Quilting the Brain: Whole-Brain iEEG Reconstruction via Incomplete Observation Linear Mixed Models

Mapping human brain function at high spatiotemporal resolution is constrained by the physical limitations of non-invasive imaging and the sparse sampling of invasive electrophysiology. While intracranial electroencephalography (iEEG) captures local field potentials with millimeter precision, clinical implantation strategies result in a ``coverage paradox'': observations are restricted to disjoint, patient-specific patches, leaving most of the cortex unobserved. This study introduces the Incomplete Observation Linear Mixed-Effect Model (IOLMM), a statistical framework that resolves this paradox by ``quilting'' fragmented observations into continuous, whole-brain source activity maps. Our approach integrates two innovations: (1) Sure Independence Screening (SIS) adapted from ultra-high-dimensional statistics to distinguish true physiological signals from volume-conducted ``ghost sources''; (2) a hierarchical IOLMM that decouples group-level physiological fixed effects from subject-specific instrumental random effects, solving the scaling ambiguities that plague iEEG group analyses. Applied to the MNI Open iEEG Atlas, the framework is validated through sleep stage-dependent cortical source power reconstruction across Wake, N2, N3, and REM states, recovering the frontal predominance of NREM slow-wave activity and the graded electrophysiological hierarchy from fragmented recordings of 106 patients. This work establishes the first cortical surface-level normative electrophysiological atlas derived from iEEG, providing a quantitative reference for detecting and predicting epileptogenic lesions and bridging the gap between the microscopic precision of electrophysiology and the macroscopic scope of systems neuroscience.