A block algorithm for blind signal deconvolution

We present a simple efficient local unsupervised learning algorithm for online adaptive multichannel blind deconvolution and separation of i.i.d. sources. Under mild conditions, there exits a stable inverse system so that the source signals can be exactly recovered from their convolutive mixtures. Based on the existence of the inverse filter, we construct a two-stage neural network which consists of blind equalization and source separation. In the blind equalization stage, we employ anti-Hebbian learning in the temporal domain for decorrelation. For blind separation, we can apply any existing algorithms. Extensive computer simulations confirm the validity and high performance of our proposed learning algorithm.

The main inherent property of medical ultrasound imaging is speckle noise which generally obscures and reduces the diagnostic image resolution and contrast. Consequently, the substantial improvement of ultrasound images is an important prerequisite, whenever ultrasound is used as one of the most utilized diagnostic modalities. The problem of reconstruction of ultrasound images by means of blind deconvolution has long been recognized as a prerequisite in ultrasound imaging processing in the recent decades. Recently, the Total Variation (TV) regularization method has become extremely effective approach for image reconstruction, especially for restoring edges of the blurring image. In this paper, we present a new blind iterative TV deconvolution algorithm for reconstructing ultrasound images from blurry and noisy observations. First, it proposes the initial estimation of the point-spread function (PSF) based on a generalization of two-dimensional homomorphic filtering in cepstrum domain. It is demonstrated that the initial PSF can be effectively estimated by applying a proper smoothing low-pass filtering in cepstrum domain. Second, it introduces a novel blind iterative TV deconvolution which is derived from an alternating minimization algorithm. Fast Fourier Transform (FFT) is used in the pre-iteration computation. The innovative blind deconvolution is based on either concurrent or successive estimation of the PSF function and the image of interest. The iterative scheme is devised to recover the image and simultaneously identify the PSF function. The estimated PSF and restored image will be close to real values in the subsequent iterative deconvolution. Final, tests on phantom and clinical images have proven our novel blind iterative TV deconvolution gives more positive results of higher spatial resolution and better defined tissue structures than other deconvolution methods.

In this paper, a method for MIMO blind deconvolution is proposed. The method is applicable to the case of non-Gaussian i.i.d. input signals. The core of the method is an algorithm which extracts one of the input signals from the information of the output signals only. This algorithm is an non-trivial generalization of the Shalvi-Weinstein algorithm for SISO blind deconvolution and converges in super-exponential rate possibly after finite iterations. By recursive use of this algorithm, extraction of all input signals can be achieved.

We enhance the performance of the nonnegativity and support constraints recursive inverse filtering (NAS-RIF) algorithm for blind image deconvolution. The original cost function is modified to overcome the problem of operation on images with different scales for the representation of pixel intensity levels. Algorithm resetting is used to enhance the convergence of the conjugate gradient algorithm. A simple pixel classification approach is used to automate the selection of the support constraint. The performance of the resulting enhanced NAS-RIF algorithm is demonstrated on various images.

In order to alleviate the shortcomings of most blind deconvolution algorithms, this paper proposes an improved fast algorithm for blind deconvolution based on decorrelation technique and broadband block matrix. Althougth the original algorithm can overcome the shortcomings of current blind deconvolution algorithms, it has a constraint that the number of the source signals must be less than that of the channels. The improved algorithm deletes this constraint by using decorrelation technique. Besides, the improved algorithm raises the separation speed in terms of improving the computing methods of the output signal matrix. Simulation results demonstrate the validation and fast separation of the improved algorithm.

The present paper illustrates a geodesic-based learning algorithm over a curved parameter space for blind deconvolution application. The chosen deconvolving structure appears as a single neuron model whose learning rule arises from criterion-function minimization over a smooth manifold. In particular, we propose here a learning stepsize selection theory for the algorithm at hand. We consider the blind deconvolution performances of the algorithm as well as its computational burden. Also, a numerical comparison with seven blind-deconvolution algorithms known from the scientific literature is illustrated and discussed. Results of numerical tests conducted on a noiseless as well as a noisy system will confirm that the algorithm discussed in the present paper performs in a satisfactory way. Also, the performances of the presented algorithm will be compared with those exhibited by other blind deconvolution algorithms known from the literature.

Blind deconvolution is a challenging problem, but in low-light it is even more difficult. Existing algorithms, both classical and deep-learning based, are not designed for this condition. When the photon shot noise is strong, conventional deconvolution methods fail because (1) the image does not have enough signal-to-noise ratio to perform the blur estimation; (2) While deep neural networks are powerful, many of them do not consider the forward process. When the noise is strong, these networks fail to simultaneously deblur and denoise; (3) While iterative schemes are known to be robust in the classical frameworks, they are seldom considered in deep neural networks because it requires a differentiable non-blind solver. This paper addresses the above challenges by presenting an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">unsupervised</i> blind deconvolution method. At the core of this method is a reformulation of the general blind deconvolution framework from the conventional image-kernel alternating minimization to a purely kernel-based minimization. This kernel-based minimization leads to a new iterative scheme that backpropagates an unsupervised loss through a pre-trained non-blind solver to update the blur kernel. Experimental results show that the proposed framework achieves superior results than state-of-the-art blind deconvolution algorithms in low-light conditions.

