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Development of a flexible Erlang mixture model for survival analysis is introduced. The model for the survival density is built from a structured mixture of Erlang densities, mixing on the integer shape parameter with a common scale parameter. The mixture weights are constructed through increments of a distribution function on the positive real line, which is assigned a Dirichlet process prior. The model has a relatively simple structure, balancing flexibility with efficient posterior computation. Moreover, it implies a mixture representation for the hazard function that involves time-dependent mixture weights, thus offering a general approach to hazard estimation. Extension of the model is made to accommodate survival responses corresponding to multiple experimental groups, using a dependent Dirichlet process prior for the group-specific distributions that define the mixture weights. Model properties, prior specification, and posterior simulation are discussed, and the methodology is illustrated with synthetic and real data examples. 

We use specially designed plasmonic photodetectors to develop a new method for image differentiation that can produce edge-enhanced images without external optical elements and under incoherent illumination, unlike traditional optical spatial filters. 

Photonics provides a promising approach for image processing by spatial filtering, with the advantage of faster speeds and lower power consumption compared to electronic digital solutions. However, traditional optical spatial filters suffer from bulky form factors that limit their portability. Here we present a new approach based on pixel arrays of plasmonic directional image sensors, designed to selectively detect light incident along a small, geometrically tunable set of directions. The resulting imaging systems can function as optical spatial filters without any external filtering elements, leading to extreme size miniaturization. Furthermore, they offer the distinct capability to perform multiple filtering operations at the same time, through the use of sensor arrays partitioned into blocks of adjacent pixels with different angular responses. To establish the image processing capabilities of these devices, we present a rigorous theoretical model of their filter transfer function under both coherent and incoherent illumination. Next, we use the measured angle-resolved responsivity of prototype devices to demonstrate two examples of relevant functionalities: (1) the visualization of otherwise invisible phase objects and (2) spatial differentiation with incoherent light. These results are significant for a multitude of imaging applications ranging from microscopy in biomedicine to object recognition for computer vision. 

Intensity Diffraction Tomography (IDT) is a new computational microscopy technique providing quantitative, volumetric, large field-of-view (FOV) phase imaging of biological samples. This approach uses computationally efficient inverse scattering models to recover 3D phase volumes of weakly scattering objects from intensity measurements taken under diverse illumination at a single focal plane. IDT is easily implemented in a standard microscope equipped with an LED array source and requires no exogenous contrast agents, making the technology widely accessible for biological research.Here, we discuss model and learning-based approaches for complex 3D object recovery with IDT. We present two model-based computational illumination strategies, multiplexed IDT (mIDT) [1] and annular IDT (aIDT) [2], that achieve high-throughput quantitative 3D object phase recovery at hardware-limited 4Hz and 10Hz volume rates, respectively. We illustrate these techniques on living epithelial buccal cells and Caenorhabditis elegans worms. For strong scattering object recovery with IDT, we present an uncertainty quantification framework for assessing the reliability of deep learning-based phase recovery methods [3]. This framework provides per-pixel evaluation of a neural network predictions confidence level, allowing for efficient and reliable complex object recovery. This uncertainty learning framework is widely applicable for reliable deep learning-based biomedical imaging techniques and shows significant potential for IDT. 

Angle-sensitive plasmonic photodetectors that can perform optical-domain spatial filtering operations are developed. The edge enhancement capabilities of these devices are demonstrated via computational imaging simulations based on their measured angular response.