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.
Dictionary learning is an effective technique that has attracted a great deal of attention in image denoising. Dictionary learning based methods @cite_32 @cite_7 generally achieve lower reconstruction error than wavelet-based methods. However, the learning procedure requires a large amount of training images, and may involve manual tuning. Owing to these limitations, our main focus in this paper is to integrate relatively simple and fast image denoisers into compressive imaging reconstruction algorithms.
@cite_32 @cite_7
2119047398 2088254198 2153663612 2020741214
We develop a Bayesian nonparametric model for reconstructing magnetic resonance images (MRIs) from highly undersampled (k ) -space data. We perform dictionary learning as part of the image reconstruction process. To this end, we use the beta process as a nonparametric dictionary learning prior for representing an image patch as a sparse combination of dictionary elements. The size of the dictionary and patch-specific sparsity pattern are inferred from the data, in addition to other dictionary learning variables. Dictionary learning is performed directly on the compressed image, and so is tailored to the MRI being considered. In addition, we investigate a total variation penalty term in combination with the dictionary learning model, and show how the denoising property of dictionary learning removes dependence on regularization parameters in the noisy setting. We derive a stochastic optimization algorithm based on Markov chain Monte Carlo for the Bayesian model, and use the alternating direction method of multipliers for efficiently performing total variation minimization. We present empirical results on several MRI, which show that the proposed regularization framework can improve reconstruction accuracy over other methods. In this paper, we propose a novel coupled dictionary training method for single-image super-resolution (SR) based on patchwise sparse recovery, where the learned couple dictionaries relate the low- and high-resolution (HR) image patch spaces via sparse representation. The learning process enforces that the sparse representation of a low-resolution (LR) image patch in terms of the LR dictionary can well reconstruct its underlying HR image patch with the dictionary in the high-resolution image patch space. We model the learning problem as a bilevel optimization problem, where the optimization includes an l1-norm minimization problem in its constraints. Implicit differentiation is employed to calculate the desired gradient for stochastic gradient descent. We demonstrate that our coupled dictionary learning method can outperform the existing joint dictionary training method both quantitatively and qualitatively. Furthermore, for real applications, we speed up the algorithm approximately 10 times by learning a neural network model for fast sparse inference and selectively processing only those visually salient regions. Extensive experimental comparisons with state-of-the-art SR algorithms validate the effectiveness of our proposed approach. We address the image denoising problem, where zero-mean white and homogeneous Gaussian additive noise is to be removed from a given image. The approach taken is based on sparse and redundant representations over trained dictionaries. Using the K-SVD algorithm, we obtain a dictionary that describes the image content effectively. Two training options are considered: using the corrupted image itself, or training on a corpus of high-quality image database. Since the K-SVD is limited in handling small image patches, we extend its deployment to arbitrary image sizes by defining a global image prior that forces sparsity over patches in every location in the image. We show how such Bayesian treatment leads to a simple and effective denoising algorithm. This leads to a state-of-the-art denoising performance, equivalent and sometimes surpassing recently published leading alternative denoising methods Image recovery from undersampled data has always been challenging due to its implicit ill-posed nature but becomes fascinating with the emerging compressed sensing (CS) theory. This paper proposes a novel gradient based dictionary learning method for image recovery, which effectively integrates the popular total variation (TV) and dictionary learning technique into the same framework. Specifically, we first train dictionaries from the horizontal and vertical gradients of the image and then reconstruct the desired image using the sparse representations of both derivatives. The proposed method enables local features in the gradient images to be captured effectively, and can be viewed as an adaptive extension of the TV regularization. The results of various experiments on MR images consistently demonstrate that the proposed algorithm efficiently recovers images and presents advantages over the current leading CS reconstruction approaches.