Nonuniform sampling, image recovery from sparse data and the discrete sampling theorem.

In many applications, sampled data are collected in irregular fashion or are partly lost or unavailable. In these cases, it is necessary to convert irregularly sampled signals to regularly sampled ones or to restore missing data. We address this problem in the framework of a discrete sampling theorem for band-limited discrete signals that have a limited number of nonzero transform coefficients in a certain transform domain. Conditions for the image unique recovery, from sparse samples, are formulated and then analyzed for various transforms. Applications are demonstrated on examples of image superresolution and image reconstruction from sparse projections.

Stochastic nonlinear dynamics pattern formation and growth models.

Stochastic evolutionary growth and pattern formation models are treated in a unified way in terms of algorithmic models of nonlinear dynamic systems with feedback built of a standard set of signal processing units. A number of concrete models is described and illustrated by numerous examples of artificially generated patterns that closely imitate wide variety of patterns found in the nature.

Image processing for a high-resolution optoelectronic retinal prosthesis.

In an effort to restore visual perception in retinal diseases such as age-related macular degeneration or retinitis pigmentosa, a design was recently presented for a high-resolution optoelectronic retinal prosthesis having thousands of electrodes. This system requires real-time image processing fast enough to convert a video stream of images into electrical stimulus patterns that can be properly interpreted by the brain. Here, we present image-processing and tracking algorithms for a subretinal implant designed to stimulate the second neuron in the visual pathway, bypassing the degenerated first synaptic layer. For this task, we have developed and implemented: 1) A tracking algorithm that determines the implant's position in each frame. 2) Image cropping outside of the implant boundaries. 3) A geometrical transformation that distorts the image appropriate to the geometry of the fovea. 4) Spatio-temporal image filtering to reproduce the visual processing normally occurring in photoceptors and at the photoreceptor-bipolar cell synapse. 5) Conversion of the filtered visual information into a pattern of electrical current. Methods to accelerate real-time transformations include the exploitation of data redundancy in the time domain, and the use of precomputed lookup tables that are adjustable to retinal physiology and allow flexible control of stimulation parameters. A software implementation of these algorithms processes natural visual scenes with sufficient speed for real-time operation. This computationally efficient algorithm resembles, in some aspects, biological strategies of efficient coding in the retina and could provide a refresh rate higher than fifty frames per second on our system.