A combined first and second order variational approach for image reconstruction

In this paper we study a variational problem in the space of functions of bounded Hessian. Our model constitutes a straightforward higher-order extension of the well known ROF functional (total variation minimisation) to which we add a non-smooth second order regulariser. It combines convex functions of the total variation and the total variation of the first derivatives. In what follows, we prove existence and uniqueness of minimisers of the combined model and present the numerical solution of the corresponding discretised problem by employing the split Bregman method. The paper is furnished with applications of our model to image denoising, deblurring as well as image inpainting. The obtained numerical results are compared with results obtained from total generalised variation (TGV), infimal convolution and Euler's elastica, three other state of the art higher-order models. The numerical discussion confirms that the proposed higher-order model competes with models of its kind in avoiding the creation of undesirable artifacts and blocky-like structures in the reconstructed images -- a known disadvantage of the ROF model -- while being simple and efficiently numerically solvable.Comment: 34 pages, 89 figure

Evidence for an association of HLA-DRB1*15 and DRB1*09 with leprosy and the impact of DRB1*09 on disease onset in a Chinese Han population

<p>Abstract</p> <p>Background</p> <p>Human leukocyte antigens (HLAs) have been proposed to modulate the immune response to <it>Mycobacterium leprae</it>. The association of HLA-DRB1 with leprosy has been reported in several populations, but not in a Chinese population.</p> <p>Methods</p> <p>The polymerase chain reaction-sequence-specific oligonucleotide probe with Luminex100 (PCR-SSOP-Luminex) method was used to genotype HLA-DRB1 alleles in 305 leprosy patients and 527 healthy control individuals.</p> <p>Results</p> <p>The HLA-DRB1*15 allele was significantly more prevalent among leprosy patients than healthy controls, whereas the frequency of the HLA-DRB1*09 allele was lower among leprosy patients, especially those with early-onset disease.</p> <p>Conclusion</p> <p>HLA-DRB1 alleles are associated with leprosy susceptibility in a Chinese population. The HLA-DRB1*09 allele was found to be protective exclusively in a subset of early-onset leprosy patients.</p

Comparison of two-pulse sodium inactivation with reactivation in Myxicola giant axons.

Values for the time constant of reactivation of the sodium conductance following depolarization sufficient to completely inactivate GNa have been compared over a 15 mV range of membrane potential with the time constants of inactivation during a depolarization prepulse. Over this range the reactivation time constants were consistently 30-50% larger than the inactivation time constants determined simultaneously at the same potential in the same axon. The data suggests that inactivation and reactivation do not occur by identical mechanisms, and therefore implies that there are at least three kinds of experimental procedures necessary to fully characterize the sodium inactivation process in any particular system

Evidence for negative gating charges in Myxicola axons.

In Myxicola giant axons, the total amount of intramembrane charge available to move over the range -80 to + 120 mV decreases by 23% when the external pH is reduced from 7.3 to 5.5. The remaining charge moves more slowly at the onset of depolarizing pulse, but the rate of charge movement at the end of the pulse is unchanged. In contrast to acidic external pH, intramembrane charge movements are insensitive to alkaline external pH or any change in the internal pH. The results are consistent with a hypothesis in which a portion of the initial outward gating current consists of titratable negative charges moving inward

Survival of the K+ channel in axons externally and internally perfused with K+-free media.

In perfused squid giant axons, potassium channels irreversibly deteriorate when the internal K+ is removed and replaced by impermeant ions. Under the same conditions in perfused Myxicola giant axons, the K+ conductance is also irreversibly lost with a time constant of 10-15 min. In contrast, the K+ conductance in Myxicola giant axons dialyzed with impermeant ions and bathed in monovalent cation free solutions does not deteriorate, even over 5-6 h. Thus we suggest that washout of some internal component may be an important additional factor in the deterioration of K+ channels in perfused giant axons