Sparse Signal Representation in Digital and Biological Systems

Theories of sparse signal representation, wherein a signal is decomposed as the sum of a small number of constituent elements, play increasing roles in both mathematical signal processing and neuroscience. This happens despite the differences between signal models in the two domains. After reviewing preliminary material on sparse signal models, I use work on compressed sensing for the electron tomography of biological structures as a target for exploring the efficacy of sparse signal reconstruction in a challenging application domain. My research in this area addresses a topic of keen interest to the biological microscopy community, and has resulted in the development of tomographic reconstruction software which is competitive with the state of the art in its field. Moving from the linear signal domain into the nonlinear dynamics of neural encoding, I explain the sparse coding hypothesis in neuroscience and its relationship with olfaction in locusts. I implement a numerical ODE model of the activity of neural populations responsible for sparse odor coding in locusts as part of a project involving offset spiking in the Kenyon cells. I also explain the validation procedures we have devised to help assess the model's similarity to the biology. The thesis concludes with the development of a new, simplified model of locust olfactory network activity, which seeks with some success to explain statistical properties of the sparse coding processes carried out in the network.

Photochemistry and transport of tropospheric ozone and its precursors in urban and remote environments

Tropospheric ozone (O3) adversely affects human health, reduces crop yields, and contributes to climate forcing. To limit these effects, the processes controlling O3 abundance as well as that of its precursor molecules must be fully characterized. Here, I examine three facets of O3 production, both in heavily polluted and remote environments. First, using in situ observations from the DISCOVER-AQ field campaign in the Baltimore/Washington region, I evaluate the emissions of the O3 precursors CO and NOx (NOx = NO + NO2) in the National Emissions Inventory (NEI). I find that CO/NOx emissions ratios derived from observations are 21% higher than those predicted by the NEI. Comparisons to output from the CMAQ model suggest that CO in the NEI is accurate within 15 ± 11%, while NOx emissions are overestimated by 51-70%, likely due to errors in mobile sources. These results imply that ambient ozone concentrations will respond more efficiently to NOx controls than current models suggest. I then investigate the source of high O3 and low H2O structures in the Tropical Western Pacific (TWP). A combination of in situ observations, satellite data, and models show that the high O3 results from photochemical production in biomass burning plumes from fires in tropical Southeast Asia and Central Africa; the low relative humidity results from large-scale descent in the tropics. Because these structures have frequently been attributed to mid-latitude pollution, biomass burning in the tropics likely contributes more to the radiative forcing of climate than previously believed. Finally, I evaluate the processes controlling formaldehyde (HCHO) in the TWP. Convective transport of near surface HCHO leads to a 33% increase in upper tropospheric HCHO mixing ratios; convection also likely increases upper tropospheric CH3OOH to ~230 pptv, enough to maintain background HCHO at ~75 pptv. The long-range transport of polluted air, with NO four times the convectively controlled background, intensifies the conversion of HO2 to OH, increasing OH by a factor of 1.4. Comparisons between the global chemistry model CAM-Chem and observations show that consistent underestimates of HCHO by CAM-Chem throughout the troposphere result from underestimates in both NO and acetaldehyde.