Yoram Bresler

• PhD, Stanford University, EE
• University of Illinois Urbana-Champaign

Dynamic imaging involves the reconstruction of a spatio-temporal object at all times using its undersampled measurements. In particular, in dynamic computed tomography (dCT), only a single projection at one view angle is available at a time, making the inverse problem very challenging. Moreover, ground-truth dynamic data is usually either unavailab...

The Bayesian Cram\'er-Rao bound (BCRB) is a crucial tool in signal processing for assessing the fundamental limitations of any estimation problem as well as benchmarking within a Bayesian frameworks. However, the BCRB cannot be computed without full knowledge of the prior and the measurement distributions. In this work, we propose a fully learned B...

Dynamic imaging addresses the recovery of a timevarying 2D or 3D object at each time instant using its undersampled measurements. In particular, in the case of dynamic tomography, only a single projection at a single view angle may be available at a time, making the problem severely ill-posed. We propose an approach, RED-PSM, which combines for the...

Dynamic imaging addresses the recovery of a time-varying 2D or 3D object at each time instant using its undersampled measurements. In particular, in the case of dynamic tomography, only a single projection at a single view angle may be available at a time, making the problem severely ill-posed. In this work, we propose an approach, RED-PSM, which c...

In dynamic tomography the object undergoes changes while projections are being acquired sequentially in time. The resulting inconsistent set of projections cannot be used directly to reconstruct an object corresponding to a time instant. Instead, the objective is to reconstruct a spatio-temporal representation of the object, which can be displayed...

Scatter due to interaction of photons with the imaged object is a fundamental problem in X-ray Computed Tomography (CT). It manifests as various artifacts in the reconstruction, making its abatement or correction critical for image quality. Despite success in specific settings, hardware-based methods require modification in the hardware, or increas...

A fundamental problem in X-ray Computed Tomography (CT) is the scatter due to interaction of photons with the imaged object. Unless corrected, scatter manifests itself as degradations in the reconstructions in the form of various artifacts. Scatter correction is therefore critical for reconstruction quality. Scatter correction methods can be divide...

Ultrasound Localization Microscopy (ULM) offers a cost-effective modality for microvascular imaging by using intravascular contrast agents (microbubbles). However, ULM has a fundamental trade-off between acquisition time and spatial resolution, which makes clinical translation challenging. In this paper, in order to circumvent the trade-off, we int...

Low-dimensional embeddings for data from disparate sources play critical roles in multi-modal machine learning, multimedia information retrieval, and bioinformatics. In this paper, we propose a supervised dimensionality reduction method that learns linear embeddings jointly for two feature vectors representing data of different modalities or data f...

Chemical imaging provides information about the distribution of chemicals within a target. When combined with structural information about the target, in situ chemical imaging opens the door to applications ranging from tissue classification to industrial process monitoring. The combination of infrared spectroscopy and optical microscopy is a power...

Photon scattering in X-ray CT creates streaks, cupping, shading artifacts and decreased contrast in the reconstructions. We describe a novel physics-motivated deep-learning-based method using opposite views to estimate and correct scatter. The method incorporates an initial reconstruction, and the sum and the difference of opposite scatter-corrupte...

Super-resolution ultrasound localization microscopy (ULM), based on localization and tracking of individual microbubbles (MBs), offers unprecedented microvascular imaging resolution at clinically relevant penetration depths. However, ULM is currently limited by the requirement of dilute MB concentrations to ensure spatially sparse MB events for acc...

Image prior modeling is the key issue in image recovery, computational imaging, compresses sensing, and other inverse problems. Recent algorithms combining multiple effective priors such as the sparse or low-rank models, have demonstrated superior performance in various applications. However, the relationships among the popular image models are unc...

Recent works on adaptive sparse and on low-rank signal modeling have demonstrated their usefulness in various image/video processing applications. Patch-based methods exploit local patch sparsity, whereas other works apply low-rankness of grouped patches to exploit image non-local structures. However, using either approach alone usually limits perf...

