Software & Hardware
Software
The use of photoactivated fluorescent molecules to create long sequences of low emitterdensity diffractionlimited images enables highprecision emitter localization. However, this is achieved at the cost of lengthy imaging times, limiting temporal resolution. In recent years, a variety of approaches have been suggested to reduce imaging times, ranging from classical optimization and statistical algorithms to deep learning methods.
In this software, we combine a recent highperforming classical method, SPARCOM, with modelbased deep learning, using the algorithm unfolding approach which relies on an iterative algorithm to design a compact neural network considering domain knowledge.
The resulting network, Learned SPARCOM (LSPARCOM), requires far fewer layers and parameters, and can be trained on a single field of view. Nonetheless it yields comparable or superior results to those obtained by SPARCOM with no heuristic parameter determination or explicit knowledge of the point spread function, and is able to generalize better than standard deep learning techniques.
Sparse and lowrank decomposition, also known as robust principle component analysis has been applied successfully in numerous applications.
Typically, this approach leads to a minimization problem which is solved using iterative algorithms.
Drawing inspiration from recurrent networks, in recent years deeplearning strategies have been extended to mimic the behavior of iterative algorithms, with reduced complexity.
In this work, we propose an extension of these deep architectures to robust principle component analysis in which fully connected layers are replaced with convolutional ones.
This strategy offers spatial invariance and significant reduction in the number of learned parameters.
We then apply the proposed method to contrast enhanced ultrasound, in which lowrank tissue signal is ought to be removed to visualize blood vessels.
We demonstrate the effectiveness of our approach on simulations and invivo rat brain scans.
The resulting images exhibit improved visual quality and contrast compared with images obtained by commonly practiced methods.
In this work, we introduce a new approach for quantitative MRI using MRF, called Magnetic Resonance Fingerprinting with Low Rank (FLOR).
We exploit the low rank property of the concatenated imaging constrasts, on top of the fact that the MRF signal is sparsely represented in the generated dictionary domain.
We present an iterative scheme based on the proximal gradient method, which consists of a gradientstep followed by a low rank projection using the singular value decomposition.
Experiments on real MRI data, acquired using a spirallysampled MRF FISP sequence, demonstrate better resolution compared to other compressedsensing based method for MRF.
Ultrasound localization microscopy offers new radiationfree diagnostic tools for vascular imaging deep within the tissue.
Despite its high spatial resolution, low microbubble concentrations dictate the acquisition of tens of thousands of images, over the course of several seconds to tens of seconds, to produce a single superresolved image.
To address this limitation, sparsitybased approaches have recently been proposed to significantly reduce the total acquisition time, by resolving the vasculature in settings with considerable microbubble overlap.
Here, we report on initial results of improving the spatial resolution and visual vascular reconstruction quality of sparsitybased superresolution ultrasound imaging from low framerate acquisitions, by exploiting the inherent kinematics of microbubbles' flow.
Our method relies on simultaneous tracking and sparsitybased detection of individual microbubbles.
We present a new method for superresolution in fluorescence microscopy, "sparsitybased superresolution correlation microscopy" (SPARCOM).
SPARCOM exploits sparsity in the correlation domain to dramatically reduce the number of required frames to produce a single superresolved image.
SPARCOM achieves spatialresolution comparable to singlemolecule techniques, while maintaining short integration time.
The proposed method, termed autocorrelation retrieval  Kolmogorov (CoRK), optimally solves the 1D Fourier phase retrieval problem.
The phase retrieval problem is first equivalently reformulated with respect to the autocorrelation of the signal, resulting in a convex quadratic programming problem.
An ADMM algorithm is then designed to efficiently solve this problem. Finally, a solution is extracted from the autocorrelation using Kolmogorov's algorithm, which has the property of minimum phase.
To ensure uniqueness of the solution, we add an impulse to the signal, with magnitude larger than the ℓ_{1} norm of the signal, before measuring the Fourier intensities.
We present a MATLAB based simulation tool for the acquisition process of a movie of fluctuating emitters with varying densities in an epifluorescence optical microscope. The simulator encompasses the physical aspects of the data acquisition process, including sample geometry, diffraction of light, camera quantization effects and noise. The simulator can be operated using a user friendly GUI or directly from the MATLAB command line, and is configurable via a simple text file.
We propose a gradient descent algorithm to recover a signal from its phaseless STFT measurements. The algorithm is initialized by the principle eigenvector, with proper normalization, of a designed matrix. This matrix is constructed as the solution of a simple leastsquares problem. In contrast to previous works, the algorithm is computationally efficient, stable in the presence of noise and enjoys theoretical guarantees.
