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Objective To explore whether modified Chevron osteotomy together with distal soft tissue release would correct moderate to severe HV deformity and what is the minimal clinical important difference (MCID) for objective and subjective evaluating parameters. Methods From March 2018 to January 2019, 40 hallux valgus patients (including moderate to severe) were enrolled in this retrospective study. The cohort included four males and 36 females. The average age at surgery was 50.95 (range 22–75) years. All patients underwent modified Chevron osteotomy together with distal soft tissue release and completed at least one follow‐up at clinic. The American Orthopaedic Foot and Ankle forefoot score (AOFAS, forefoot), Visual Analog Scale (VAS), and Foot Function Index (FFI) were all collected before and after surgery. Besides, the hallux valgus angle (HVA), 1st–2nd intermetatarsal angle (IMA) and distal metatarsal articular angle (DMAA) were measured both before surgery and at last follow‐up. All MCID values were calculated by employing distribution‐based method. Results Thirty‐seven patients (92.5%) showed satisfied result at a mean 14.3‐month follow‐up (range 13–22 month). Two patients complained about residual pain at the bunion, and overcorrection (hallux varus) occurred in one patient. Meanwhile, no patient observed nonunion. Being female, age more than 60, residual HVA deformity (>15°), and post IMA more than 9° showed no statistical relationship with the post‐operation residual pain (P > 0.05). However, high VAS score before surgery (more than 7) showed strong correlation with residual pain (P < 0.01). The subjective MCID value was 9.50 for AOFAS, 18.92 for FFI, and 1.27 for VAS, respectively. Conclusion The modified Chevron osteotomy together with distal soft tissue release could achieve a satisfied result for moderate to severe HV deformity at early follow‐up. The residual pain was associated with severe pain before surgery (VAS more than 7).

Complex-valued shift-invariant canonical polyadic decomposition (CPD) under a spatial phase sparsity constraint (pcsCPD) shows excellent separation performance when applied to band-pass filtered complex-valued multi-subject fMRI data. However, some useful information may also be eliminated when using a band-pass filter to suppress unwanted noise. As such, we propose an alternating rank- ${R}$ and rank-1 least squares optimization to relax the CPD model. Based upon this optimization method, we present a novel constrained CPD algorithm with temporal shift-invariance and spatial sparsity and orthonormality constraints. More specifically, four steps are conducted until convergence for each iteration of the proposed algorithm: 1) use rank- ${R}$ least-squares fit under spatial phase sparsity constraint to update shared spatial maps after phase de-ambiguity; 2) use orthonormality constraint to minimize the cross-talk between shared spatial maps; 3) update the aggregating mixing matrix using rank- ${R}$ least-squares fit; 4) utilize shift-invariant rank-1 least-squares on a series of rank-1 matrices reconstructed by each column of the aggregating mixing matrix to update shared time courses, and subject-specific time delays and intensities. The experimental results of simulated and actual complex-valued fMRI data show that the proposed algorithm improves the estimates for task-related sensorimotor and auditory networks, compared to pcsCPD and tensorial spatial ICA. The proposed alternating rank- ${R}$ and rank-1 least squares optimization is also flexible to improve CPD-related algorithm using alternating least squares.

We consider the joint estimation of direction-of-arrival (DOA) and polarization of constant modulus (CM) signals based on an electromagnetic vector-sensor (EMVS) array. Two algebraic algorithms for canonical polyadic decomposition (CPD) with CM constraint are proposed in two scenarios, in which the source signals are fully and partially CM, respectively. The proposed algorithms use the analytic CM algorithm in the first step to calculate the source matrix, and then exploit the CPD structure of the data tensor to compute the remaining factor matrices, from which the DOA and polarization parameters can finally be obtained. Due to the algebraic nature, the proposed algorithms are faster and more stable than the optimization based algorithms, and can be used to effectively initialize the latter. We have shown that the proposed algorithms have more relaxed uniqueness conditions than unconstrained CPD, and thus can be applied in highly underdetermined cases where the number of source signals greatly exceeds that of the EMVSs. Simulation results are provided to illustrate the performance of the proposed algorithms.

Joint blind source separation (J-BSS) has emerged as a data-driven technique for multi-set data fusion applications. In this paper, we propose a Jacobi generalized orthogonal joint diagonalization (GOJD) algorithm for J-BSS of multiset signals. By the use of second-order statistics, we can obtain multiple sets of auto-covariance and cross-covariance matrices from the multi-set signals, which together admit a GOJD formulation. For computing the GOJD, we propose a computationally efficient Jacobi algorithm, which uses a sequence of Givens rotations to simultaneously diagonalize the covariance matrices. In comparison with other GOJD algorithms, the proposed algorithm is shown to have fast convergence. Moreover, as the optimal Givens rotation matrix in each update is calculated in closed-form, this algorithm is computationally very efficient. In the application aspect, we have considered the scenario where different data sets in J-BSS may have different number of sources, among which there exist both similar components that are consistently present in multiple data sets, and diverse components that are uniquely present in each data set. We have shown how J-BSS based on the proposed GOJD algorithm can effectively extract both similar and diverse source components. Simulation results are given to show the nice performance of the proposed algorithm, with regards to both speed and accuracy, in comparison with other algorithms of similar type.

Joint estimation of direction-of-arrival (DOA) and polarization with electromagnetic vector-sensors (EMVS) is considered in the framework of complex-valued non-orthogonal joint diagonalization (CNJD). Two new CNJD algorithms are presented, which propose to tackle the high dimensional optimization problem in CNJD via a sequence of simple sub-optimization problems, by using LU or LQ decompositions of the target matrices as well as the Jacobi-type scheme. Furthermore, based on the above CNJD algorithms we present a novel strategy to exploit the multi-dimensional structure present in the second-order statistics of EMVS outputs for simultaneous DOA and polarization estimation. Simulations are provided to compare the proposed strategy with existing tensorial or joint diagonalization based methods.