—The l 1-norm minimization problem plays an important role in the compressed sensing (CS) theory. We present in this letter an algorithm for solving the problem of l 1 Index Terms—L-norm minimization for quaternion signals by converting it to second-order cone programming. An application example of the proposed algorithm is also given for practical guidelines of perfect recovery of quaternion s...

Isotonic regression, the problem of finding values that best fit given observations and conform to specific ordering constraints, has found many applications in biomedical research and other fields. When the constraints form a partial ordering, solving the problem under the L1 error measure takes O(n) when there are n observations. The analysis of large-scale microarray data, which is one of th...

We investigate C1-smooth univariate curvature-based cubic L1 interpolating splines in Cartesian and polar coordinates. The coefficients of these splines are calculated by minimizing the L1 norm of curvature. We compare these curvature-based cubic L1 splines with second-derivative-based cubic L1 splines and with cubic L2 splines based on the L2 norm of curvature and of the second derivative. In ...

The l1 norm is the tight convex relaxation for the l0 “norm” and has been successfully applied for recovering sparse signals. However, for problems with fewer samples than required for accurate l1 recovery, one needs to apply nonconvex penalties such as lp “norm”. As one method for solving lp minimization problems, iteratively reweighted l1 minimization updates the weight for each component bas...

We prove additivity of the minimal conditional entropy associated with a quantum channel Φ, represented by a completely positive (CP), trace-preserving map, when the infimum of S(γ12)−S(γ1) is restricted to states of the form (I⊗Φ) ( |ψ〉〈ψ| ) . We show that this follows from multiplicativity of the completely bounded norm of Φ considered as a map from L1 → Lp for Lp spaces defined by the Schatt...

Immunotherapy approaches currently make their way into the clinics to improve the outcome of standard radiochemotherapy (RCT). The programed cell death receptor ligand 1 (PD-L1) is one possible target that, upon blockade, allows T cell-dependent antitumor immune responses to be executed. To date, it is unclear which RCT protocol and which fractionation scheme leads to increased PD-L1 expression...

The Huber function is an hybrid l1-l2 misfit measure. We demonstrate, on velocity analysis examples, that the Huber function is more robust to outlier effects, and more stable with respect to the number of iterations than the l2 norm. We also show that the Huber threshold which controls the transition between the l1 and the l2 norm may be chosen within a certain range of values without damaging...

We reformulate the zero-norm minimization problem as an equivalent mathematical program with equilibrium constraints and establish that its penalty problem, induced by adding the complementarity constraint to the objective, is exact. Then, by the special structure of the exact penalty problem, we propose a decomposition method that can seek a global optimal solution of the zero-norm minimizatio...

This study concerns decentralized control of interconnected positive systems. The main issue is how to design a controller for each subsystem locally so that positivity and stability of the overall interconnected system can be attained. Under a specific interconnection structure, we will show that such a controller can be designed optimally without any information about the rest of the positive...