We introduce a model-based image reconstruction framework with a convolution neural network (CNN) based regularization prior. The proposed formulation provides a systematic approach for deriving deep architectures for inverse problems with the arbitrary structure. Since the forward model is explicitly accounted for, a smaller network with fewer parameters is sufficient to capture the image information compared to direct inversion approaches, thus reducing the demand for training data and training time. Since we rely on end-to-end training with weight sharing across iterations, the CNN weights are customized to the forward model, thus offering improved performance over approaches that rely on pre-trained denoisers. Our experiments show that the decoupling of the number of iterations from the network complexity offered by this approach provides benefits including lower demand for training data, reduced risk of overfitting, and implementations with significantly reduced memory footprint. We propose to enforce data-consistency by using numerical optimization blocks such as conjugate gradients algorithm within the network; this approach offers faster convergence per iteration, compared to methods that rely on proximal gradients steps to enforce data consistency. Our experiments show that the faster convergence translates to improved performance, primarily when the available GPU memory restricts the number of iterations.

This letter introduces a hyperspectral denoising algorithm based on spatio-spectral total variation. The denoising problem has been formulated as a mixed noise reduction problem. A general noise model has been considered which accounts for not only Gaussian noise but also sparse noise. The inherent structure of hyperspectral images has been exploited by utilizing 2-D total variation along the spatial dimension and 1-D total variation along the spectral dimension. The denoising problem has been formulated as an optimization problem whose solution has been derived using the split-Bregman approach. Experimental results demonstrate that the proposed algorithm is able to reduce a significant amount of noise from real noisy hyperspectral images. The proposed algorithm has been compared with existing state-of-the-art approaches. The quantitative and qualitative results demonstrate the superiority of the proposed algorithm in terms of peak signal-to-noise ratio, structural similarity, and the visual quality.

Modern MRI schemes, which rely on compressed sensing or deep learning algorithms to recover MRI data from undersampled multichannel Fourier measurements, are widely used to reduce the scan time. The image quality of these approaches is heavily dependent on the sampling pattern. In this article, we introduce a continuous strategy to optimize the sampling pattern and the network parameters jointly. We use a multichannel forward model, consisting of a non-uniform Fourier transform with continuously defined sampling locations, to realize the data consistency block within a model-based deep learning image reconstruction scheme. This approach facilitates the joint and continuous optimization of the sampling pattern and the CNN parameters to improve image quality. We observe that the joint optimization of the sampling patterns and the reconstruction module significantly improves the performance of most deep learning reconstruction algorithms. The source code of the proposed joint learning framework is available at https://github.com/hkaggarwal/J-MoDL.

Structured low-rank (SLR) algorithms, which exploit annihilation relations between the Fourier samples of a signal resulting from different properties, is a powerful image reconstruction framework in several applications. This scheme relies on low-rank matrix completion to estimate the annihilation relations from the measurements. The main challenge with this strategy is the high computational complexity of matrix completion. We introduce a deep learning (DL) approach to significantly reduce the computational complexity. Specifically, we use a convolutional neural network (CNN)-based filterbank that is trained to estimate the annihilation relations from imperfect (under-sampled and noisy) k-space measurements of Magnetic Resonance Imaging (MRI). The main reason for the computational efficiency is the pre-learning of the parameters of the non-linear CNN from exemplar data, compared to SLR schemes that learn the linear filterbank parameters from the dataset itself. Experimental comparisons show that the proposed scheme can enable calibration-less parallel MRI; it can offer performance similar to SLR schemes while reducing the runtime by around three orders of magnitude. Unlike pre-calibrated and self-calibrated approaches, the proposed uncalibrated approach is insensitive to motion errors and affords higher acceleration. The proposed scheme also incorporates image domain priors that are complementary, thus significantly improving the performance over that of SLR schemes.

Hyperspectral unmixing is the process of estimating constituent endmembers and their fractional abundances present at each pixel in a hyperspectral image. A hyperspectral image is often corrupted by several kinds of noise. This work addresses the hyperspectral unmixing problem in a general scenario that considers the presence of mixed noise. The unmixing model explicitly takes into account both Gaussian noise and sparse noise. The unmixing problem has been formulated to exploit joint-sparsity of abundance maps. A total-variation-based regularization has also been utilized for modeling smoothness of abundance maps. The split-Bregman technique has been utilized to derive an algorithm for solving resulting optimization problem. Detailed experimental results on both synthetic and real hyperspectral images demonstrate the advantages of proposed technique.