Sparse Deconvolution Research Articles

Characterization of nanoporous Al2O3 films at terahertz frequencies.

Terahertz birefringence in nanoporous Al2O3 films grown on Al substrates is characterized nondestructively by polarization-resolved terahertz spectroscopy. Sparse deconvolution is used to find the film thicknesses from the data, showing good agreement with the values measured directly by destructive cross-sectional field-emission scanning electron microscopy.

A Sparse Spike Deconvolution Algorithm Based on a Recurrent Neural Network and the Iterative Shrinkage-Thresholding Algorithm

Conventional sparse spike deconvolution algorithms that are based on the iterative shrinkage-thresholding algorithm (ISTA) are widely used. The aim of this type of algorithm is to obtain accurate seismic wavelets. When this is not fulfilled, the processing stops being optimum. Using a recurrent neural network (RNN) as deep learning method and applying backpropagation to ISTA, we have developed an RNN-like ISTA as an alternative sparse spike deconvolution algorithm. The algorithm is tested with both synthetic and real seismic data. The algorithm first builds a training dataset from existing well-logs seismic data and then extracts wavelets from those seismic data for further processing. Based on the extracted wavelets, the new method uses ISTA to calculate the reflection coefficients. Next, inspired by the backpropagation through time (BPTT) algorithm, backward error correction is performed on the wavelets while using the errors between the calculated reflection coefficients and the reflection coefficients corresponding to the training dataset. Finally, after performing backward correction over multiple iterations, a set of acceptable seismic wavelets is obtained, which is then used to deduce the sequence of reflection coefficients of the real data. The new algorithm improves the accuracy of the deconvolution results by reducing the effect of wrong seismic wavelets that are given by conventional ISTA. In this study, we account for the mechanism and the derivation of the proposed algorithm, and verify its effectiveness through experimentation using theoretical and real data.

Resolution Improvement of Ultrasonic Signals Using Sparse Deconvolution and Variational Mode Decomposition Algorithms

Over the past few years, the use of ultrasonic arrays for nondestructive testing (NDT) applications has grown rapidly and led to use new algorithms of signal processing. The present paper’s main objective is to improve the resolution of defect detection and make the detection process as fast and accurate as possible. This paper introduces a novel method to improve the resolution of ultrasonic phased array. The proposed method is based on the variational decomposition of signal and on a deconvolution method. To reduce the level of signal’s noise, a method based on the variational mode decomposition (VMD) is used and to improve the resolution, a sparse deconvolution algorithm optimized using the majorization-minimization (MM) method is used. A simulation study has been carried out simulating a block of stainless steel containing several defects in different positions. Experimental tests were performed on a sample of stainless steel containing several defects. The obtained results show that the proposed method can improve the quality of ultrasonic data which enhances the localization of defects.

Blind deconvolution for spike inference from fluorescence recordings

The parallel developments of genetically-encoded calcium indicators and fast fluorescence imaging techniques allows one to simultaneously record neural activity of extended neuronal populations in vivo. To fully harness the potential of functional imaging, one needs to infer the sequence of action potentials from fluorescence traces. Here we build on recently proposed computational approaches to develop a blind sparse deconvolution (BSD) algorithm based on a generative model for inferring spike trains from fluorescence traces. BSD features, (1) automatic (fully unsupervised) estimation of the hyperparameters, such as spike amplitude, noise level and rise and decay time constants, (2) a novel analytical estimate of the sparsity prior, which yields enhanced robustness and computational speed with respect to existing methods, (3) automatic thresholding for binarizing spikes that maximizes the precision-recall performance, (4) super-resolution capabilities increasing the temporal resolution beyond the fluorescence signal acquisition rate. BSD also uniquely provides theoretically-grounded estimates of the expected performance of the spike reconstruction in terms of precision-recall and temporal accuracy for each recording. The performance of the algorithm is established using synthetic data and through the SpikeFinder challenge, a community-based initiative for spike-rate inference benchmarking based on a collection of joint electrophysiological and fluorescence recordings. Our method outperforms classical sparse deconvolution algorithms in terms of robustness, speed and/or accuracy and performs competitively in the SpikeFinder challenge. This algorithm is modular, easy-to-use and made freely available. Its novel features can thus be incorporated in a straightforward way into existing calcium imaging packages.

