By designing appropriate preconditioners to the measurement matrix, we show gradient enhanced ℓ1 minimization leads to stable and accurate coefficient recovery.
Taking random matrix as measurement matrix, we also discuss the advantage of our condition.
To obtain a more suitable measurement matrix, we exploit the features of EMV.
In order to analyze the performance and characteristics of the Kronecker product measurement matrix, we apply the measurement matrix to a 2-D image acquisition simulation experiment and compare it with the Gaussian random matrix, Fourier matrix, Bernoulli matrix, Toeplitz matrix, polynomial matrix, and measurement matrix which are commonly used.
Otherwise, due to the random feature of the measurement matrix, we got the average criterion value of a subgroup by calculating three times and acquired the mean value as the criterion value.
In terms of a block variant of the restricted isometry property of measurement matrix, we present weaker sufficient conditions for exact and robust block-sparse signal recovery than those known for l 2/l 1 minimization.
To effectively reduce the storage space of a random measurement matrix, we propose an STP approach for the CS algorithm (STP-CS), which can reduce storage space to at least a quarter of the size while maintaining the quality of reconstructed signals or images.
With the sparse vector x and Gaussian random measurement matrices Φ t), we obtained the measurement vectors of length M = 128 by (7).
When we derive a vector of measurements y M×1 by a random measurement matrix Φ t), we initialize the algorithm by taking w 0 = (1, ⋯ , 1 1 × N , x 0 = (1, ⋯1)1 × N, and ε 0 = 1.
To optimize measurement matrix Φ, we exploit the EMV features and propose a FAWC optimization method in this paper.
