Wearable electronics capable of recording and transmitting biosignals can provide convenient and pervasive health monitoring. A typical EEG recording produces large amount of data. Conventional compression methods cannot compress date below Nyquist rate, thus resulting in large amount of data even after compression. This needs large storage and hence long transmission time. Compressed sensing has proposed solution to this problem and given a way to compress data below Nyquist rate. In this paper, double temporal sparsity based reconstruction algorithm has been applied for the recovery of compressively sampled EEG data. The results are further improved by modifying the double temporal sparsity based reconstruction algorithm using schattern-p norm along with decorrelation transformation of EEG data before processing. The proposed modified double temporal sparsity based reconstruction algorithm out-perform block sparse bayesian learning and Rackness based compressed sensing algorithms in terms of SNDR and NMSE. Simulation results further show that the proposed algorithm has better convergence rate and less execution time.
The application of compressed sensing (CS) to magnetic resonance (MR) images utilizes the transformed domain sparsity to enable the reconstruction from an under-sampled k-space (Fourier) data using a non-linear recovery algorithm. In order to estimate the missing k-space data from the partial Fourier samples, the reconstruction algorithms minimize an objective function based on mixed l 1 -l 2 norms. Iterative-shrinkage algorithms, such as parallel coordinate descent (PCD) and separable surrogate functional, provide an efficient numerical technique to minimize the l 1 -regularized least square optimization problem. These algorithms require a thresholding step to induce sparsity in the solution, which is an essential requirement of the CS recovery. This paper introduces a novel soft-thresholding method based on the hyperbolic tangent function. It has been shown that by using the proposed thresholding function in the sparsifying domain and a data consistency step in the k-space, the iterative-shrinkage algorithms can be used effectively to recover the under-sampled MR images. For the purpose of demonstration, we use the proposed soft-thresholding and data consistency with the PCD algorithm and compare its performance with the conventional PCD, projection onto convex sets and low-resolution reconstruction methods. The metrics used to compare the various algorithms are the artifact power, the peak signal-to-noise ratio, the correlation and the structural similarity index. The experimental results are validated using SheppLogan phantom image as well as real human head MR images taken from the MRI scanner at
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