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

Nonlinear multigrid methods for total variation image denoising

The liver cell entry of enalaprilat, the polar, pharmacologically active dicarboxylic acid metabolite arising from esterolysis of enalapril, a new angiotensin-converting enzyme inhibitor, was examined in the perfused rat liver by use of the multiple-indicator dilution technique. [Phenylpropyl-2,3-3H]enalaprilat was injected into the portal vein in a bolus of blood containing 51Cr-labeled red blood cells (a vascular reference) and 125I-labeled albumin and [14C]sucrose (interstitial references that do not enter cells), with observation of the time courses of their outflow into the hepatic venous blood. A quantitative evaluation of the data was carried out by use of the barrier-limited, space-distributed variable transit time model (C.A. Goresky, G.G. Bach, and B. E. Nadeau, J. Clin. Invest. 52:991-1009, 1973). For data up to 60 s after injection, the transfer coefficients for influx, efflux, and sequestration were 0.018 +/- 0.004 (means +/- SD), 0.044 +/- 0.017, and 0.033 +/- 0.007 s-1, respectively. The influx permeability surface area product (influx clearance) per gram was 0.0057 +/- 0.0013 ml.min-1.g-1, and the rapidly accessible cellular equilibrium distribution space for enalaprilat was 0.137 +/- 0.022 ml water/g wet wt. At times beyond 60 s, the fitted data deviated systematically from the experimental data, suggesting the presence of an additional intracellular pool. With this addition, the coefficients for transfer between the intracellular pools were 0.0150 +/- 0.0045 s-1 for the direction cytoplasmic pool (pool 1)----additional pool (pool 2) and 0.0234 +/- 0.0069 s-1 for the opposite direction, and the fitted volumes of pools 1 and 2 became 0.126 +/- 0.021 and 0.082 +/- 0.018 ml/g, the total accessible cellular distribution space became 0.208 +/- 0.036 ml/g wet wt, and the sequestration transfer coefficient became 0.027 +/- 0.007 s-1. The data indicate that, as previously postulated (I. A. M. de Lannoy and K. S. Pang, Drug Metab. Dispos. 14: 513-520, 1986), the enalaprilat flux across liver cell membranes is retarded by a diffusional barrier. The results also indicate that enalaprilat is excluded from part of the volume of hepatocytes, as expected for an anionic compound crossing the membrane in charged rather than protonated form, given the negative electrical potential of the cytosol vs. the extracellular space