Nondestructive measurement of mill-scale thickness on steel by terahertz time-of-flight tomography

We measure in a nondestructive and noncontact fashion the thicknesses of three scale films with thicknesses 28.5 ± 1.4 μm, 13.4± 0.9 μm, and 5.1 ± 0.3 μm on steel substrates employing terahertz time-of-flight tomography combined with advanced signal-processing techniques. Wüstite is the dominant phase in the scale films, though magnetite and hematite are also present. Because wüstite is electrically insulating, the incident terahertz electromagnetic pulses largely penetrate into the scale film; however, the pulses are entirely reflected by the underlying electrically conductive steel substrate. Because the film layers are thin, in some cases optically thin, the distinct pulses reflected at the air/scale and scale/steel interfaces overlap in time and thus are not visually evident in the reflected terahertz signal, necessitating the use of deconvolution techniques to recover the sample structure. We compare the merits of three deconvolution techniques, one unsuccessful (frequency-wavelet domain deconvolution) and two successful (sparse deconvolution and autoregressive extrapolation), to characterize the thicknesses of these scale films.

A Simple Deconvolutional Mechanism for Point Clouds and Sparse Unordered Data (Student Abstract)

This paper presents a novel deconvolution mechanism, called the Sparse Deconvolution, that generalizes the classical transpose convolution operation to sparse unstructured domains, enabling the fast and accurate generation and upsampling of point clouds and other irregular data. Specifically, the approach uses deconvolutional kernels, which each map an input feature vector and set of trainable scalar weights to the feature vectors of multiple child output elements. Unlike previous approaches, the Sparse Deconvolution does not require any voxelization or structured formulation of data, it is scalable to a large number of elements, and it is capable of utilizing local feature information. As a result, these capabilities allow for the practical generation of unstructured data in unsupervised settings. Preliminary experiments are performed here, where Sparse Deconvolution layers are used as a generator within an autoencoder trained on the 3D MNIST dataset.

A criterion for automatic image deconvolution with L0‐norm regularization

AbstractAutomatic penalty adjustment in sparse deconvolution with penalized least squares is required for improved reliability and broader applicability. In sparse deconvolution with an L0‐norm penalty, the latent signal is by nature discontinuous, and the magnitudes of the residuals and sparsity regularization terms are of different order of magnitude. This makes approaches such as generalized cross validation or L‐curve unsuitable in practice. The criterion proposed in this paper is based on the representation of the sum of the normalized residuals and regularization terms (SNT) as a function of the penalty parameter. We observed that the minimum of the SNT corresponds to the optimal value of the penalty parameter. This approach was tested in the context of super‐resolution fluorescence microscopy imaging. Both simulated and real live‐cell images characterized by different complexities and emitter densities were analyzed to assess the performance of the developed optimization strategy and to demonstrate its usefulness over manual tuning.

Exact Recovery of Multichannel Sparse Blind Deconvolution via Gradient Descent

We study the multichannel sparse blind deconvolution (MCS-BD) problem, whose task is to simultaneously recover a kernel $a$ and multiple sparse inputs $\{x_i\}_{i=1}^p$ from their circulant convolu...

Identifiability Conditions for Compressive Multichannel Blind Deconvolution

In applications such as multi-receiver radars and ultrasound array systems, the observed signals are often modeled as the convolution of the transmit pulse signal and a set of sparse filters representing the sparse target scenes. A sparse multichannel blind deconvolution (MBD) problem simultaneously identifies the unknown signal and sparse filters, which is in general ill-posed. In this paper, we consider the identifiability problem of sparse-MBD and show that, similar to compressive sensing, it is possible to identify the sparse filters from compressive measurements of the output sequences. Specifically, we consider compressible measurements in the Fourier domain and derive deterministic identifiability conditions. Our main results demonstrate that $L$ -sparse filters can be identified from $\text{2}L^2$ Fourier measurements from two or more coprime channels. We also show that $\text{2}L$ measurements per channel are necessary. The sufficient condition sharpens as the number of channels increases and is asymptotically optimal, i.e., it suffices to acquire on the order of $L$ Fourier samples per channel. We also propose a kernel-based sampling scheme that acquires Fourier measurements from a commensurate number of time-domain samples. The gap between the sufficient and necessary conditions is illustrated through numerical experiments including comparing practical reconstruction algorithms. The proposed compressive MBD results require fewer measurements and fewer channels for identifiability compared to previous results, which aids in building cost-effective receivers.

