The 'Methods for Image and Data Analysis (MIDA)' group at the Dipartimento di Matematica, Università di Genova, has been founded with the aim of
  • formulating data and image analysis problems within methodological settings of strong mathematical flavor;
  • applying data and image analysis methods to problems of interests for physics and physiology;
  • formulating models for the interpretation of the results of the data and image analysis procedures.
From a computational viewpoint we develop qualitative and quantitative methods for the inversion of acoustical and electromagnetic scattering data, deterministic and statistical techniques for the regularization of linear and non-linear ill-posed problems and soft computing algorithms for the automatic recognition of patterns in images or large amounts of data. Our applications are mainly concerned with the formulation of spectroscopy, imaging and imaging spectroscopy methods in high energy solar physics, the modeling of acceleration mechanisms in solar flares, the reconstruction of images from data acquired by different diagnostic modalities, the compartmental analysis of nuclear medicine data, the exploitation of neurophysiological data recorded by EEG and MEG, the formulation of mathematical models for neurophysiology. MIDA is also active in the development of prototypal techniques (like microwave mammography and cryosurgery) and in the production of software packages in collaboration with high-tech industries and SMEs.

MIDA has been a protagonist of the construction of a computational corpus in Solar SoftWare for the analysis of data collected during the NASA 'Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI)' mission. For example, MIDA invented an original approach to the analysis of RHESSI visibilities that allows the creation of maps of solar flares in which the pixel content is related to the quantity of electrons involved in the bremsstrahlung emission of X-rays from the solar atmosphere. MIDA is currently collaborating at the realization of the ESA mission 'Spectrometer Telescope for Imaging      X-rays (STIX)' in SolarOrbiter.
The Linear Sampling Method provides a qualitative approach to inverse scattering characterized by notable computational effectiveness. MIDA has given contributions to its mathematical foundation and to its application to medical imaging and non-destructive testing. We have worked and are currently working at hybrid techniques in which linear sampling is matched with the Reciprocity Gap Functional method in microwave tomography and with the Contrast Source Inversion method for an optimized solution of the Lippmann-Schwinger equation.
Regularization methods reduce the instability of the solution of ill-posed problems in applied sciences. We work at the formulation of statistical and deterministic regularization algorithms characterized by computational effectiveness and able to enhance the sparsity of the solution. In the statistical framework, our current main interest is filtering dynamical inverse problems by means of particle filters and sequential Monte Carlo methods. We also study iterative approaches to maximum-likelihood and the way to optimally stop them. As far as deterministic regularization is concerned, we are investigating relations between the Hough transform and the Radon transform and searching for possible applicative consequences of such connections.
Medical imaging requires reconstruction techniques able to create images from acquired data and processing techniques able to enhance the quality of the reconstructed images and interpret their content. MIDA systematically works at both problems. Specifically we develop reconstruction methods for spatial resolution enhancement in Positron Emission Tomography (PET), algorithms for distortion reduction in Magnetic Resonance Imaging (MRI), methods for integration of either PET and X-ray CT or PET and MRI data, spectral and statistical techniques for compartmental analysis of nuclear medicine data. MIDA is responsible for all data analysis tasks in the micro-PET core operating at the IRCCS San Martino IST, Genova.
In collaboration with the Nuclear Medicine Unit of the IRCCS San Martino IST, Genova and the Stem Cells Department of the IRCCS G Gaslini, Genova, MIDA is developing an innovative approach to the diagnosis and assessment of hematological diseases by means of the analysis of nuclear medicine data and their integration with structural data provided by X-ray CT and MRI. Our main result thus far has been the realization of a software tool that measures the whole bone marrow asset in humans by integrating PET and CT imaging. The outcomes of this tool are now utilized for both evaluating the impact of leukemic pathologies onto the hematopoietic tissue and functions and validating PDE-based models of stem cells trafficking, homing and engraftment.
MIDA provides computational tools to the development of innovative image-based diagnostic modalities. For example we work at image-based statistical optimization approaches for the design of cryosurgical operations and study inverse scattering approaches for the early detection of breast cancer using microwaves.
'Highly Automated Dipole EStimation (HADES)' is the result of our last years' work in this field. HADES is a particle filter for estimating current dipoles from MEG data under general hypotheses. HADES is a set of Matlab functions and scripts, with a (hopefully) user-friendly Graphical User Interface. Particle filtering and, more in general, Bayesian methods are our favorite approaches to the analysis of EEG and MEG time series. We study the influence of cortical constraints on this kind of methods and develop sequential Monte Carlo techniques that can be adopted for the spatio-temporal localization of cortical rhythms.
MIDA is interested in the formulation and validation of mathematical models that explain specific visual or motor tasks. For example, we use MEG data and our computational tools for their analysis, to validate and extend a neuroscientific model of the human visual stream during visual recognition tasks (in collaboration with the Department of Cognitive, Linguistic and Psychological Sciences, Brown University) and to study the role of mirror neurons during the realization of motor tasks by autistic children (in collaboration with the Dipartimento di Neuroscienze, Università di Parma).

MIDA studies innovative methods for the automatic clustering of large amounts of data, for the automatic recognition of edges in images and for the segmentation of different homogeneous image regions. In particular we like soft computing techniques like fuzzy clustering algorithms and evolutionary strategies but we also work at the generalization of the Hough transform to the automatic recognition of algebraic curves.
MIDA's methods and specifically the ones for pattern recognition are systematically applied to industrial problems we address in collaboration with companies and SMEs with high technological content. Examples of such activity are the implementation of a neural network and a clustering algorithm for the monitoring of malfunctions in two nuclear plants and the realization of a software package for fat-water segmentation in DIXON-MRI sequences.