Generative models based on deep neural networks are quite powerful in modelling natural image statistics. In particular, deep auto-regressive models provide state of the art performance, in terms of log likelihood scores, by modelling tractable densities over the image manifold. In this work, we employ a learned deep auto-regressive model as data prior for solving different inverse problems in computational imaging. We demonstrate how our approach can reconstruct images which have better pixel-level consistencies, as compared to the existing deep auto-encoder based approaches. We also show how randomly dropping the update of some pixels in every iteration helps in a better image reconstruction. We test our approach on three computational imaging setups: Single Pixel Camera, LiSens and FlatCam with real and simulated measurements. We obtain better reconstructions than the state-of-the-art methods for these problems, in terms of both perceptual quality and quantitative metrics such as PSNR and SSIM.
A denoising algorithm seeks to remove noise, errors, or perturbations from a signal. Extensive research has been devoted to this arena over the last several decades, and as a result, todays denoisers can effectively remove large amounts of additive white Gaussian noise. A compressed sensing (CS) reconstruction algorithm seeks to recover a structured signal acquired using a small number of randomized measurements. Typical CS reconstruction algorithms can be cast as iteratively estimating a signal from a perturbed observation. This paper answers a natural question: How can one effectively employ a generic denoiser in a CS reconstruction algorithm? In response, we develop an extension of the approximate message passing (AMP) framework, called denoising-based AMP (D-AMP), that can integrate a wide class of denoisers within its iterations. We demonstrate that, when used with a high-performance denoiser for natural images, D-AMP offers the state-of-the-art CS recovery performance while operating tens of times faster than competing methods. We explain the exceptional performance of D-AMP by analyzing some of its theoretical features. A key element in D-AMP is the use of an appropriate Onsager correction term in its iterations, which coerces the signal perturbation at each iteration to be very close to the white Gaussian noise that denoisers are typically designed to remove. Compressive sensing (CS)-based spatial-multiplexing cameras (SMCs) sample a scene through a series of coded projections using a spatial light modulator and a few optical sensor elements. SMC architectures are particularly useful when imaging at wavelengths for which full-frame sensors are too cumbersome or expensive. While existing recovery algorithms for SMCs perform well for static images, they typically fail for time-varying scenes (videos). In this paper, we propose a novel CS multi-scale video (CS-MUVI) sensing and recovery framework for SMCs. Our framework features a co-designed video CS sensing matrix and recovery algorithm that provide an efficiently computable low-resolution video preview. We estimate the scene's optical flow from the video preview and feed it into a convex-optimization algorithm to recover the high-resolution video. We demonstrate the performance and capabilities of the CS-MUVI framework for different scenes.     A constrained optimization type of numerical algorithm for removing noise from images is presented. The total variation of the image is minimized subject to constraints involving the statistics of the noise. The constraints are imposed using Lagrange multipliers. The solution is obtained using the gradient-projection method. This amounts to solving a time dependent partial differential equation on a manifold determined by the constraints. As t--- 0o the solution converges to a steady state which is the denoised image. The numerical algorithm is simple and relatively fast. The results appear to be state-of-the-art for very noisy images. The method is noninvasive, yielding sharp edges in the image. The technique could be interpreted as a first step of moving each level set of the image normal to itself with velocity equal to the curvature of the level set divided by the magnitude of the gradient of the image, and a second step which projects the image back onto the constraint set. 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.  Reconstruction of signals from compressively sensed measurements is an ill-posed problem. In this paper, we leverage the recurrent generative model, RIDE, as an image prior for compressive image reconstruction. Recurrent networks can model long-range dependencies in images and hence are suitable to handle global multiplexing in reconstruction from compressive imaging. We perform MAP inference with RIDE using back-propagation to the inputs and projected gradient method. We propose an entropy thresholding based approach for preserving texture in images well. Our approach shows superior reconstructions compared to recent global reconstruction approaches like D-AMP and TVAL3 on both simulated and real data.