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.
Many algorithms have been proposed for compressive image reconstruction. Typically, reconstruction algorithms use @math regularization, exploiting the sparsity of spatial gradients in natural images. Total Variation (TV) minimization prior @cite_31 @cite_3 is the most commonly used reconstruction algorithm based on this sparsity. @cite_21 propose an efficient augmented Lagrangian based TV minimization for CS reconstruction. Recent approaches involving compressive architectures such as fpa-cs @cite_13 , LiSens @cite_16 , and video CS @cite_15 , demonstrated successful results with TV minimization prior. However, at lower measurement rates, reconstructions suffer from the piece-wise smooth modeling of TV prior and results tend to be blocky, as is noted by recent works @cite_36 @cite_2 . @cite_14 propose a denoiser based CS reconstruction algorithm. Specifically, use a Gaussian denoiser with approximate message passing algorithm (D-AMP). At very low measurement rates, the denoiser tends to result in overly smooth images as is recently shown by @cite_25 , @cite_36 .
@cite_14 @cite_15 @cite_36 @cite_21 @cite_3 @cite_2 @cite_31 @cite_16 @cite_13 @cite_25
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We consider compressive imaging problems, where images are reconstructed from a reduced number of linear measurements. Our objective is to improve over existing compressive imaging algorithms in terms of both reconstruction error and runtime. To pursue our objective, we propose compressive imaging algorithms that employ the approximate message passing (AMP) framework. AMP is an iterative signal reconstruction algorithm that performs scalar denoising at each iteration; in order for AMP to reconstruct the original input signal well, a good denoiser must be used. We apply two wavelet-based image denoisers within AMP. The first denoiser is the “amplitude-scale-invariant Bayes estimator” (ABE), and the second is an adaptive Wiener filter; we call our AMP-based algorithms for compressive imaging AMP-ABE and AMP-Wiener. Numerical results show that both AMP-ABE and AMP-Wiener significantly improve over the state of the art in terms of runtime. In terms of reconstruction quality, AMP-Wiener offers lower mean-square error (MSE) than existing compressive imaging algorithms. In contrast, AMP-ABE has higher MSE, because ABE does not denoise as well as the adaptive Wiener filter. A major problem in imaging applications such as magnetic resonance imaging and synthetic aperture radar is the task of trying to reconstruct an image with the smallest possible set of Fourier samples, every single one of which has a potential time and or power cost. The theory of compressive sensing (CS) points to ways of exploiting inherent sparsity in such images in order to achieve accurate recovery using sub-Nyquist sampling schemes. Traditional CS approaches to this problem consist of solving total-variation (TV) minimization programs with Fourier measurement constraints or other variations thereof. This paper takes a different approach. Since the horizontal and vertical differences of a medical image are each more sparse or compressible than the corresponding TV image, CS methods will be more successful in recovering these differences individually. We develop an algorithm called GradientRec that uses a CS algorithm to recover the horizontal and vertical gradients and then estimates the original image from these gradients. We present two methods of solving the latter inverse problem, i.e., one based on least-square optimization and the other based on a generalized Poisson solver. After a thorough derivation of our complete algorithm, we present the results of various experiments that compare the effectiveness of the proposed method against other leading methods. The goal of this paper is to present a non-iterative and more importantly an extremely fast algorithm to reconstruct images from compressively sensed (CS) random measurements. To this end, we propose a novel convolutional neural network (CNN) architecture which takes in CS measurements of an image as input and outputs an intermediate reconstruction. We call this network, ReconNet. The intermediate reconstruction is fed into an off-the-shelf denoiser to obtain the final reconstructed image. On a standard dataset of images we show significant improvements in reconstruction results (both in terms of PSNR and time complexity) over state-of-the-art iterative CS reconstruction algorithms at various measurement rates. Further, through qualitative experiments on real data collected using our block single pixel camera (SPC), we show that our network is highly robust to sensor noise and can recover visually better quality images than competitive algorithms at extremely low sensing rates of 0.1 and 0.04. To demonstrate that our algorithm can recover semantically informative images even at a low measurement rate of 0.01, we present a very robust proof of concept real-time visual tracking application. The goal of this paper is to present a non-iterative and more importantly an extremely fast algorithm to reconstruct images from compressively sensed (CS) random measurements. To this end, we propose a novel convolutional neural network (CNN) architecture which takes in CS measurements of an image as input and outputs an intermediate reconstruction. We call this network, ReconNet. The intermediate reconstruction is fed into an off-the-shelf denoiser to obtain the final reconstructed image. On a standard dataset of images we show significant improvements in reconstruction results (both in terms of PSNR and time complexity) over state-of-the-art iterative CS reconstruction algorithms at various measurement rates. Further, through qualitative experiments on real data collected using our block single pixel camera (SPC), we show that our network is highly robust to sensor noise and can recover visually better quality images than competitive algorithms at extremely low sensing rates of 0.1 and 0.04. To demonstrate that our algorithm can recover semantically informative images even at a low measurement rate of 0.01, we present a very robust proof of concept real-time visual tracking application.