We are interested in the restoration of noisy and blurry images where the texture mainly follows a single direction (i.e., directional images). Problems of this type arise, for example, in microscopy or computed tomography for carbon or glass fibres. In order to deal with these problems, the Directional Total Generalized Variation (DTGV) was developed by Kongskov et al. in 2017 and 2019, in the case of impulse and Gaussian noise. In this article we focus on images corrupted by Poisson noise, extending the DTGV regularization to image restoration models where the data fitting term is the generalized Kullback–Leibler divergence. We also propose a technique for the identification of the main texture direction, which improves upon the techniques used in the aforementioned work about DTGV. We solve the problem by an ADMM algorithm with proven convergence and subproblems that can be solved exactly at a low computational cost. Numerical results on both phantom and real images demonstrate the effectiveness of our approach.

It is recognized that biochar undergoes changes when it is applied to soils. However, the mechanisms of biochar alterations are not fully understood yet. To this purpose, the present study is designed to investigate the transformations in the soil of two different biochars obtained from pyrolysis of fir-wood pellets. The production of the biochars differed for the dry and wet quenching procedures used to terminate the pyrolysis. Both biochars were applied to clay soil (26% sand, 6% silt, and 68% clay) placed into lysimeters. After water saturation and 15 days of equilibration, seeds of watercress (Lepidium sativum) were cultivated. After a further 7 weeks, the biochars were manually separated from the systems. A total of four samples were collected. They were analyzed for chemical–physical characteristics by using an innovative technique referred to as fast field cycling nuclear magnetic resonance relaxometry. The results showed that the dry−quenching produced a material that was mainly chemically altered after application to soil compared to the biochar obtained by the wet−quenching. Indeed, the latter was both chemically and physically modified. In particular, results showed that water was better retained in the soil treated with the dry−quenched material. Consequently, we may suggest that crop productivity and environmental remediation may be modulated by applying either the dry−quenched or the wet−quenched biochar.