相关论文: Audio Inpainting via $\ell_1$-Minimization and Dic…
Sparsity promoting regularization is an important technique for signal reconstruction and several other ill-posed problems. Theoretical investigation typically bases on the assumption that the unknown solution has a sparse representation…
In this work, we introduce a challenging image restoration task, referred to as SuperInpaint, which aims to reconstruct missing regions in low-resolution images and generate completed images with arbitrarily higher resolutions. We have…
This paper studies the problem of recovering a non-negative sparse signal $\x \in \Re^n$ from highly corrupted linear measurements $\y = A\x + \e \in \Re^m$, where $\e$ is an unknown error vector whose nonzero entries may be unbounded.…
$\ell_1$ minimization is often used for finding the sparse solutions of an under-determined linear system. In this paper we focus on finding sharp performance bounds on recovering approximately sparse signals using $\ell_1$ minimization,…
Monitoring of bird populations has played a vital role in conservation efforts and in understanding biodiversity loss. The automation of this process has been facilitated by both sensing technologies, such as passive acoustic monitoring,…
Many applications in signal processing benefit from the sparsity of signals in a certain transform domain or dictionary. Synthesis sparsifying dictionaries that are directly adapted to data have been popular in applications such as image…
Phase retrieval refers to a classical nonconvex problem of recovering a signal from its Fourier magnitude measurements. Inspired by the compressed sensing technique, signal sparsity is exploited in recent studies of phase retrieval to…
Sparsity-based models and techniques have been exploited in many signal processing and imaging applications. Data-driven methods based on dictionary and sparsifying transform learning enable learning rich image features from data, and can…
Image inpainting is an effective method to enhance distorted digital images. Different inpainting methods use the information of neighboring pixels to predict the value of missing pixels. Recently deep neural networks have been used to…
As an important component of multimedia analysis tasks, audio classification aims to discriminate between different audio signal types and has received intensive attention due to its wide applications. Generally speaking, the raw signal can…
Analysis $\ell_1$-recovery refers to a technique of recovering a signal that is sparse in some transform domain from incomplete corrupted measurements. This includes total variation minimization as an important special case when the…
Recently, the worse-case analysis, probabilistic analysis and empirical justification have been employed to address the fundamental question: When does $\ell_1$-minimization find the sparsest solution to an underdetermined linear system? In…
The speaker extraction technique seeks to single out the voice of a target speaker from the interfering voices in a speech mixture. Typically an auxiliary reference of the target speaker is used to form voluntary attention. Either a…
Dynamic range limitations in signal processing often lead to clipping, or saturation, in signals. The task of audio declipping is estimating the original audio signal, given its clipped measurements, and has attracted much interest in…
Sparse coding refers to the pursuit of the sparsest representation of a signal in a typically overcomplete dictionary. From a Bayesian perspective, sparse coding provides a Maximum a Posteriori (MAP) estimate of the unknown vector under a…
In this paper, we introduce a weighted $\ell_2/\ell_1$ minimization to recover block sparse signals with arbitrary prior support information. When partial prior support information is available, a sufficient condition based on the high…
We propose a novel training-free method for inpainting with off-the-shelf text-to-image models. While guidance-based methods in theory allow generic models to be used for inverse problems such as inpainting, in practice, their effectiveness…
Dictionary-sparse phase retrieval, which is also known as phase retrieval with redundant dictionary, aims to reconstruct an original dictionary-sparse signal from its measurements without phase information. It is proved that if the…
This paper provides novel results for the recovery of signals from undersampled measurements based on analysis $\ell_1$-minimization, when the analysis operator is given by a frame. We both provide so-called uniform and nonuniform recovery…
In this paper we look at a well known linear inverse problem that is one of the mathematical cornerstones of the compressed sensing field. In seminal works \cite{CRT,DOnoho06CS} $\ell_1$ optimization and its success when used for recovering…