Finding an optimal dictionary of different wavelet types using sparse modeling to denoise ECG signal

Sparse signal modeling often reconstructs a signal with few atoms from a pre-defined dictionary. Hence the choice of wavelet dictionary that represents the sparsity of the target signal is crucial in sparse modeling approach. The challenge of finding an optimal dictionary of different wavelet types using sparse denoising model (SDM) to denoise ECG signal is investigated in this work. A method of finding an optimal wavelet dictionary from a set of orthogonal wavelet sub-dictionaries by the means of the best correlation with ECG signal, is developed. The highly correlated sub-dictionaries from three wavelet dictionaries, namely daubechies, symlets, coiflets and discrete cosine transform are combined to construct an overcomplete dictionary. The weight of Akaike’s information criterion and the signal-to-noise ratio improvement are considered as a criterion to evaluate the performance of the proposed SDM. The results indicate that multi-wavelet dictionary of different types is highly sparse and efficient in denoising the target signal, e.g., ECG.

A Two-Step Compressed Sensing Approach for Single-Snapshot DOA Estimation of Closely Spaced Signals

Single-snapshot direction-of-arrival (DOA) estimation plays an important role in dynamic target detection and tracking applications. Because a single-snapshot signal provides few information for statistics calculation, recently compressed sensing (CS) theory is applied to solve single-snapshot DOA estimation, instead of the traditional DOA methods based on statistics. However, when the unknown sources are closely located, the spatial signals are highly correlated, and its overcomplete dictionary is made up of dense grids, which leads to a serious decrease in the estimation accuracy of the CS-based algorithm. In order to solve this problem, this paper proposed a two-step compressed sensing-based algorithm for the single-snapshot DOA estimation of closely spaced signals. The overcomplete dictionaries with coarse and refined grids are used in the two steps, respectively. The measurement matrix is constructed by using a very sparse projection scheme based on chaotic sequences because chaotic sequences have determinism and pseudo-randomness property. Such measurement matrix is mainly proposed for compressing the overcomplete dictionary in preestimation step, while it is well designed by choosing the steering vectors of true DOA in the accurate estimation step, in which the neighborhood information around the true DOAs partly solved in the previous step will be used. Monte Carlo simulation results demonstrate that the proposed algorithm can perform better than other existing single-snapshot DOA estimation methods. Especially, it can work well to solve the issues caused by closely spaced signals and single snapshot.

SAR Image Target Recognition Based on Monogenic Signal and Sparse Representation

It is necessary to recognize the target in the situation of military battlefield monitoring and civilian real-time monitoring. Sparse representation-based SAR image target recognition method uses training samples or feature information to construct an overcomplete dictionary, which will inevitably affect the recognition speed. In this paper, a method based on monogenic signal and sparse representation is presented for SAR image target recognition. In this method, the extended maximum average correlation height filter is used to train the samples and generate the templates. The monogenic features of the templates are extracted to construct subdictionaries, and the subdictionaries are combined to construct a cascade dictionary. Sparse representation coefficients of the testing samples over the cascade dictionary are calculated by the orthogonal matching tracking algorithm, and recognition is realized according to the energy of the sparse coefficients and voting recognition. The experimental results suggest that the new approach has good results in terms of recognition accuracy and recognition time.

Shadow Separation of Pavement Images Based on Morphological Component Analysis

The shadow of pavement images will affect the accuracy of road crack recognition and increase the rate of error detection. A shadow separation algorithm based on morphological component analysis (MCA) is proposed herein to solve the shadow problem of road imaging. The main assumption of MCA is that the image geometric structure and texture structure components are sparse within a class under a specific base or overcomplete dictionary, while the base or overcomplete dictionaries of each sparse representation of morphological components are incoherent. Thereafter, the corresponding image signal is transformed according to the dictionary to obtain the sparse representation coefficients of each part of the information, and the coefficients are shrunk by soft thresholding to obtain new coefficients. Experimental results show the effectiveness of the shadow separation method proposed in this paper.

An Accurate Sparse Recovery Algorithm for Range-Angle Localization of Targets via Double-Pulse FDA-MIMO Radar

In this paper, a sparse recovery algorithm based on a double-pulse FDA-MIMO radar is proposed to jointly extract the angle and range estimates of targets. Firstly, the angle estimates of targets are calculated by transmitting a pulse with a zero frequency increment and employing the improved l 1 -SVD method. Subsequently, the range estimates of targets are achieved by utilizing a pulse with a nonzero frequency increment. Specifically, after obtaining the angle estimates of targets, we perform dimensionality reduction processing on the overcomplete dictionary to achieve the automatically paired range and angle in range estimation. Grid partition will bring a heavy computational burden. Therefore, we adopt an iterative grid refinement method to alleviate the above limitation on parameter estimation and propose a new iteration criterion to improve the error between real parameters and their estimates to get a trade-off between the high-precision grid and the atomic correlation. Finally, the proposed algorithm is evaluated by providing the results of the Cramér-Rao lower bound (CRLB) and numerical root mean square error (RMSE).

Design and Application of a Greedy Pursuit Algorithm Adapted to Overcomplete Dictionary for Sparse Signal Recovery

Compressive sensing (CS) is a novel paradigm to recover a sparse signal in compressed domain. In some overcomplete dictionaries, most practical signals are sparse rather than orthonormal. Signal space greedy method can derive the optimal or near-optimal projections, making it possible to identify a few most relevant dictionary atoms of an arbitrary signal. More practically, such projections can be processed by standard CS recovery algorithms. This paper proposes a signal space subspace pursuit (SSSP) method to compute spare signal representations with overcomplete dictionaries, whenever the sensing matrix satisfies the restricted isometry property adapted to dictionary (D-RIP). Specifically, theoretical guarantees were provided to recover the signals from their measurements with overwhelming probability, as long as the sensing matrix satisfies the D-RIP. In addition, a thorough analysis was performed to minimize the number of measurements required for such guarantees. Simulation results demonstrate the validity of our hypothetical theory, as well as the superiority of the proposed approach.