We revisit the Blind Deconvolution problem with a focus on understanding its robustness and convergence properties. Provable robustness to noise and other perturbations is receiving recent interest in vision, from obtaining immunity to adversarial attacks to assessing and describing failure modes of algorithms in mission critical applications. Further, many blind deconvolution methods based on ...

The present contribution discusses a Riemannian-gradient-based algorithm and a projection-based learning algorithm over a curved parameter space for single-neuron learning. We consider the ‘blind deconvolution’ signal processing problem. The learning rule naturally arises from a criterion-function minimization over the unitary hyper-sphere setting. We consider the blind deconvolution performanc...

We present a novel progressive framework for blind image restoration. Common blind restoration schemes first estimate the blur kernel, then employ non-blind deblurring. However, despite recent progress, the accuracy of PSF estimation is limited. Furthermore, the outcome of non-blind deblurring is highly sensitive to errors in the assumed PSF. Therefore, high quality blind deblurring has remaine...

Here, we introduce the blind subspace deconvolution (BSSD) problem, which is the extension of both the blind source deconvolution (BSD) and the independent subspace analysis (ISA) tasks. We treat the undercomplete BSSD (uBSSD) case. Applying temporal concatenation we reduce this problem to ISA. The associated ‘high dimensional’ ISA problem can be handled by a recent technique called joint f-dec...

Cocktail-party Problems (increasing generality): • Independent component analysis (ICA) [1, 2]: onedimensional sound sources. • Independent subspace analysis (ISA) [3]: independent groups of people. • Blind source deconvolution (BSD) [4]: one-dimensional sound sources and echoic room. • Blind subspace deconvolution (BSSD) [5]: independent source groups and echoes. Separation Theorem: • ISA ([3]...

Blind deconvolution involves the estimation of a sharp signal or image given only a blurry observation. Because this problem is fundamentally ill-posed, strong priors on both the sharp image and blur kernel are required to regularize the solution space. While this naturally leads to a standard MAP estimation framework, performance is compromised by unknown trade-off parameter settings, optimiza...

To reduce the influence of atmospheric turbulence on images of space-based objects we are developing a maximum a posteriori deconvolution approach. In contrast to techniques found in the literature, we are focusing on the statistics of the point-spread function (PSF) instead of the object. We incorporated statistical information about the PSF into multi-frame blind deconvolution. Theoretical co...

Image restoration involves the removal or minimization of degradation (blur, clutter, noise, etc.) in an image using a priori knowledge about the degradation phenomena. Blind restoration is the process of estimating both the true image and the blur from the degraded image characteristics, using only partial information about degradation sources and the imaging system. Our main interest concerns...

In seismic data processing, deconvolution plays a very important role because it permits to increase the temporal resolution of seismic sections and to equalize sources. The deconvolution problem when the wavelet is known is an ill-posed problem that can be tackled via regularization methods. However, the seismic source wavelet is unknown and therefore, it must be estimated from the data prior ...