Sensing Matrix Optimization Based on Equiangular Tight Frames With Consideration of Sparse Representation Error

Approximate equiangular tight frames for compressed sensing and CDMA applications

“…(5). Our comparison includes the work presented in [22] and [26]; similar results were obtained by comparing with other existing algorithms [23,24,30]. Figure 4 demonstrates typical results obtained with [22] and [26] for a 64 × 128 frame.…”

“…Eq. 4 provides a representation of the Gram matrix of [26], [30] and proposed method. The optimal lowest bound (Welch bound) for these dimensions is μ opt = 0.0887 and μ opt = 0.0512, respectively an ETF that enables a decoupling optimization strategy: the signature matrix can be directly optimized without being subjected to incoherence constraints.…”

“…Thus, a category of algorithms that produce incoherent frames has been developed in the latest years [22][23][24][25][26][27][28][29][30]. Most of the existing algorithms are inspired by the work of [17] and are based on a "shrinkage" operation on the Gram matrix.…”

“…The proposed constructions are compared with random Gaussian matrices and incoherent tight frames produced with [26] and [30]. Both [26] and [30] attain small mutual coherence; however, they do not exhibit the approximate equiangularity property like the proposed constructions.…”

“…The obtained measurements are used to find the unknown sparse signal, using OMP, a well-known algorithm for sparse signal recovery. The experiments are realized using random Gaussian matrices, incoherent UNTFs produced with [26], [30], and the frames produced with Algorithms 3 and 4. Varying the number of measurements m = {15, 20, 25, 30, 35}, for every value of m, we perform 10,000 experiments.…”