NC-PDNet: A Density-Compensated Unrolled Network for 2D and 3D Non-Cartesian MRI Reconstruction.

Deep Learning has become a very promising avenue for magnetic resonance image (MRI) reconstruction. In this work, we explore the potential of unrolled networks for non-Cartesian acquisition settings. We design the NC-PDNet (Non-Cartesian Primal Dual Netwok), the first density-compensated (DCp) unrolled neural network, and validate the need for its key components via an ablation study.

Results of the 2020 fastMRI Challenge for Machine Learning MR Image Reconstruction.

Accelerating MRI scans is one of the principal outstanding problems in the MRI research community. Towards this goal, we hosted the second fastMRI competition targeted towards reconstructing MR images with subsampled k-space data. We provided participants with data from 7,299 clinical brain scans (de-identified via a HIPAA-compliant procedure by NYU Langone Health), holding back the fully-sampled data from 894 of these scans for challenge evaluation purposes.

A proximal iteration for deconvolving Poisson noisy images using sparse representations.

We propose an image deconvolution algorithm when the data is contaminated by Poisson noise. The image to restore is assumed to be sparsely represented in a dictionary of waveforms such as the wavelet or curvelet transforms. Our key contributions are as follows.

Wavelets, ridgelets, and curvelets for Poisson noise removal.

In order to denoise Poisson count data, we introduce a variance stabilizing transform (VST) applied on a filtered discrete Poisson process, yielding a near Gaussian process with asymptotic constant variance. This new transform, which can be deemed as an extension of the Anscombe transform to filtered data, is simple, fast, and efficient in (very) low-count situations. We combine this VST with the filter banks of wavelets, ridgelets and curvelets, leading to multiscale VSTs (MS-VSTs) and nonlinear decomposition schemes.

The curvelet transform for image denoising.

We describe approximate digital implementations of two new mathematical transforms, namely, the ridgelet transform and the curvelet transform. Our implementations offer exact reconstruction, stability against perturbations, ease of implementation, and low computational complexity. A central tool is Fourier-domain computation of an approximate digital Radon transform.

Gray and color image contrast enhancement by the curvelet transform.

We present in this paper a new method for contrast enhancement based on the curvelet transform. The curvelet transform represents edges better than wavelets, and is therefore well-suited for multiscale edge enhancement. We compare this approach with enhancement based on the wavelet transform, and the Multiscale Retinex.

Morphological component analysis: an adaptive thresholding strategy.

In a recent paper, a method called morphological component analysis (MCA) has been proposed to separate the texture from the natural part in images. MCA relies on an iterative thresholding algorithm, using a threshold which decreases linearly towards zero along the iterations. This paper shows how the MCA convergence can be drastically improved using the mutual incoherence of the dictionaries associated to the different components.

Sparsity and morphological diversity in blind source separation.

Over the last few years, the development of multichannel sensors motivated interest in methods for the coherent processing of multivariate data. Some specific issues have already been addressed as testified by the wide literature on the so-caIled blind source separation (BSS) problem. In this context, as clearly emphasized by previous work, it is fundamental that the sources to be retrieved present some quantitatively measurable diversity.

The undecimated wavelet decomposition and its reconstruction.

This paper describes the undecimated wavelet transform and its reconstruction. In the first part, we show the relation between two well known undecimated wavelet transforms, the standard undecimated wavelet transform and the isotropic undecimated wavelet transform. Then we present new filter banks specially designed for undecimated wavelet decompositions which have some useful properties such as being robust to ringing artifacts which appear generally in wavelet-based denoising methods.

Dark matter maps reveal cosmic scaffolding.

Ordinary baryonic particles (such as protons and neutrons) account for only one-sixth of the total matter in the Universe. The remainder is a mysterious 'dark matter' component, which does not interact via electromagnetism and thus neither emits nor reflects light. As dark matter cannot be seen directly using traditional observations, very little is currently known about its properties.

Wavelet-based combined signal filtering and prediction.

We survey a number of applications of the wavelet transform in time series prediction. We show how multiresolution prediction can capture short-range and long-term dependencies with only a few parameters to be estimated. We then develop a new multiresolution methodology for combined noise filtering and prediction, based on an approach which is similar to the Kalman filter.

Image decomposition via the combination of sparse representations and a variational approach.

The separation of image content into semantic parts plays a vital role in applications such as compression, enhancement, restoration, and more. In recent years, several pioneering works suggested such a separation be based on variational formulation and others using independent component analysis and sparsity. This paper presents a novel method for separating images into texture and piecewise smooth (cartoon) parts, exploiting both the variational and the sparsity mechanisms.