This paper considers the problem of outlier censoring from secondary data, where the number, amplitude and location of outliers is unknown. To this end, a novel sparse recovery technique based on joint block sparse learning via iterative minimization (BSLIM) and model order selection (MOS), called JBM, is proposed which exploits the inherent sparse nature of the outliers in homogeneous background. The cost function proposed here, unlike many similar works in this field, does not require a dictionary matrix.

In this paper, we show that the adaptive projected subgradient method (APSM) is bounded perturbation resilient. To illustrate a potential application of this result, we propose a set-theoretic framework for MIMO detection, and we devise algorithms based on a superiorized APSM. Various low-complexity MIMO detection algorithms achieve excellent performance on i.i.d. Gaussian channels, but they typically incur high performance loss if realistic channel models (e.g., correlated channels) are considered.

In the second part of the series papers, we set out to study the algorithmic efficiency of sparsity-constrained sensing. Stemmed from co-prime sampling/array, we propose a generalized framework, termed Diophantine sensing, which utilizes generic Diophantine equation theory and higher-order sparse ruler to strengthen the sampling time (delay), the degree of freedom (DoF), and the sampling sparsity, simultaneously. It is well known that co-prime sensing can reconstruct the autocorrelation of a sequence with significantly more lags based on Bézout theorem.

In this paper, new results in random matrix theory are derived, which allow us to construct a shrinkage estimator of the global minimum variance (GMV) portfolio when the shrinkage target is a random object. More specifically, the shrinkage target is determined as the holding portfolio estimated from previous data. The theoretical findings are applied to develop theory for dynamic estimation of the GMV portfolio, where the new estimator of its weights is shrunk to the holding portfolio at each time of reconstruction.

This paper deals with joint adaptive radar detection and target bearing estimation in the presence of mutual coupling among the array elements. First of all, a suitable model of the signal received by the multichannel radar is developed via a linearization procedure of the Uniform Linear Array (ULA) manifold around the nominal array looking direction together with the use of symmetric Toeplitz structured matrices to represent the mutual coupling effects. Hence, the Generalized Likelihood Ratio Test (GLRT) detector is evaluated under the assumption of homogeneous radar environment.