We present an algorithm for resampling a function from its values on a nonCartesian grid onto a Cartesian grid. This problem arises in many applications such as MRI, CT, radio astronomy and geophysics. Our algorithm, termed SParse Uniform ReSampling (SPURS), employs methods from modern sampling theory to achieve a small approximation error while maintaining low computational cost.
We propose an adaptive MRI reconstruction approach from undersampled MRI measurement. Our general framework utilizes a reference image that exists in many MRI imaging scenarios. This reference can take on different forms: different imaging contrasts as done routinely in MRI acquisition, adjacent slices, or prior scans of the same patient. Our software package consists of examples of using this prior information in a compressed sensing framework, where the validity of the reference scan is determined during reconstruction in an adaptive fashion.
We extend the ideas of compressed sensing to general nonlinear measurement models. More specifically, we provide a software package to treat the problem of minimizing a general continuously differentiable function subject to sparsity constraints. Our algorithms are based on the notions of stationarity and coordinatewise optimality. We present three algorithms: iterative hard thresholding, greedy and partial sparsesimplex methods. The latter two methods are generalization of orthogonal matching pursuit to the nonlinear setting.
We propose GESPAR (GrEedy Sparse PhAse Retrieval): An efficient method for phase retrieval of sparse signals, with good recovery performance. Our algorithm is based on a fast 2opt local search method applied to a sparsity constrained nonlinear optimization formulation of the problem. In essence, GESPAR is a localsearch method, where the support of the sought signal is updated iteratively, according to certain selection rules. A local minimum of the objective function is then found given the current support using the damped Gauss Newton algorithm. GESPAR is fast, and is shown to lead to superior performance over Fienup and SDP based methods.
A 1D piecewise constant segmentation method, based on wavelet decomposition and thresholding, which detects significant breakpoints in the data.Over 1,000 times faster than leading approaches, with similar performance.
Simulation package of subNyquist sampling and support recovery using the modulated wideband converter (MWC). This page describes the MWC design, the Matlab code, and offers two software packages: analog and digital versions. The former simulates the samples that would have been obtained by true hardware. The latter provides a digital approximation of the MWC. The analog simulations consume more time but are more accurate.
A GUI package written in Matlab that provides a userfriendly introduction of the MWC. The GUI environment guides the user through 4 steps: building a multiband model, configuring the MWC and subNyquist sampling, support recovery using the continuoustofinite (CTF) block, and finally continuous reconstruction.
The modulated wideband converter (MWC) enables subNyquist sampling of narrowband transmissions, when their carrier frequencies are unknown to the sampler. Reconstruction from the MWC subNyquist samples is demonstrated in the package above. This GUI package provides signal processing of the narrowband transmissions by estimating the carrier frequencies from the lowrate samples. It also recovers the information bits that are encoded in the narrowband transmission of interest.
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 essential for the recovery process. Blind compressed sensing (BCS) avoids the need to know the sparsity basis in both the sampling and the recovery process under suitable conditions. This webpage explains the fundamentals of BCS and provides software for solving certain cases of the BCS framework.
Blind minimax estimation (BME) is a biased estimation technique for the linear regression problem, which provably dominates the ordinary leastsquares approach. In other words, BME always achieves lower meansquared error than leastsquares. This web page contains a friendly introduction to BME as well as downloadable Matlab files implementing the BME algorithms.
Bayesian estimation techniques require knowledge of the statistical relation between the desired signal and the measurements. In many practical scenarios, however, this relation is not fully known. This software implements our instrumental variable approach for treating such situations, which is based on a worstcase design strategy.
We describe an alternative to the popular total leastsquares (TLS) method for solving linear systems of equations with uncertainty in the model matrix. This approach, referred to as total maximumlikelihood (TML), is based on maximumlikelihood optimization. Statistical analysis, as well as numerical simulations, demonstrate the superiority of the TML approach over TLS. We describe the TML method and provide a software package for evaluating the TML estimate under a broad set of conditions.
FIA (Fluxomers Iterative Algorithm) is an opensource software for analysis of 13c metabolic tracer experiments.
The software is based upon Fluxomers, a new set of variables resulting with a very efficient investigation of complex metabolic networks.
The software supports the 13CFLUX software FTBL input file format, as well as its new (but very similar) textual FIA declaration input file.
Structured sparsity models like blocksparsity and wavelet trees have drawn considerable
attention in recent years. A general framework for capturing dependencies between dictionary atoms is achieved by a
statistical model that is based on a Boltzmann machine (BM) prior on the sparsity pattern. The BMbased framework allows
us to revisit the sparse recovery problem. This webpage explains the fundamentals of the BMbased model and sparse recovery,
and provides downloadable Matlab files implementing the BMbased algorithms.
