For the data projection r and noise estimation e, we can get the closed-form solutions for them respectively, as shown in Algorithm 1.1. In particular, the closed-form solution to a projection to 1-ball in updating e involves a soft thresholding operator S λ [·] Hale et al. (2008), which is defined as:

| We consider the problem of synthesizing feasible signals in a Hilbert space in the presence of inconsistent convex constraints, some of which must imperatively be satissed. This problem is formalized as that of minimizing a convex objective measuring the amount of violation of the soft constraints over the intersection of the sets associated with the hard ones. The resulting convex optimizati...

We investigate valued fields which admit a valuation basis. Given a countable ordered abelian group G and a real closed, or algebraically closed field F , we give a sufficient condition for a valued subfield of the field of generalized power series F ((G)) to admit a K-valuation basis. We show that the field of rational functions F (G) and the field F (G) of power series in F ((G)) algebraic ov...

Generally converter when operated at high frequency results in losses. In this paper a single stage soft switching PFC converter analysis is done. It is developed with a new active snubber cell which provides zero-voltage transition turn ON and zero-current transition turn OFF. This type of converter circuit design does not have additional resonant components. Operating the proposed converter a...

We investigate valued fields which admit a valuation basis. Given a countable ordered abelian group G and a real closed or algebraically closed field F with subfield K, we give a sufficient condition for a valued subfield of the field of generalized power series F ((G)) to admit aK-valuation basis. We show that the field of rational functions F (G) and the field F (G) of power series in F ((G))...

Two vertices u and v in a nontrivial connected graph G are twins if u and v have the same neighbors in V (G) − {u, v}. If u and v are adjacent, they are referred to as true twins; while if u and v are nonadjacent, they are false twins. For a positive integer k, let c : V (G) → Zk be a vertex coloring where adjacent vertices may be assigned the same color. The coloring c induces another vertex c...

Let G=(V, E) be an Eulerian graph embedded on a triangulizable surface S. We show that E can be decomposed into closed curves C1 , ..., Ck such that mincr(G, D)= i=1 mincr(Ci , D) for each closed curve D on S. Here mincr(G, D) denotes the minimum number of intersections of G and D$ (counting multiplicities), where D$ ranges over all closed curves D$ freely homotopic to D and not intersecting V....

Ligamentous injuries of the lower limb are a common entity sustained during sports activities and military training. Magnetic resonance (MR) imaging of the knee and ankle is playing an increasingly important role in the detection, diagnosis and prognosis of these injuries and their associated complications. MR imaging with its exquisite soft tissue contrast resolution and multiplanar capability...