The proposed framework consists of noise detection and identification, noise-aware dictionary learning, sparse signal decomposition and reconstruction. The noise detection and identification is performed based on the moving average filter, first-order difference, and temporal features such as number of turning points, maximum absolute amplitude, zerocrossings, and autocorrelation features. The representation dictionary is learned based on the type of noise identified in the previous stage. The proposed framework is evaluated using noise-free and noisy ECG signals. Results demonstrate that the proposed method can significantly reduce computational load as compared with conventional dictionary learning-based ECG denoising approaches. Further, comparative results show that the method outperforms existing methods in automatically removing noises such as baseline wanders, power-line interference, muscle artefacts and their combinations without distorting the morphological content of local waves of ECG signal.
Journal Article
Adaptive variable step algorithm for missing samples recovery in sparse signals
Recovery of arbitrarily positioned samples that are missing in sparse signals recently attracted significant research interest. Sparse signals with heavily corrupted arbitrary positioned samples could be analysed in the same way as compressive sensed signals by omitting the corrupted samples and considering them as unavailable during the recovery process. The reconstruction of the missing samples is done by using one of the well-known reconstruction algorithms. In this study, the authors will propose a very simple and efficient algorithm, applied directly to the concentration measures, without reformulating the reconstruction problem within the standard linear programming form. Direct application of the gradient approach to the non-differentiable forms of measures lead us to introduce a variable step size algorithm. A criterion for changing the adaptive algorithm parameters is presented. The results are illustrated on the examples with sparse signals, including approximately sparse signals and noisy sparse signals.
Journal Article
Subspace weighted ℓ2,1 minimization for sparse signal recovery
In this article, we propose a weighted
ℓ
2,1
minimization algorithm for jointly-sparse signal recovery problem. The proposed algorithm exploits the relationship between the noise subspace and the overcomplete basis matrix for designing weights, i.e., large weights are appointed to the entries, whose indices are more likely to be outside of the row support of the jointly sparse signals, so that their indices are expelled from the row support in the solution, and small weights are appointed to the entries, whose indices correspond to the row support of the jointly sparse signals, so that the solution prefers to reserve their indices. Compared with the regular
ℓ
2,1
minimization, the proposed algorithm can not only further enhance the sparseness of the solution but also reduce the requirements on both the number of snapshots and the signal-to-noise ratio (SNR) for stable recovery. Both simulations and experiments on real data demonstrate that the proposed algorithm outperforms the
ℓ
1
-SVD algorithm, which exploits straightforwardly
ℓ
2,1
minimization, for both deterministic basis matrix and random basis matrix.
Journal Article
Near optimal bound of orthogonal matching pursuit using restricted isometric constant
As a paradigm for reconstructing sparse signals using a set of under sampled measurements, compressed sensing has received much attention in recent years. In identifying the sufficient condition under which the perfect recovery of sparse signals is ensured, a property of the sensing matrix referred to as the restricted isometry property (RIP) is popularly employed. In this article, we propose the RIP based bound of the orthogonal matching pursuit (OMP) algorithm guaranteeing the exact reconstruction of sparse signals. Our proof is built on an observation that the general step of the OMP process is in essence the same as the initial step in the sense that the residual is considered as a new measurement preserving the sparsity level of an input vector. Our main conclusion is that if the restricted isometry constant
δ
K
of the sensing matrix satisfies
δ
K
<
K
-
1
K
-
1
+
K
then the OMP algorithm can perfectly recover
K
(> 1)-sparse signals from measurements. We show that our bound is sharp and indeed close to the limit conjectured by Dai and Milenkovic.
Journal Article
Detection of unknown and arbitrary sparse signals against noise
The detection of sparse signals against background noise is difficult since the information in the signal is only carried by a small portion of it. Prior information is usually assumed to ease detection. This study considers the general unknown and arbitrary sparse signal detection problem when no prior information is available. Under a Neyman–Pearson hypothesis-testing problem model, a new detection scheme referred to as the likelihood ratio test with sparse estimation (LRT-SE) is proposed. The SE technique from the compressive sensing theory is incorporated into the LRT-SE to achieve the detection of sparse signals with unknown support sets and arbitrary non-zero entries. An analysis of the effectiveness of LRT-SE is first given in terms of the characterisation of the conditions for the Chernoff-consistent detection. A large deviation analysis is then given to characterise the error exponent of LRT-SE with respect to the signal-to-noise ratio and the angle between the sparse signal and its estimate. Numerical results demonstrate superior detection performance of the proposed scheme over existing asymptotically optimal sparse detectors for finite signal dimensions. In addition, the simulation shows that the error probability of the proposed scheme decays exponentially with the number of observations.