Sparse Reconstruction-Based Inverse Scattering Imaging in a Shallow Water Environment

Bistatic sonar or multistatic sonar system can collect more scattering information of targets than a monostatic sonar system. In this paper, sparse learning via iterative minimization method (SLIM) is introduced to distinguish wave components for time-domain (TD) back-propagation (BP) inverse scattering imaging improvement. Unlike the prevailing high central frequency (>100 kHz) and wideband imaging sonar systems, a relatively low-frequency band (1–10 kHz) is considered here. Due to the low sidelobe output of SLIM, the investigated object’s surface in TD-BP image is much clearer in an ideal two-dimensional free field case. Furthermore, when the environmental information is known, this sparse reconstruction-based channel deconvolution method can be implemented to recognize, categorize the main propagating paths and then rectify their time of arrivals. Compared with the phase conjugation-based channel deconvolution method, the proposed approach’s results have fewer sidelobes and higher signal-to-background ratio in the simulation.

Boosting Compressed Sensing Using Local Measurements and Sliding Window Reconstruction

In the framework of compressed sensing, image data is measured using less measurements than the total number of pixels. Each measurement consists of a (random) linear combination of all pixels. Since image data is approximately sparse in an appropriate transform domain, a reasonable reconstruction is possible for many measurement matrices, especially for i.i.d. Gaussian measurement matrices. In a seemingly different field, non-regular sampling techniques such as three-quarter sampling have shown promising results to enhance the resolution of an imaging sensor by effectively sub-sampling a higher resolution image. Here, the measurements can be described as linear combinations of only three pixels, which can also be seen as a (spectral) compressed sensing measurement. Since each measurement is spatially localized, the reconstruction can be performed in overlapping sliding windows. In this work, we show that compressed sensing reconstruction algorithms can greatly benefit from such an overlapping sliding window reconstruction. Compared to conventional block-wise compressed sensing with i.i.d. Gaussian measurement matrices, the reconstruction quality in terms of the PSNR increases up to +5dB using small, local i.d.d. Gaussian measurement blocks. Additionally, we propose a local joint sparse deconvolution and extrapolation (L-JSDE) to reconstruct images from arbitrary local measurements. For several applications with local measurements we show that L-JSDE increases the PSNR by +2.2dB relative to conventional block-wise i.i.d. Gaussian measurements reconstructed with the state-of-the-art reconstruction algorithm D-AMP using the same overall sampling density.

Sparse deconvolution via off-grid T.V minimization

We present a grid-less solution to the total variation minimization approach to the sparse deconvolution problem. Unlike the existing methods [1, 2], our algorithm works directly with time domain data, and does not suffer from the consequences of leakage errors incurred while transforming the time domain measurements to frequency domain. The total variation minimization problem requires us to optimize the total variation of a function. This is an infinite dimensional problem. To deal with the underlying infinite dimensionality, we consider its finite dimensional semi-infinite duals with point-wise constraints. We provide a finite parameterization to handle the point-wise constraints in a computationally tractable manner. This parameterization exploits the underlying bandlimitedness of the convolution kernel by employing Prolate Spheroidal Wave Functions. Consequently, we are able to reduce the total variation minimization problem into a semidefinite program, which can be solved in polynomial time. We demonstrate its utility via numerical simulation studies as well as real world signal reconstruction examples.

Sparse deconvolution of proton radiography data to estimate water equivalent thickness maps.

In proton therapy, the conversion of the planning computed tomography (CT) into proton stopping powers is tainted by uncertainties which may jeopardize dose conformity. Proton radiography provides a direct information on the energy reduction of protons in the patient. However, it is currently limited by the degradation ("blurring") of the one-dimensional depth-dose deposition profiles which constitute the pixels. An iterative algorithm is implemented to extract high-resolution water equivalent thickness (WET) maps from the measurements of depth-dose profiles acquired with a multilayer ionization chamber. The method relies on the assumption that those curves are a function of the WET, which can benefit from a sparse representation. When used without relying on any prior knowledge derived from the planning CT, the method already outperforms the published one in terms of accuracy. We also propose a variant which integrates the planning CT in a robust fashion to further improve the deconvolution result and reach an accuracy of 1.5mm on the estimated WET. The methods are applied to both synthetic data and actual proton radiography acquisitions on phantoms. Besides the increase in accuracy achieved in the estimation of WET maps from proton radiography data, we demonstrate that the proposed deconvolution algorithm is also more robust with respect to confounding factors such as residual setup errors or changes in the anatomy. Therefore, proton radiography using a range probe provides both the required accuracy to assess and reduce range uncertainty in proton therapy and the simplicity of integrated-mode proton radiography.

