arXiv subjects

Aswin C. Sankaranarayanan

Publications and source records attributed to Aswin C. Sankaranarayanan.

29 records · Page 2Linked to original sources

arXiv2018

Signal Processing Based Pile-up Compensation for Gated Single-Photon Avalanche Diodes

Single-photon avalanche diode (SPAD) based transient imaging suffers from an aberration called pile-up. When multiple photons arrive within a single repetition period of the illuminating laser, the SPAD records only the arrival of the first photon; this leads to a bias in the recorded light transient wherein the transient response at later time-instants are under-estimated. An unfortunate consequence of this is the need to operate the illumination at low-power levels to reduce the probability of multiple photons returning in a single period. Operating the laser at low power results in either low signal-to-noise ratio (SNR) in the measured transients or reduced frame rate due to longer exposure durations to achieve a high SNR. In this paper, we propose a signal processing-based approach to compensate pile-up in post-processing, thereby enabling high power operation of the illuminating laser. While increasing illumination does cause a fundamental information loss in the data captured by SPAD, we quantify this information loss using Cramer-Rao bound and show that the errors in our framework are only limited to this information loss. We experimentally validate our hypotheses using real data from a lab prototype.

physics.ins-det↗

arXiv2017

Illuminant Spectra-based Source Separation Using Flash Photography

Real-world lighting often consists of multiple illuminants with different spectra. Separating and manipulating these illuminants in post-process is a challenging problem that requires either significant manual input or calibrated scene geometry and lighting. In this work, we leverage a flash/no-flash image pair to analyze and edit scene illuminants based on their spectral differences. We derive a novel physics-based relationship between color variations in the observed flash/no-flash intensities and the spectra and surface shading corresponding to individual scene illuminants. Our technique uses this constraint to automatically separate an image into constituent images lit by each illuminant. This separation can be used to support applications like white balancing, lighting editing, and RGB photometric stereo, where we demonstrate results that outperform state-of-the-art techniques on a wide range of images.

cs.CV↗

arXiv2017

One Network to Solve Them All --- Solving Linear Inverse Problems using Deep Projection Models

While deep learning methods have achieved state-of-the-art performance in many challenging inverse problems like image inpainting and super-resolution, they invariably involve problem-specific training of the networks. Under this approach, different problems require different networks. In scenarios where we need to solve a wide variety of problems, e.g., on a mobile camera, it is inefficient and costly to use these specially-trained networks. On the other hand, traditional methods using signal priors can be used in all linear inverse problems but often have worse performance on challenging tasks. In this work, we provide a middle ground between the two kinds of methods --- we propose a general framework to train a single deep neural network that solves arbitrary linear inverse problems. The proposed network acts as a proximal operator for an optimization algorithm and projects non-image signals onto the set of natural images defined by the decision boundary of a classifier. In our experiments, the proposed framework demonstrates superior performance over traditional methods using a wavelet sparsity prior and achieves comparable performance of specially-trained networks on tasks including compressive sensing and pixel-wise inpainting.

cs.CV↗

arXiv2015

Video Compressive Sensing for Spatial Multiplexing Cameras using Motion-Flow Models

Spatial multiplexing cameras (SMCs) acquire a (typically static) scene through a series of coded projections using a spatial light modulator (e.g., a digital micro-mirror device) and a few optical sensors. This approach finds use in imaging applications where full-frame sensors are either too expensive (e.g., for short-wave infrared wavelengths) or unavailable. Existing SMC systems reconstruct static scenes using techniques from compressive sensing (CS). For videos, however, existing acquisition and recovery methods deliver poor quality. In this paper, we propose the CS multi-scale video (CS-MUVI) sensing and recovery framework for high-quality video acquisition and recovery using SMCs. Our framework features novel sensing matrices that enable the efficient computation of a low-resolution video preview, while enabling high-resolution video recovery using convex optimization. To further improve the quality of the reconstructed videos, we extract optical-flow estimates from the low-resolution previews and impose them as constraints in the recovery procedure. We demonstrate the efficacy of our CS-MUVI framework for a host of synthetic and real measured SMC video data, and we show that high-quality videos can be recovered at roughly $60\times$ compression.

cs.CV↗

arXiv2015

FPA-CS: Focal Plane Array-based Compressive Imaging in Short-wave Infrared

Cameras for imaging in short and mid-wave infrared spectra are significantly more expensive than their counterparts in visible imaging. As a result, high-resolution imaging in those spectrum remains beyond the reach of most consumers. Over the last decade, compressive sensing (CS) has emerged as a potential means to realize inexpensive short-wave infrared cameras. One approach for doing this is the single-pixel camera (SPC) where a single detector acquires coded measurements of a high-resolution image. A computational reconstruction algorithm is then used to recover the image from these coded measurements. Unfortunately, the measurement rate of a SPC is insufficient to enable imaging at high spatial and temporal resolutions. We present a focal plane array-based compressive sensing (FPA-CS) architecture that achieves high spatial and temporal resolutions. The idea is to use an array of SPCs that sense in parallel to increase the measurement rate, and consequently, the achievable spatio-temporal resolution of the camera. We develop a proof-of-concept prototype in the short-wave infrared using a sensor with 64$\times$ 64 pixels; the prototype provides a 4096$\times$ increase in the measurement rate compared to the SPC and achieves a megapixel resolution at video rate using CS techniques.

cs.CV↗

arXiv2015

A Dictionary-based Approach for Estimating Shape and Spatially-Varying Reflectance

