Neural coding Miller did his doctoral work on neural codes in the
Auditory system under the direction of Murray B. Sachs and Eric D. Young in the Neural Encoding Laboratory at Johns Hopkins University. With Sachs and Young, Miller focused on
rate-
timing population codes of complex features of speech including voice-pitch and consonant-vowel syllables encoded in the discharge patterns across the primary
auditory nerve. These neural codes were one of the scientific works discussed as the strategy for neuroprosthesis design at the 1982 New York Academy of Science meeting on the efficacy and timeliness of
Cochlear implants.
Medical imaging Miller's work in the field of
brain mapping via
Medical imaging, specifically
statistical methods for
iterative image reconstruction, began in the mid-1980s when he joined Donald L. Snyder at Washington University to work on time-of-flight
positron emission tomography (PET) systems being instrumented in
Michel Ter-Pogossian's group. With Snyder, Miller worked to stabilize
likelihood-estimators of radioactive tracer intensities via the
method-of-sieves . This became one of the approaches for controlling noise artifacts in the
Shepp-Vardi algorithm in the context of low-count, time-of-flight emission tomography. It was during this period that Miller met
Lawrence (Larry) Shepp, and he subsequently visited Shepp several times at
Bell Labs to speak as part of the
Henry Landau seminar series.
Pattern theory and computational anatomy During the mid-1990s, Miller joined the
Pattern Theory group at Brown University and worked with Ulf Grenander on problems in image analysis within the Bayesian framework of
Markov random fields. They established the
ergodic properties of
jump-diffusion processes for inference in
hybrid parameter spaces, which was presented by Miller at the
Journal of the Royal Statistical Society as a discussed paper. These were an early class of random sampling algorithms with ergodic properties proven to sample from distributions supported across discrete sample spaces and simultaneously over the continuum, likening it to the extremely popular
Gibb's sampler of Geman and Geman. and in a subsequent publication. In the same year with
Paul Dupuis, they established the necessary Sobolev smoothness conditions requiring vector fields to have strictly greater than 2.5 square-integrable, generalized derivatives (in the space of 3-dimensions) to ensure that smooth submanifold shapes are carried smoothly via integration of the flows. The
Computational anatomy framework via diffeomorphisms at the 1mm morphological scale is one of the de facto standards for cross-section analyses of populations. Codes now exist for diffeomorphic template or atlas mapping, including ANTS, DARTEL, DEMONS,
LDDMM, StationaryLDDMM, all actively used codes for constructing correspondences between coordinate systems based on
sparse features and dense images.
Shape and form David Mumford appreciated the smoothness results on existence of flows, and encouraged collaboration between Miller and the
École normale supérieure de Cachan group that had been working independently. In 1998, Mumford organized a Trimestre on "Questions Mathématiques en Traitement du Signal et de l'Image" at the
Institute Henri Poincaré; from this emerged the ongoing collaboration on shape between Miller, Alain Trouve and Laurent Younes. They published three significant papers together over the subsequent 15 years; the equations for geodesics generalizing the
Euler equation on fluids supporting localized scale or compressibility appeared in 2002, the conservation of momentum law for shape momentum appeared in 2006, and the summary of
Hamiltonian formalism appeared in 2015.
Neurodegeneration in brain mapping Miller and John Csernansky developed a long-term research effort on neuroanatomical phenotyping of
Alzheimer's disease,
Schizophrenia and
mood disorder. In 2005, they published with John Morris an early work on predicting conversion to Alzheimer's disease based on clinically available MRI measurements using diffeomorphometry technologies. This was one of the papers that contributed to a deeper understanding of the disorder in its earlier stages and the recommendations of the working group to revise the diagnostic criteria for Alzheimer's disease dementia for the first time in 27 years. In 2009, the Johns Hopkins University BIOCARD project was initiated, led by Marilyn Albert, to study preclinical Alzheimer's disease. In 2014, Miller and Younes demonstrated that the original
Braak staging of the earliest change associated to the
entorhinal cortex in the
medial temporal lobe could be demonstrated via diffeomorphometry methods in the population of clinical MRIs, and subsequently that this could be measured via MRI in clinical populations upwards of 10 years before clinical symptoms appeared. ==Books==