Adaptive step-size fast iterative shrinkage-thresholding algorithm and sparse-spike deconvolution

The standard Fast Iterative Shrinkage-Thresholding Algorithm (FISTA) adopts a search approach consisting of linear increases to determine the step size of the internal gradient. If the input of the initial step-size is not accurate, the convergence of FISTA may be restricted when the linear search scheme is applied. To overcome this problem, we tentatively reduce the step size before each iteration to then obtain the most suitable step-size using a linear search approach. To ensure the convergence of the algorithm, we introduce the step size for the previous and subsequent iterations during the calculation process. This has allowed us sparse-spike deconvolution based on an adaptive step size algorithm (ASFISTA), which to a certain extent solves the problem of the degree of convergence of the standard method. In this paper we first present the new algorithm and then we test its convergence. In order to check the effectiveness of the modified algorithm, we use both the standard FISTA method and the improved ASFISTA method to conduct sparse spike deconvolution on a theoretical model. Finally, we carry out a similar analysis aimed at the recovery of the sparse real signal.

Reinforced concrete mapping using full-waveform inversion of GPR data

Mapping the location and dimension of reinforcing bars in concrete can be critical for assessing the structure and state of reinforced concrete. Concrete structures, such as bridge pilings or cell phone tower foundations, are integral to modern life. Ground penetrating radar (GPR) is commonly used for mapping rebar grids, but traditional GPR data processing techniques fail to provide reliable information on the diameter of bars. Full-waveform inversion (FWI) of surface-coupled common-offset GPR B-scans (profiles) over reinforced concrete improves estimates of rebar diameters over more conventional ray-based methods. The method applies a sparse blind deconvolution (SBD) technique to obtain the optimized source wavelet and a sparse representation of the subsurface reflectivity series. A ray-based analysis is then performed on the estimated reflectivity model to define the initial geometry model to start the FWI. Applying this method to a synthetic data set and two real data cases with 1 and 2.6 GHz center frequency antennas results in errors in the rebar diameter estimates of less than 11% for rebars with concrete cover of 7.5 cm or less. These results compare favorably with those obtained from other methods that require cross-polarized antennas or ancillary equipment. The synthetic model demonstrates that the combination of SBD and FWI also improves ray-based estimates of the concrete permittivity and conductivity.

The comparative sense of sparse deconvolution and least-squares deconvolution methods in increasing the temporal resolution of GPR data

Improving the temporal resolution of ground-penetrating radar (GPR) data is a fundamental factor in presenting the characteristics of the underground structures. The advantages of sparse signal processing using the majorization-minimization (MM) method in GPR signal compression are investigated. In this method, minimizing the cost function is determined with L1 and L2 norms; also, the banded structures of matrices resulting from the sparse deconvolution problem are regarded. Then, the MM algorithm has been implemented with least-squares deconvolution (LSQR) on the synthetic and real data collected by a system with dual-frequency antennas of 300 and 800 MHz. The compression process has resulted in a high-resolution image from the subsurface layers and anomalies. Analysis of the outputs reported that the reflection coefficient improved significantly by application of the MM algorithm to the synthetic and real data compared with the least-squares deconvolution which only filters the data. The power spectrum after using the MM algorithm shows acceptable compression. Moreover, this algorithm leads to a considerable improvement on the amplitudes so that the hidden anomalies are better restored.