We present a technique for estimating the shape and reflectance of an object in terms of its surface normals and spatially-varying BRDF. We assume that multiple images of the object are obtained under fixed view-point and varying illumination, i.e, the setting of photometric stereo. Assuming that the BRDF at each pixel lies in the non-negative span of a known BRDF dictionary, we derive a per-pixel surface normal and BRDF estimation framework that requires neither iterative optimization techniques nor careful initialization, both of which are endemic to most state-of-the-art techniques. We showcase the performance of our technique on a wide range of simulated and real scenes where we outperform competing methods.

cs.CV↗

arXiv2015

LiSens --- A Scalable Architecture for Video Compressive Sensing

The measurement rate of cameras that take spatially multiplexed measurements by using spatial light modulators (SLM) is often limited by the switching speed of the SLMs. This is especially true for single-pixel cameras where the photodetector operates at a rate that is many orders-of-magnitude greater than the SLM. We study the factors that determine the measurement rate for such spatial multiplexing cameras (SMC) and show that increasing the number of pixels in the device improves the measurement rate, but there is an optimum number of pixels (typically, few thousands) beyond which the measurement rate does not increase. This motivates the design of LiSens, a novel imaging architecture, that replaces the photodetector in the single-pixel camera with a 1D linear array or a line-sensor. We illustrate the optical architecture underlying LiSens, build a prototype, and demonstrate results of a range of indoor and outdoor scenes. LiSens delivers on the promise of SMCs: imaging at a megapixel resolution, at video rate, using an inexpensive low-resolution sensor.

cs.CV↗

arXiv2015

Adaptive-Rate Sparse Signal Reconstruction With Application in Compressive Background Subtraction

We propose and analyze an online algorithm for reconstructing a sequence of signals from a limited number of linear measurements. The signals are assumed sparse, with unknown support, and evolve over time according to a generic nonlinear dynamical model. Our algorithm, based on recent theoretical results for $\ell_1$-$\ell_1$ minimization, is recursive and computes the number of measurements to be taken at each time on-the-fly. As an example, we apply the algorithm to compressive video background subtraction, a problem that can be stated as follows: given a set of measurements of a sequence of images with a static background, simultaneously reconstruct each image while separating its foreground from the background. The performance of our method is illustrated on sequences of real images: we observe that it allows a dramatic reduction in the number of measurements with respect to state-of-the-art compressive background subtraction schemes.

math.OC↗

arXiv2014

Video Compressive Sensing for Dynamic MRI

We present a video compressive sensing framework, termed kt-CSLDS, to accelerate the image acquisition process of dynamic magnetic resonance imaging (MRI). We are inspired by a state-of-the-art model for video compressive sensing that utilizes a linear dynamical system (LDS) to model the motion manifold. Given compressive measurements, the state sequence of an LDS can be first estimated using system identification techniques. We then reconstruct the observation matrix using a joint structured sparsity assumption. In particular, we minimize an objective function with a mixture of wavelet sparsity and joint sparsity within the observation matrix. We derive an efficient convex optimization algorithm through alternating direction method of multipliers (ADMM), and provide a theoretical guarantee for global convergence. We demonstrate the performance of our approach for video compressive sensing, in terms of reconstruction accuracy. We also investigate the impact of various sampling strategies. We apply this framework to accelerate the acquisition process of dynamic MRI and show it achieves the best reconstruction accuracy with the least computational time compared with existing algorithms in the literature.

cs.CV↗

arXiv2013

Greedy Feature Selection for Subspace Clustering

Unions of subspaces provide a powerful generalization to linear subspace models for collections of high-dimensional data. To learn a union of subspaces from a collection of data, sets of signals in the collection that belong to the same subspace must be identified in order to obtain accurate estimates of the subspace structures present in the data. Recently, sparse recovery methods have been shown to provide a provable and robust strategy for exact feature selection (EFS)--recovering subsets of points from the ensemble that live in the same subspace. In parallel with recent studies of EFS with L1-minimization, in this paper, we develop sufficient conditions for EFS with a greedy method for sparse signal recovery known as orthogonal matching pursuit (OMP). Following our analysis, we provide an empirical study of feature selection strategies for signals living on unions of subspaces and characterize the gap between sparse recovery methods and nearest neighbor (NN)-based approaches. In particular, we demonstrate that sparse recovery methods provide significant advantages over NN methods and the gap between the two approaches is particularly pronounced when the sampling of subspaces in the dataset is sparse. Our results suggest that OMP may be employed to reliably recover exact feature sets in a number of regimes where NN approaches fail to reveal the subspace membership of points in the ensemble.

cs.LG↗

arXiv2011

A Theory for Optical flow-based Transport on Image Manifolds

An image articulation manifold (IAM) is the collection of images formed when an object is articulated in front of a camera. IAMs arise in a variety of image processing and computer vision applications, where they provide a natural low-dimensional embedding of the collection of high-dimensional images. To date IAMs have been studied as embedded submanifolds of Euclidean spaces. Unfortunately, their promise has not been realized in practice, because real world imagery typically contains sharp edges that render an IAM non-differentiable and hence non-isometric to the low-dimensional parameter space under the Euclidean metric. As a result, the standard tools from differential geometry, in particular using linear tangent spaces to transport along the IAM, have limited utility. In this paper, we explore a nonlinear transport operator for IAMs based on the optical flow between images and develop new analytical tools reminiscent of those from differential geometry using the idea of optical flow manifolds (OFMs). We define a new metric for IAMs that satisfies certain local isometry conditions, and we show how to use this metric to develop a new tools such as flow fields on IAMs, parallel flow fields, parallel transport, as well as a intuitive notion of curvature. The space of optical flow fields along a path of constant curvature has a natural multi-scale structure via a monoid structure on the space of all flow fields along a path. We also develop lower bounds on approximation errors while approximating non-parallel flow fields by parallel flow fields.

cs.CV↗