Related papers: Blind Recovery of Sparse Signals from Subsampled C…
The blind deconvolution problem amounts to reconstructing both a signal and a filter from the convolution of these two. It constitutes a prominent topic in mathematical and engineering literature. In this work, we analyze a sparse version…
We derive near optimal performance guarantees for subsampled blind deconvolution. Blind deconvolution is an ill-posed bilinear inverse problem and additional subsampling makes the problem even more challenging. Sparsity and spectral…
The success of the compressed sensing paradigm has shown that a substantial reduction in sampling and storage complexity can be achieved in certain linear and non-adaptive estimation problems. It is therefore an advisable strategy for…
In the blind deconvolution problem, we observe the convolution of an unknown filter and unknown signal and attempt to reconstruct the filter and signal. The problem seems impossible in general, since there are seemingly many more unknowns…
Blind deconvolution is an ubiquitous non-linear inverse problem in applications like wireless communications and image processing. This problem is generally ill-posed, and there have been efforts to use sparse models for regularizing blind…
Blind deconvolution is a ubiquitous problem of recovering two unknown signals from their convolution. Unfortunately, this is an ill-posed problem in general. This paper focuses on the {\em short and sparse} blind deconvolution problem,…
Blind deconvolution is an ubiquitous non-linear inverse problem in applications like wireless communications and image processing. This problem is generally ill-posed since signal identifiability is a key concern, and there have been…
Multi-channel sparse blind deconvolution, or convolutional sparse coding, refers to the problem of learning an unknown filter by observing its circulant convolutions with multiple input signals that are sparse. This problem finds numerous…
We investigate a compressive sensing framework in which the sensors introduce a distortion to the measurements in the form of unknown gains. We focus on blind calibration, using measures performed on multiple unknown (but sparse) signals…
Deconvolution is a fundamental inverse problem in signal processing and the prototypical model for recovering a signal from its noisy measurement. Nevertheless, the majority of model-based inversion techniques require knowledge on the…
The fundamental principle underlying compressed sensing is that a signal, which is sparse under some basis representation, can be recovered from a small number of linear measurements. However, prior knowledge of the sparsity basis is…
Blind deconvolution over graphs involves using (observed) output graph signals to obtain both the inputs (sources) as well as the filter that drives (models) the graph diffusion process. This is an ill-posed problem that requires additional…
Natural signals and images are well-known to be approximately sparse in transform domains such as Wavelets and DCT. This property has been heavily exploited in various applications in image processing and medical imaging. Compressed sensing…
Blind deconvolution is the problem of recovering a convolutional kernel $\boldsymbol a_0$ and an activation signal $\boldsymbol x_0$ from their convolution $\boldsymbol y = \boldsymbol a_0 \circledast \boldsymbol x_0$. This problem is…
Multichannel blind deconvolution is the problem of recovering an unknown signal $f$ and multiple unknown channels $x_i$ from their circular convolution $y_i=x_i \circledast f$ ($i=1,2,\dots,N$). We consider the case where the $x_i$'s are…
We consider an important class of signal processing problems where the signal of interest is known to be sparse, and can be recovered from data given auxiliary information about how the data was generated. For example, a sparse Green's…
The task of finding a sparse signal decomposition in an overcomplete dictionary is made more complicated when the signal undergoes an unknown modulation (or convolution in the complementary Fourier domain). Such simultaneous sparse recovery…
The problem of sparse multichannel blind deconvolution (S-MBD) arises frequently in many engineering applications such as radar/sonar/ultrasound imaging. To reduce its computational and implementation cost, we propose a compression method…
This paper proposes a verification-based decoding approach for reconstruction of a sparse signal with incremental sparse measurements. In its first step, the verification-based decoding algorithm is employed to reconstruct the signal with a…
Parsimony in signal representation is a topic of active research. Sparse signal processing and representation is the outcome of this line of research which has many applications in information processing and has shown significant…