One of the main parameters influencing microalgae production is light, which provides energy to support metabolism but, if present in excess, can lead to oxidative stress and growth inhibition. In this work, the influence of illumination on Scenedesmus obliquus growth was assessed by cultivating cells at different light intensities in a flat plate photobioreactor. S. obliquus showed a maximum growth rate at 150 μmol photons m(-2) s(-1). Below this value, light was limiting for growth, while with more intense illumination photosaturation effects were observed, although cells still showed the ability to duplicate. Looking at the biochemical composition, light affected the pigment contents only while carbohydrate, lipid, and protein contents remained stable. By considering that in industrial photobioreactors microalgae cells are subjected to light-dark cycles due to mixing, algae were also grown under pulsed illumination (5, 10, and 15 Hz). Interestingly, the ability to exploit pulsed light with good efficiency required a pre-acclimation to the same conditions, suggesting the presence of a biological response to these conditions.
This article adapts the framework of metamorphosis to solve inverse problems in imaging that includes joint reconstruction and image registration. The deformations in question have two components, one that is a geometric deformation moving intensities and the other a deformation of intensity values itself, which, e.g., allows for appearance of a new structure. The idea developed here is to reconstruct an image from noisy and indirect observations by registering, via metamorphosis, a template to the observed data. Unlike a registration with only geometrical changes, this framework gives good results when intensities of the template are poorly chosen. We show that this method is a well-defined regularisation method (proving existence, stability and convergence) and present several numerical examples.In particular, we have shown that (ν ∞ , ζ ∞ ) minimises J γ,τ ( · ; g).Our final results concerns convergence, which investigates the behaviour of the solution as data error tends to zero and regularization parameters are adapted accordingly through a parameter choice rule against the data error.Proposition 6 (Convergence). Let g ∈ Y and assume A W(ϕ ν 0,1 , I ν,ζ 1 ) = g for some (ν, ζ) ∈ L 2 ([0, 1], V × X).Next, for parameter choice rules δ → γ(δ) and δ → τ (δ) with δ > 0, define (ν δ , ζ δ ) ∈ arg min (ν,ζ) J γ(δ),τ (δ) (ν, ζ; g + e δ )
We propose a new variational model for joint image reconstruction and motion estimation in spatiotemporal imaging, which is investigated along a general framework that we present with shape theory. This model consists of two components, one for conducting modified static image reconstruction, and the other performs sequentially indirect image registration. For the latter, we generalize the large deformation diffeomorphic metric mapping framework into the sequentially indirect registration setting. The proposed model is compared theoretically against alternative approaches (optical flow based model and diffeomorphic motion models), and we demonstrate that the proposed model has desirable properties in terms of the optimal solution. The theoretical derivations and efficient algorithms are also presented for a time-discretized scenario of the proposed model, which show that the optimal solution of the time-discretized version is consistent with that of the time-continuous one, and most of the computational components is the easy-implemented linearized deformation. The complexity of the algorithm is analyzed as well. This work is concluded by some numerical examples in 2D space + time tomography with very sparse and/or highly noisy data.
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