Current popular methods for Magnetic Resonance Fingerprint (MRF) recovery are bottlenecked by the heavy storage and computation requirements of a dictionary-matching (DM) step due to the growing size and complexity of the fingerprint dictionaries in multi-parametric quantitative MRI applications. In this paper we study a deep learning approach to address these shortcomings. Coupled with a dimensionality reduction first layer, the proposed MRF-Net is able to reconstruct quantitative maps by saving more than 60 times in memory and computations required for a DM baseline. Fine-grid manifold enumeration i.e. the MRF dictionary is only used for training the network and not during image reconstruction. We show that the MRF-Net provides a piece-wise affine approximation to the Bloch response manifold projection and that rather than memorizing the dictionary, the network efficiently clusters this manifold and learns a set of hierarchical matched-filters for affine regression of the NMR characteristics in each segment.

Sensor selection refers to the problem of intelligently selecting a small subset of a collection of available sensors to reduce the sensing cost while preserving signal acquisition performance. The majority of sensor selection algorithms find the subset of sensors that best recovers an arbitrary signal from a number of linear measurements that is larger than the dimension of the signal. In this paper, we develop a new sensor selection algorithm for sparse (or near sparse) signals that finds a subset of sensors that best recovers such signals from a number of measurements that is much smaller than the dimension of the signal. Existing sensor selection algorithms cannot be applied in such situations. Our proposed Incoherent Sensor Selection (Insense) algorithm minimizes a coherence-based cost function that is adapted from recent results in sparse recovery theory. Using three datasets, including a real-world dataset on microbial diagnostics, we demonstrate the superior performance of Insense for sparse-signal sensor selection.

We propose a structure-adaptive variant of the state-of-the-art stochastic variance-reduced gradient algorithm Katyusha for regularized empirical risk minimization. The proposed method is able to exploit the intrinsic low-dimensional structure of the solution, such as sparsity or low rank which is enforced by a non-smooth regularization, to achieve even faster convergence rate. This provable algorithmic improvement is done by restarting the Katyusha algorithm according to restricted strong-convexity constants. We demonstrate the effectiveness of our approach via numerical experiments.

We study the convergence of the iterative projected gradient (IPG) algorithm for arbitrary (possibly non-convex) sets when both the gradient and projection oracles are computed approximately. We consider different notions of approximation of which we show that the progressive fixed precision and the (1+ ε)-optimal oracles can achieve the same accuracy as for the exact IPG algorithm. We show that the former scheme is also able to maintain the (linear) rate of convergence of the exact algorithm under the same embedding assumption. In contrast, the (1+ε)-approximate oracle requires a stronger embedding condition, moderate compression ratios and it typically slows down the convergence. We apply our results to accelerate solving a class of data driven compressed sensing problems, where we replace iterative exhaustive searches over large data sets by fast approximate nearest neighbor search strategies based on the cover tree data structure. For data sets with low intrinsic dimensions, our proposed algorithm achieves a complexity logarithmic in terms of the data set population as opposed to the linear complexity of a brute force search. By running several numerical experiments, we conclude similar observations as predicted by our theoretical analysis.

We propose a randomized first order optimization algorithm Gradient Projection Iterative Sketch (GPIS) and an accelerated variant for efficiently solving large scale constrained Least Squares (LS). We provide the first theoretical convergence analysis for both algorithms. An efficient implementation using a tailored line-search scheme is also proposed. We demonstrate our methods’ computational efficiency compared to the classical accelerated gradient method, and the variance-reduced stochastic gradient methods through numerical experiments in various large synthetic/real data sets.

We tackle the speech separation problem through modeling the acoustics of the reverberant chambers. Our approach exploits structured sparsity models to perform speech recovery and room acoustic modeling from recordings of concurrent unknown sources. The speakers are assumed to lie on a two-dimensional plane and the multipath channel is characterized using the image model. We propose an algorithm for room geometry estimation relying on localization of the early images of the speakers by sparse approximation of the spatial spectrum of the virtual sources in a free-space model. The images are then clustered exploiting the low-rank structure of the spectro-temporal components belonging to each source. This enables us to identify the early support of the room impulse response function and its unique map to the room geometry. To further tackle the ambiguity of the reflection ratios, we propose a novel formulation of the reverberation model and estimate the absorption coefficients through a convex optimization exploiting joint sparsity model formulated upon spatio-spectral sparsity of concurrent speech representation. The acoustic parameters are then incorporated for separating individual speech signals through either structured sparse recovery or inverse filtering the acoustic channels. The experiments conducted on real data recordings of spatially stationary sources demonstrate the effectiveness of the proposed approach for speech separation and recognition.

We propose and analyze a new model for hyperspectral images (HSIs) based on the assumption that the whole signal is composed of a linear combination of few sources, each of which has a specific spectral signature, and that the spatial abundance maps of these sources are themselves piecewise smooth and therefore efficiently encoded via typical sparse models. We derive new sampling schemes exploiting this assumption and give theoretical lower bounds on the number of measurements required to reconstruct HSI data and recover their source model parameters. This allows us to segment HSIs into their source abundance maps directly from compressed measurements. We also propose efficient optimization algorithms and perform extensive experimentation on synthetic and real datasets, which reveals that our approach can be used to encode HSI with far less measurements and computational effort than traditional compressive sensing methods.

We propose a novel approach to reconstruct Hyperspectral images from very few number of noisy compressive measurements. Our reconstruction approach is based on a convex minimization which penalizes both the nuclear norm and the ℓ2,1mixed-norm of the data matrix. Thus, the solution tends to have a simultaneous low-rank and joint-sparse structure. We explain how these two assumptions fit Hyperspectral data, and by severals simulations we show that our proposed reconstruction scheme significantly enhances the state-of-the-art tradeoffs between the reconstruction error and the required number of CS measurements.

This paper presents a novel approach to capture light field in camera arrays based on the compressive sensing framework. Light fields are captured by a linear array of cameras with overlapping field of view. In this work, we design a redundant dictionary to exploit cross-cameras correlated structures to sparsely represent cameras image. Our main contributions are threefold. First, we exploit the correlations between the set of views by making use of a specially designed redundant dictionary. We show experimentally that the projection of complex scenes onto this dictionary yields very sparse coefficients. Second, we propose an efficient compressive encoding scheme based on the random convolution framework [1]. Finally, we develop a joint sparse recovery algorithm for decoding the compressed measurements and show a marked improvement over independent decoding of CS measurements.

In this paper we propose a novel and efficient model for compressed sensing of hyperspectral images. A large-size hyperspectral image can be subsampled by retaining only 3% of its original size, yet robustly recovered using the new approach we present here. Our reconstruction approach is based on minimizing a convex functional which penalizes both the trace norm and the TV norm of the data matrix. Thus, the solution tends to have a simultaneous low-rank and piecewise smooth structure: the two important priors explaining the underlying correlation structure of such data. Through simulations we will show our approach significantly enhances the conventional compression rate-distortion tradeoffs. In particular, in the strong undersampling regimes our method outperforms the standard TV denoising image recovery scheme by more than 17dB in the reconstruction MSE.

This paper analyzes the performance of the simple thresholding algorithm for sparse signal representations. In particular, in order to be more realistic we introduce a new probabilistic signal model which assumes randomness for both the amplitude and also the location of nonzero entries. Based on this model we show that thresholding in average can correctly recover signals for much higher sparsity levels than was previously reported. The bounds we obtain in this paper are based on a new concept of average dictionary coherence and are shown to be much sharper than in former works [1,2].