In computational sensing and imaging, optics can perform some of the processing tasks traditionally performed by digital signal processing and, conversely, digital signal processing can perform some of the processing tasks traditionally performed by optics. This approach thus provides a new framework for reducing electrical power dissipated by sensors: for a criterion end-to-end functional performance, design the optics such that the digital computation cost is as low as possible. There are two such strategies to designing optics to reduce electrical power dissipation: creating optics that produce an optical signal that either 1) requires less digital processing for the criterion functional performance or 2) requires fewer pixels and hence less read, A/D conversion, and signal transfer power. A special-purpose diffractive optical element integrated with a CMOS image sensor photodetector array with simple on-chip processing reveal power reduction in one operational mode roughly two orders of magnitude compared to that in a functionally equivalent traditional lens-based sensors.

Low dose X-ray Computed Tomography (CT) is clinically desired to reduce the risk of cancer caused by X-ray radiation. Compressed Sensing (CS), which allows images to be formed from incomplete data, enables large dose reduction to be achieved. Though this remains to be clinically unrealized due to excessive computation times. In this paper we demonstrate a fast, complete CS-based ℓ2-TV minimizing CT reconstruction method applicable to both parallel and fan beam geometries to recover high quality images from highly undersampled (thus low-dose) data. We apply the fast pseudo-polar Fourier algorithm and the Central Slice Theorem to reduce the computation time of CS recovery. On a typical desktop computer, we are able to reconstruct a 512×512 CT image in approximately 30 seconds: a clinically-significant speedup compared to the many hours required by previous CS methods.

Information theory has been used as an organizing principle in neuroscience for several decades. Estimates of the mutual information (MI) between signals acquired in neurophysiological experiments are believed to yield insights into the structure of the underlying information processing architectures. With the pervasive availability of recordings from many neurons, several information and redundancy measures have been proposed in the recent literature. A typical scenario is that only a small number of stimuli can be tested, while ample response data may be available for each of the tested stimuli. The resulting asymmetric information estimation problem is considered. It is shown that the direct plug-in information estimate has a negative bias. An anthropic correction is introduced that has a positive bias. These two complementary estimators and their combinations are natural candidates for information estimation in neuroscience. Tail and variance bounds are given for both estimates. The proposed information estimates are applied to the analysis of neural discrimination and redundancy in the avian auditory system.

A novel estimator for mutual information is proposed. The estimator is useful for the (asymmetric) scenario where only a few samples for one random variable are available, but for each sample, the conditional distribution of the other random variable can be accurately characterized. Such asymmetry is common in neuroscience where it is often necessary to repeat the same stimulus many times to obtain a stable response.