Sensing Beyond Barriers: Theory, Algorithms and Applications

Data capture via imaging and sensing has become a common aspect of our existence and helps extend human vision and perception. Whether it is a microscope used for cell counting or the latest version of autonomous vehicle which aims to see through the fog; the sensing apparatus is expensive and limited in functionality. For example, the cameras of a self-driving car may white out due to exposure to excessive light when coming out of a tunnel. In many of applications, hardware (that captures data) and algorithms (which recover meaningful information from data) are treated decoupled entities; first capture data, extract information later. Hence, there is a limit to what can be recovered from the data based on the limitations of the hardware. Can we go beyond such limitations? The purpose of this research is to achieve a synergistic balance between hardware and algorithms by means of a co-design, so that popularly held limits in data capture and imaging can be broken, thus making the invisible, visible. Questions that we seek to answer include: Can we do bio-imaging with low-cost sensors (e.g. Microsoft Kinect)? Can we capture information beyond the usual dynamic range? Can we non-invasively classify blood cells by inferring cell geometry? Can we remove reflections in photographs? Can we see through diffusive media? These questions require us to go beyond the conventional barriers (e.g. dynamic range, spatio-temporal resolution, how fast the data is captured etc). The work in this proposal relies a co-design approach where carefully optimized capture process yields computationally encoded measurements from which the information is decoded using recovery algorithms. This approach is used to modify hardware and develop new algorithms to recover information. Application areas span from bio-imaging (cell-classification, fluorescence lifetime imaging, terahertz spectroscopy), consumer imaging (autonomous vehicles) to conceptualization of new sensing hardware. Three specific barriers are considered: (1) Dynamic Range Barrier. We propose the use of recording measurements that are non-linearly mapped by modulo operations. This is a fundamentally new way of sensing or digitising information and is largely unexplored. Our initial work shows that a simple correction to the Nyquist rate linked with Shannon's sampling theory allows for recovery of a bandlimited signal from modulo information. Remarkably, the sampling bound is independent of the the threshold. In this proposal we study a larger class of signals including sum-of-sinusoids, sparse signals and smooth signal and their link with application areas such as direction-of-arrival estimation and beamforming. (2) Resolution Barrier. Recovering spikes from low-pass filtered measurements is a classical problem and is known as super-resolution. However, in many practical cases of interest, the pulse or filter may be distorted due to physical properties of propagation and transmission. Such cases can not be handled well by existing signal models. Inspired by problems in spectroscopy, ground penetrating radar, photoacoustic imaging and ultra-wide band arrays, on which we base our experiments, in this work we take a step towards recovering spikes from time-varying pulses and prepare algorithms for non-ideal super-resolution. Furthermore, when the pulse or filter is smooth and not necessarily bandlimited, optimial bandwith selction for sparse-deconvolution is an open problem that is addressed in this work. (3) Bandwidth Barrier. We define the notion of bandwidth in context of Special Affine Fourier transforms which generalises a number of well known transformations. This allows us to prepare a unifying approach for studying sampling theory which is applicable to a wider class of signal models. Our algorithms are validated on experimentally acquired data with the help of inter-disciplinary and multi-university collaborations