Complex signal and system models are considered in this paper, and a class of new criteria, which is based on the higher-order cumulant, is derived for blind deconvolution. It is pointed out that blind deconvolution may be realized by maximizing or minimizing the normalized cumulant of the system output. This is a new approach to statistical matching for blind deconvolution. As an example, a new blind deconvolution (equalization) algorithm is proposed, and computer simulation results are included to demonstrate the performance of the proposed algorithm.

A new two-stage algorithm is proposed for the deconvolution of a multi-input multi-output (MIMO) system with colored input signals. Though most blind deconvolution algorithms in the literature utilize high-order statistics of the output signals for white input signals, the additional information that the input signals are colored allows second-order statistical algorithms to be designed. In fact, practical signal sources such as speech do have distinct, non-stationary, colored power spectral density. The first stage of signal separation is derived from a matrix pencil formed between output auto-correlation matrices at different delays. The deconvolution stage is then based on an existing subspace method. Simulation results are also presented.

We propose to use the blind deconvolution and its modification to extract the point spread function (PSF) of layered metamaterials from a SNOM measurement. The measurement results are processed using the blind deconvolution algorithm to reconstruct the real-valued non-coherent PSF, or using the modified blind deconvolution introduced in this paper to reconstruct the complex-valued coherent PSF. The two algorithms are tested in simulations with a layered metamaterial deposited on a thin metallic mask with test apertures. We show that the modified algorithm is capable of recovering the approximate shape of complex PSF with a sub-wavelength full width at half maximum from a measurement in which the apertures are larger than the wavelength.

Single-image blind deconvolution is one of the most challenging fields in image processing which restores a sharp image from its blurred version. Nowadays blind deconvolution algorithms have made significant progress. However, the restoration of blurred images with little scale edges and periodic textures is still a hard work. To solve this problem, this paper proposes a new normalized sparse regularization blind deconvolution algorithm, which uses a gradient saliency map to prohibit the image small structures on image blurry kernel estimation. Firstly, salient detection is performed to select the important area which conforms with the human vision system and generates a binary mask to screen out useful gradients. Secondly, the normalized sparse regularization blind deconvolution method is applied to obtain accurate blur kernel and recover the sharp image. Finally, the experiment results show that the algorithm can effectively deblur the degraded image on different scenarios.

Non-parametric Bayesian models of response function in dynamic image sequences

Previous research has primarily focused on leak diagnosis algorithms under the interference of outside environment noise. However, the former algorithms in leak detection are easily affected by noise from the pipe, especially the one that contains elbow noise. This article was mainly concerned with the effective and reliable approach to precisely locate leaks in the buried elbow pipeline system. To overcome the drawback of elbow noise interference and extract the leak source from the mixing signal in the greatest extent, this article proposes a novel frequency-domain-independent component analysis (ICA) blind deconvolution algorithm, which is based on a popular optimized FastICA (O-FICA) called complex-optimized FastICA (CO-FICA) algorithm. In comparison, CO-FICA differs from the time-domain blind convolution separation (T-BCS) algorithm, which transforms complicated time-domain convolution into a simple frequency-domain product problem. Compared with the conventional complex FastICA (C-FICA), the proposed CO-FICA method does not need to estimate signal statistics at each step, but it displays more excellent performance in convergent speed and separated precision. Altogether, the results from this study demonstrate that the localization precision of the proposed method is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\approx 87\%$ </tex-math></inline-formula> under the interference of elbow noise.

The correction of an adaptive optics (AO) system is always partially, a post-processing technique such as blind deconvolution can be used to improve the image quality. In this paper, we propose a blind deconvolution algorithm using Zernike-polynomial-based phase fitting to recover a high resolution and contrast image from the short-exposure AO images. The strategy is to parameterize the point spread function (PSF) with phase aberrations pixel by pixel and introduce a constraint to the phase estimations using phase fitting. The algorithm is robust and can lead to a restoration free of artifacts. We evaluate the performance of our proposed algorithm by a number of simulated experiments and it is well performed.

Unconventional computer aided imaging approaches, such as bi-spectrum or multi-frame blind deconvolution, have been used for some time to obtain high resolution images of space based objects from the ground. This looking up imaging scenario is characterized by r0 diameters usually much smaller than the telescope aperture, and isoplanatic angles on the same order as the object under observation. Air to ground imaging on the other hand, is often characterized by relatively large r0 values usually about the same size of the imaging aperture, but very small isoplanatic angles. In such a case, where the scene covers many isoplanatic patches, it has been shown that improvements in image quality can be obtained by dividing the field of view into sub-regions and applying processing algorithms to each sub-region. Because r0 is roughly the diameter of the aperture, the primary aberration over a subregion is tip-tilt. Block matching algorithms that correct only the local tip-tilt over the sub-regions have been developed to run in near real time. Correcting higher order local aberrations, using a blind deconvolution algorithm, can lead to improved results but requires increased computation. In this presentation we seek to compare air-to-ground imagery with different levels of processing; first global tip-tilt only correction; second local tip-tilt correction; and finally local tip-tilt plus high order correction. The goal is to determine if the increased detail obtained at each step is worth in increased processing complexity.