Moreover, we propose an efficient implementation, whereby the shape matrix of the lifted ellipsoid is stored in sparse format, and every atom operation corresponds to a sparse update in that matrix.
Moreover, to make the coefficients conversion more reliable in the iterative process, we bring the non-local self-similarity constraint to regularize the HR sparse coefficients updates.
Based on the updated Equation 33, for better understanding, NLMS-based sparse adaptive updated equation can be generalized as h ˜ n + 1 = h ˜ n + Normalized adaptive error update ⏟ NLMS + Sparse penalty ⏟ sparse NLMS, (34).
Hence, in order to reduce the computational complexity of PNLMS and IPNLMS, the sparse partial update NLMS SPNLMSS) algorithm was recently proposed [12], which combines two adaptation strategies: sparse adaptation for improving rate of convergence and partial-updating for complexity reduction.
The sparse partial (SP) update NLMS SPNLMSS) algorithm [12] utilizes the sparse nature of network impulse response.
A practical problem with dictionary learning techniques is that they are computationally expensive because the dictionaries are learned by iteratively recovering sparse vectors and updating the dictionary atoms [45, 46].
Usually, methods that are flexible enough would separate the dictionary updates with sparse coding stage.
In order to achieve the fuzzy sparse signal representations, the update of the dictionary columns is combined with an update of the sparse representations by embedding a new mechanism of fuzzy set, which is called parameterized fuzzy K-SVD.
The maximum number of iterations for performing iterative updating between sparse channel estimation, MIMO detection and nonbinary LDPC decoding is 10, where we update both the channel estimation and the MIMO detection in each iteration.
Because the dictionary used in our work is learned as a pre-processing step employing arbitrary images, the update process of background ({P_{B}^{i}}) requires updating the sparse coefficients α i of the background model every frame or after some number of frames according to the implementation requirements.
