Related papers: Exponential Signal Reconstruction with Deep Hankel…

The random equivalent sampling (RES) is a well-known sampling technique that can be used to capture a high-speed repetitive waveform with low sampling rate. In this paper, the feasibility of spectrum-blind multiband signal reconstruction…

Pre-trained language models demonstrate general intelligence and common sense, but long inputs quickly become a bottleneck for memorizing information at inference time. We resurface a simple method, Memorizing Transformers (Wu et al.,…

Attentional mechanisms are order-invariant. Positional encoding is a crucial component to allow attention-based deep model architectures such as Transformer to address sequences or images where the position of information matters. In this…

Recently, mapping a signal/image into a low rank Hankel/Toeplitz matrix has become an emerging alternative to the traditional sparse regularization, due to its ability to alleviate the basis mismatch between the true support in the…

Various informative factors mixed in speech signals, leading to great difficulty when decoding any of the factors. An intuitive idea is to factorize each speech frame into individual informative factors, though it turns out to be highly…

Sampling a signal below the Shannon-Nyquist rate causes aliasing, meaning different frequencies to become indistinguishable. It is also well-known that recovering spectral information from a signal using a parametric method can be ill-posed…

Magnetic Resonance (MR) image reconstruction from highly undersampled $k$-space data is critical in accelerated MR imaging (MRI) techniques. In recent years, deep learning-based methods have shown great potential in this task. This paper…

Recently Fourier Ptychography (FP) has attracted great attention, due to its marked effectiveness in leveraging snapshot numbers for spatial resolution in large field-of-view imaging. To acquire high signal-to-noise-ratio (SNR) images under…

Matrix factorization is a popular approach to solving matrix estimation problems based on partial observations. Existing matrix factorization is based on least squares and aims to yield a low-rank matrix to interpret the conditional sample…

In its most elementary form, compressed sensing studies the design of decoding algorithms to recover a sufficiently sparse vector or code from a lower dimensional linear measurement vector. Typically it is assumed that the decoder has…

This dissertation is devoted to provide advanced nonconvex nonsmooth variational models of (Magnetic Resonance Image) MRI reconstruction, efficient learnable image reconstruction algorithms and parameter training algorithms that improve the…

Positional encodings are employed to capture the high frequency information of the encoded signals in implicit neural representation (INR). In this paper, we propose a novel positional encoding method which improves the reconstruction…

We study the robust matrix completion problem for the low-rank Hankel matrix, which detects the sparse corruptions caused by extreme outliers while we try to recover the original Hankel matrix from the partial observation. In this paper, we…

We develop a novel transfer learning framework to tackle the challenge of limited training data in image reconstruction problems. The proposed framework consists of two training steps, both of which are formed as bi-level optimizations. In…

Machine learning techniques have proven very efficient in assorted classification tasks. Nevertheless, processing time-dependent high-speed signals can turn into an extremely challenging task, especially when these signals have been…

This paper studies the problem of sampling vector and tensor signals, which is the process of choosing sites in vectors and tensors to place sensors for better recovery. A small core tensor and multiple factor matrices can be used to…

Matrix completion is about recovering a matrix from its partial revealed entries, and it can often be achieved by exploiting the inherent simplicity or low dimensional structure of the target matrix. For instance, a typical notion of matrix…

We derive theoretical guarantees for the exact recovery of piecewise constant two-dimensional images from a minimal number of non-uniform Fourier samples using a convex matrix completion algorithm. We assume the discontinuities of the image…

Magnetic resonance imaging is a powerful imaging modality that can provide versatile information but it has a bottleneck problem "slow imaging speed". Reducing the scanned measurements can accelerate MR imaging with the aid of powerful…

We develop a parametric high-resolution method for the estimation of the frequency nodes of linear combinations of complex exponentials with exponential damping. We use Kronecker's theorem to formulate the associated nonlinear least squares…