Synthesis versus analysis in patch-based image priors

In global models/priors (for example, using wavelet frames), there is a well known analysis vs synthesis dichotomy in the way signal/image priors are formulated. In patch-based image models/priors, this dichotomy is also present in the choice of how each patch is modeled. This paper shows that there is another analysis vs synthesis dichotomy, in terms of how the whole image is related to the patches, and that all existing patch-based formulations that provide a global image prior belong to the analysis category. We then propose a synthesis formulation, where the image is explicitly modeled as being synthesized by additively combining a collection of independent patches. We formally establish that these analysis and synthesis formulations are not equivalent in general and that both formulations are compatible with analysis and synthesis formulations at the patch level. Finally, we present an instance of the alternating direction method of multipliers (ADMM) that can be used to perform image denoising under the proposed synthesis formulation, showing its computational feasibility. Rather than showing the superiority of the synthesis or analysis formulations, the contributions of this paper is to establish the existence of both alternatives, thus closing the corresponding gap in the field of patch-based image processing.Comment: To appear in ICASSP 201

Neutrino masses from SUSY breaking in radiative seesaw models

Radiatively generated neutrino masses ($m_\nu$) are proportional to supersymmetry (SUSY) breaking, as a result of the SUSY non-renormalisation theorem. In this work, we investigate the space of SUSY radiative seesaw models with regard to their dependence on SUSY breaking (\require{cancel}\cancel{\text{SUSY}}). In addition to contributions from sources of $\cancel{\text{SUSY}}$ that are involved in electroweak symmetry breaking ($\cancel{\text{SUSY}}_\text{EWSB}$ contributions), and which are manifest from $\langle F^\dagger_H \rangle = \mu \langle \bar H \rangle \neq 0$ and $\langle D \rangle = g \sum_H \langle H^\dagger \otimes_H H \rangle \neq 0$, radiatively generated $m_\nu$ can also receive contributions from $\cancel{\text{SUSY}}$ sources that are unrelated to EWSB ($\cancel{\text{SUSY}}_\text{EWS}$ contributions). We point out that recent literature overlooks pure-$\cancel{\text{SUSY}}_\text{EWSB}$ contributions ($\propto \mu / M$) that can arise at the same order of perturbation theory as the leading order contribution from $\cancel{\text{SUSY}}_\text{EWS}$. We show that there exist realistic radiative seesaw models in which the leading order contribution to $m_\nu$ is proportional to $\cancel{\text{SUSY}}_\text{EWS}$. To our knowledge no model with such a feature exists in the literature. We give a complete description of the simplest model-topologies and their leading dependence on $\cancel{\text{SUSY}}$. We show that in one-loop realisations $L L H H$ operators are suppressed by at least $\mu \, m_\text{soft} / M^3$ or $m_\text{soft}^2 / M^3$. We construct a model example based on a one-loop type-II seesaw. An interesting aspect of these models lies in the fact that the scale of soft-$\cancel{\text{SUSY}}$ effects generating the leading order $m_\nu$ can be quite small without conflicting with lower limits on the mass of new particles.Comment: Accepted for publication in European Physical Journal C; 23 pages + appendices; references updated; minor revisions; extended conclusion

Slepton mass splittings and cLFV in the SUSY seesaw in the light of recent experimental results

Following recent experimental developments, in this study we re-evaluate if the interplay of high- and low-energy lepton flavour violating observables remains a viable probe to test the high-scale type-I supersymmetric seesaw. Our analysis shows that fully constrained supersymmetric scenarios no longer allow to explore this interplay, since recent LHC data precludes the possibility of having sizeable slepton mass differences for a slepton spectrum sufficiently light to be produced, and in association to BR(mu -> e gamma) within experimental reach. However, relaxing the strict universality of supersymmetric soft-breaking terms, and fully exploring heavy neutrino dynamics, still allows to have slepton mass splittings O(few %), for slepton masses accessible at the LHC, with associated mu -> e gamma rates within future sensitivity. For these scenarios, we illustrate how the correlation between high- and low-energy lepton flavour violating observables allows to probe the high-scale supersymmetric seesaw.Comment: 19 pages, 12 eps figures. References updated; matches version accepted by JHE