Structured Local Optima in Sparse Blind Deconvolution

Blind deconvolution is a ubiquitous problem aiming to recover a convolution kernel $\boldsymbol a_{0}\in \mathbb R ^{k}$ and an activation signal $\boldsymbol x_{0}\in \mathbb R ^{m}$ from their convolution $\boldsymbol y\in \mathbb R ^{m}$ . Unfortunately, this is an ill-posed problem in general. This paper focuses on the short and sparse blind deconvolution problem, where the convolution kernel is short ( $k\ll m$ ) and the activation signal is sparsely and randomly supported ( $\left \|{ \boldsymbol x_{0} }\right \|_{0}\ll m$ ). This variant captures the structure of the convolutional signals in several important application scenarios. In this paper, we normalize the convolution kernel to have unit Frobenius norm and then cast the blind deconvolution problem as a nonconvex optimization problem over the kernel sphere. We demonstrate that (i) in a certain region of the sphere, every local optimum is close to some shift truncation of the ground truth, and (ii) for a generic unit kernel $\boldsymbol a_{0}$ , when the sparsity of activation signal satisfies $\theta \lesssim k^{-2/3}$ and number of measurements $m\gtrsim \mathop {\mathrm {poly}}\nolimits \left ({k }\right) $ , the proposed initialization method together with a descent algorithm which escapes strict saddle points recovers some shift truncation of the ground truth kernel.

A novel reconstruction algorithm for polarization modulated fluorescence super-resolution microscopy

Due to the inherent polarization property of fluorescence, the imaging sparsity of neighboring fluorophores can be enhanced by excitation scheme with polarization modulation. Based on this fact, the super-resolution images have been successfully reconstructed from the polarization modulated wide-field fluorescence images by sparse deconvolution method realized with fast iterative shrinkage-thresholding algorithm (FISTA). Here, a new algorithm is proposed to reconstruct the super-resolution images based on the conjugate gradient method. The algorithm is analyzed theoretically and verified by simulations and the experimental data. The reconstruction results proves the feasibility of the algorithm and presents the influences of the steps of iteration and polarization modulation.

On the Global Geometry of Sphere-Constrained Sparse Blind Deconvolution.

Blind deconvolution is the problem of recovering a convolutional kernel a0 and an activation signal x0 from their convolution [Formula: see text]. This problem is ill-posed without further constraints or priors. This paper studies the situation where the nonzero entries in the activation signal are sparsely and randomly populated. We normalize the convolution kernel to have unit Frobenius norm and cast the sparse blind deconvolution problem as a nonconvex optimization problem over the sphere. With this spherical constraint, every spurious local minimum turns out to be close to some signed shift truncation of the ground truth, under certain hypotheses. This benign property motivates an effective two stage algorithm that recovers the ground truth from the partial information offered by a suboptimal local minimum. This geometry-inspired algorithm recovers the ground truth for certain microscopy problems, also exhibits promising performance in the more challenging image deblurring problem. Our insights into the global geometry and the two stage algorithm extend to the convolutional dictionary learning problem, where a superposition of multiple convolution signals is observed.

An iterative sparse deconvolution method for simultaneous multicolor 19 F-MRI of multiple contrast agents.

Purpose 19F‐MRI is gaining widespread interest for cell tracking and quantification of immune and inflammatory cells in vivo. Different fluorinated compounds can be discriminated based on their characteristic MR spectra, allowing in vivo imaging of multiple 19F compounds simultaneously, so‐called multicolor 19F‐MRI. We introduce a method for multicolor 19F‐MRI using an iterative sparse deconvolution method to separate different 19F compounds and remove chemical shift artifacts arising from multiple resonances.MethodsThe method employs cycling of the readout gradient direction to alternate the spatial orientation of the off‐resonance chemical shift artifacts, which are subsequently removed by iterative sparse deconvolution. Noise robustness and separation was investigated by numerical simulations. Mixtures of fluorinated oils (PFCE and PFOB) were measured on a 7T MR scanner to identify the relation between 19F signal intensity and compound concentration. The method was validated in a mouse model after intramuscular injection of fluorine probes, as well as after intravascular injection.ResultsNumerical simulations show efficient separation of 19F compounds, even at low signal‐to‐noise ratio. Reliable chemical shift artifact removal and separation of PFCE and PFOB signals was achieved in phantoms and in vivo. Signal intensities correlated excellently to the relative 19F compound concentrations (r−2 = 0.966/0.990 for PFOB/PFCE).ConclusionsThe method requires minimal sequence adaptation and is therefore easily implemented on different MRI systems. Simulations, phantom experiments, and in‐vivo measurements in mice showed effective separation and removal of chemical shift artifacts below noise level. We foresee applicability for simultaneous in‐vivo imaging of 19F‐containing fluorine probes or for detection of 19F‐labeled cell populations.