Journal Article
A sufficient condition for restoring sparse vectors from ℓ1−ℓ2 $\\ell _1-\\ell _2$ ‐minimization with cumulative coherence
This paper focuses on the compressed sensing ℓ1−ℓ2 $\\ell _1-\\ell _2$ ‐minimization model and develops new bounds on cumulative coherence μ1(s) $\\mu _1(s)$ . It is pointed out that if cumulative coherence μ1(s) $\\mu _1(s)$satisfies Equation (2) or (11), then the sparse signal can stably recover in noise model and exactly recover in free noise by ℓ1−ℓ2 $\\ell _1-\\ell _2$ ‐minimization model. From this paper, it is found that based on some condition of cumulative coherence, the ℓ1−ℓ2 $\\ell _1-\\ell _2$ ‐minimization model can exactly recover s‐sparse signals in noiseless cases and stably recover s‐sparse signals in the noise cases.
Journal Article
The Analysis of Block Joint Sparse Recovery Using Block Signal Space Matching Pursuit
In many practical applications, we need to recover block sparse signals. In this paper, we encounter the system model where joint sparse signals exhibit block structure. To reconstruct this category of signals, we propose a new algorithm called block signal subspace matching pursuit (BSSMP) for the block joint sparse recovery problem in compressed sensing, which simultaneously reconstructs the support of block jointly sparse signals from a common sensing matrix. To begin with, we consider the case where block joint sparse matrix
X
has full column rank and any
r
nonzero row-blocks are linearly independent. Based on these assumptions, our theoretical analysis indicates that the BSSMP algorithm could reconstruct the support of
X
through at most
k
−
r
+
⌈
r
L
⌉
iterations if sensing matrix
A
satisfies the block restricted isometry property of order
L
(
K
−
r
) +
r
+ 1 with
δ
B
L
(
K
−
r
)
+
r
+
1
<
max
{
r
K
+
r
4
+
r
4
,
L
K
d
+
L
}
. This condition improves the existing result.
Journal Article
Sparse Time-Frequency Distribution Reconstruction Using the Adaptive Compressed Sensed Area Optimized with the Multi-Objective Approach
Compressive sensing (CS) of the signal ambiguity function (AF) and enforcing the sparsity constraint on the resulting signal time-frequency distribution (TFD) has been shown to be an efficient method for time-frequency signal processing. This paper proposes a method for adaptive CS-AF area selection, which extracts the magnitude-significant AF samples through a clustering approach using the density-based spatial clustering algorithm. Moreover, an appropriate criterion for the performance of the method is formalized, i.e., component concentration and preservation, as well as interference suppression, are measured utilizing the information obtained from the short-term and the narrow-band Rényi entropies, while component connectivity is evaluated using the number of regions with continuously-connected samples. The CS-AF area selection and reconstruction algorithm parameters are optimized using an automatic multi-objective meta-heuristic optimization method, minimizing the here-proposed combination of measures as objective functions. Consistent improvement in CS-AF area selection and TFD reconstruction performance has been achieved without requiring a priori knowledge of the input signal for multiple reconstruction algorithms. This was demonstrated for both noisy synthetic and real-life signals.
Journal Article
DETECTION THRESHOLDS FOR THE β-MODEL ON SPARSE GRAPHS
In this paper, we study sharp thresholds for detecting sparse signals in β-models for potentially sparse random graphs. The results demonstrate interesting interplay between graph sparsity, signal sparsity and signal strength. In regimes of moderately dense signals, irrespective of graph sparsity, the detection thresholds mirror corresponding results in independent Gaussian sequence problems. For sparser signals, extreme graph sparsity implies that all tests are asymptotically powerless, irrespective of the signal strength. On the other hand, sharp detection thresholds are obtained, up to matching constants, on denser graphs. The phase transitions mentioned above are sharp. As a crucial ingredient, we study a version of the higher criticism test which is provably sharp up to optimal constants in the regime of sparse signals. The theoretical results are further verified by numerical simulations.
Journal Article