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This dissertation details three approaches for direction-of-arrival (DOA) estimation or beamforming in array signal processing from the perspective of sparsity. In the first part of this dissertation, we consider sparse array beamformer design based on the alternating direction method of multipliers (ADMM); in the second part of this dissertation, the problem of joint DOA estimation and distorted sensor detection is investigated; and off-grid DOA estimation is studied in the last part of this dissertation. In the first part of this thesis, we devise a sparse array design algorithm for adaptive beamforming. Our strategy is based on finding a sparse beamformer weight to maximize the output signal-to-interference-plus-noise ratio (SINR). The proposed method utilizes ADMM, and admits closed-form solutions at each ADMM iteration. The algorithm convergence properties are analyzed by showing the monotonicity and boundedness of the augmented Lagrangian function. In addition, we prove that the proposed algorithm converges to the set of Karush-Kuhn-Tucker stationary points. Numerical results exhibit its excellent performance, which is comparable to that of the exhaustive search approach, slightly better than those of the state-of-the-art solvers, and significantly outperforms several other sparse array design strategies, in terms of output SINR. Moreover, the proposed ADMM algorithm outperforms its competitors, in terms of computational cost. Distorted sensors could occur randomly and may lead to the breakdown of a sensor array system. In the second part of this thesis, we consider an array model in which a small number of sensors are distorted by unknown sensor gain and phase errors. With such an array model, the problem of joint DOA estimation and distorted sensor detection is formulated under the framework of low-rank and row-sparse decomposition. We derive an iteratively reweighted least squares (IRLS) algorithm to solve the resulting problem. The convergence property of the IRLS algorithm is analyzed by means of the monotonicity and boundedness of the objective function. Extensive simulations are conducted in view of parameter selection, convergence speed, computational complexity, and performance of DOA estimation as well as distorted sensor detection. Even though the IRLS algorithm is slightly worse than the ADMM in detecting the distorted sensors, the results show that our approach outperforms several state-of-the-art techniques in terms of convergence speed, computational cost, and DOA estimation performance. In the last part of this thesis, the problem of off-grid DOA estimation is investigated. We develop a method to jointly estimate the closest spatial frequency (the sine of DOA) grids, and the gaps between the estimated grids and the corresponding frequencies. By using a second-order Taylor approximation, the data model under the framework of joint-sparse representation is formulated. We point out an important property of the signals of interest in the model, namely the proportionality relationship. The proportionality relationship is empirically demonstrated to be useful in the sense that it increases the probability of the mixing matrix satisfying the block restricted isometry property. Simulation examples demonstrate the effectiveness and superiority of the proposed method against several state-of-the-art grid-based approaches.

This study aimed to establish an optimal model to predict the busulfan (BU) area under the curve at steady state (AUCss) by using machine learning (ML). Seventy-nine adult patients (age ≥18 years) who received BU intravenously and underwent therapeutic drug monitoring from 2013 to 2021 at Fujian Medical University Union Hospital were enrolled in this retrospective study. The whole dataset was divided into a training group and test group at the ratio of 8:2. BU AUCss were considered as the target variable. Nine different ML algorithms and one population pharmacokinetic (pop PK) model were developed and validated, and their predictive performance was compared. All ML models were superior to the pop PK model (R2 = 0.751, MSE = 0.722, 14 and RMSE = 0.830) in model fitting and had better predictive accuracy. The ML model of BU AUCss established through support vector regression (SVR) and gradient boosted regression trees (GBRT) had the best predictive ability (R2 = 0.953 and 0.953, MSE = 0.323 and 0.326, and RMSE = 0.423 and 0.425). All the ML models can potentially be used to estimate BU AUCss with the aim of facilitating rational use of BU on the individualized level, especially models built by SVR and GBRT algorithms.

Bacterial biofilms cause significant concern in a variety of fields, including infectious diseases, medical devices, food preparation, agriculture and water treatment management. Antibiotics are drugs that are intended to eradicate bacteria in their planktonic state; however, bacteria embedded within biofilms are more tolerant and resistant to these treatments. As a result, developing effective antibiofilm strategies is critical and urgent. The aim of this thesis was to develop new bioactive and stimuli-responsive nanomaterials to overcome antibiotic resistance. A pH-responsive diblock polymer was synthesised using reversible addition-fragmentation chain transfer (RAFT) polymerisation. It was comprised of poly(oligo(ethylene glycol) methyl ether acrylate) hydrophilic block and poly(3-vinyl-benzaldehyde) functional block (POEGA-b-PVBA). Furthermore, the therapeutic agents were attached to the prepared polymer via Schiff base formation. This pH-labile linkage is hydrolysable in mildly acidic conditions, such as the environment in which biofilms often exist. The current study adopted three strategies using POEGA-b-PVBA polymer as a linker to form multimodal nano-formulations with antibacterial and antibiofilm properties. These new nano-formulations are expected to improve the stability of the antibacterial components and the local concentrations of these agents at the target site, and enhance antimicrobial effects, thereby lowering the therapeutic concentration needed for each agent. In the first project, the diblock polymer, POEGA-b-PVBA, was applied to engineer Pseudomonas bacteriophages (phages) as nanorobots that could also deliver other antimicrobials precisely to target sites. Amikacin (AMK) and nitroxides (biofilm dispersal agents) were conjugated with the phages, and the antibacterial effects were investigated on P. aeruginosa biofilms. These conjugates were shown to effectively disperse biofilms and reduce the viability of biofilm bacteria. Hence, this strategy can be used to enhance phage therapy as an effective and low-cost solution to antibiotic resistance and other difficult-to-treat infections. In the second project, the prepared POEGA-b-PVBA polymer was utilised to functionalise silver nanoparticles (AgNPs) with antibiotics. POEGA-b-PVBA prepared by the RAFT polymerisation technique retains trithiocarbonate end groups, which have a strong affinity with the surface of AgNPs. The results demonstrated that the colloidal stability of AgNPs was improved, and POEGA-b-PVBA@AgNPs exhibited superior antibacterial activity when targeting the growth of P. aeruginosa bacteria compared to the citrate-capped AgNPs. In addition, conjugation of AMK with POEGA-b-PVBA@AgNPs effectively eradicated pre-established biofilms and reduced the viability of planktonic and biofilm bacteria. The third approach highlighted an innovative strategy for formulating nitroxides with AgNPs as a biofilm control agent. The objective was to attach nitroxides to POEGA-b-PVBA@AgNPs to form a nano-formulation that could enhance the local concentration of AgNPs directly at the site of nitroxide-mediated biofilm dispersal. The findings demonstrated that the presence of nitroxides effectively improved the efficacy of POEGA-b-PVBA@AgNPs therapy against P. aeruginosa biofilms. Importantly, conjugation of nitroxides on POEGA-b-PVBA@AgNPs was able to eradicate pre-established biofilms with superior killing effects at concentrations below the minimum inhibitory concentration (sub-MIC). This promising antibacterial and antibiofilm strategy can be extensively applied in many fields, including medical devices, food, agriculture, water management (anti-biofouling), and clinical biofilm-related infections. This research contributed to new knowledge in managing and treating bacterial biofilms. In addition, this study demonstrated the potential of using nanotechnology for the co-delivery of multiple therapeutic agents to enhance the antibacterial and antibiofilm properties of single entities. Altogether, the work presented in this thesis demonstrated promising strategies for controlling the eradication of biofilm that will advance a new technology that could avoid the impasse of antibiotic resistance.