Deep-learning-based methods for different applications have been shown vulnerable to adversarial examples. These examples make deployment of such models in safety-critical tasks questionable. Use of deep neural networks as inverse problem solvers has generated much excitement for medical imaging including CT and MRI, but recently a similar vulnerab...

Magnetic resonance imaging (MRI) is widely used in clinical practice, but it has been traditionally limited by its slow data acquisition. Recent advances in compressed sensing (CS) techniques for MRI reduce acquisition time while maintaining high image quality. Whereas classical CS assumes the images are sparse in known analytical dictionaries or t...

Chemical imaging provides information about the distribution of chemicals within a target. When combined with structural information about the target, in situ chemical imaging opens the door applications ranging from tissue classification to industrial process monitoring. The combination of infrared spectroscopy and optical microscopy is a powerful...

Magnetic resonance imaging (MRI) is widely used in clinical practice for visualizing both biological structure and function, but its use has been traditionally limited by its slow data acquisition. Recent advances in compressed sensing (CS) techniques for MRI that exploit sparsity models of images reduce acquisition time while maintaining high imag...

A Generative Adversarial Network (GAN) with generator $G$ trained to model the prior of images has been shown to perform better than sparsity-based regularizers in ill-posed inverse problems. In this work, we propose a new method of deploying a GAN-based prior to solve linear inverse problems using projected gradient descent (PGD). Our method learn...

Recent works on adaptive sparse and on low-rank signal modeling have demonstrated their usefulness in various image / video processing applications. Patch-based methods exploit local patch sparsity, whereas other works apply low-rankness of grouped patches to exploit image non-local structures. However, using either approach alone usually limits pe...

Multichannel blind deconvolution is the problem of recovering an unknown signal $f$ and multiple unknown channels $x_i$ from convolutional measurements $y_i=x_i \circledast f$ ($i=1,2,\dots,N$). We consider the case where the $x_i$'s are sparse, and convolution with $f$ is invertible. Our nonconvex optimization formulation solves for a filter $h$ o...

Data is said to follow the transform (or analysis) sparsity model if it becomes sparse when acted on by a linear operator called a sparsifying transform. Several algorithms have been designed to learn such a transform directly from data, and data-adaptive sparsifying transforms have demonstrated excellent performance in signal restoration tasks. Sp...

Data is said to follow the transform (or analysis) sparsity model if it becomes sparse when acted on by a linear operator called a sparsifying transform. Several algorithms have been designed to learn such a transform directly from data, and data-adaptive sparsifying transforms have demonstrated excellent performance in signal restoration tasks. Sp...

The extremal values of multivariate trigonometric polynomials are of interest in fields ranging from control theory to filter design, but finding the extremal values of such a polynomial is generally NP-Hard. In this paper, we develop simple and efficiently computable estimates of the extremal values of a multivariate trigonometric polynomial direc...

The extremal values of multivariate trigonometric polynomials are of interest in fields ranging from control theory to filter design, but finding the extremal values of such a polynomial is generally NP-Hard. In this paper, we develop simple and efficiently computable estimates of the extremal values of a multivariate trigonometric polynomial direc...

Tremendous efforts have been made to study the theoretical and algorithmic aspects of sparse recovery and low-rank matrix recovery. This paper fills a theoretical gap in matrix recovery: the optimal sample complexity for stable recovery without constants or log factors. We treat sparsity, low-rankness, and potentially other parsimonious structures...

Blind gain and phase calibration (BGPC) is a bilinear inverse problem involving the determination of unknown gains and phases of the sensing system, and the unknown signal, jointly. BGPC arises in numerous applications, e.g., blind albedo estimation in inverse rendering, synthetic aperture radar autofocus, and sensor array auto-calibration. In some...

Blind gain and phase calibration (BGPC) is a bilinear inverse problem involving the determination of unknown gains and phases of the sensing system, and the unknown signal, jointly. BGPC arises in numerous applications, e.g., blind albedo estimation in inverse rendering, synthetic aperture radar autofocus, and sensor array auto-calibration. In some...

Techniques exploiting the sparsity of images in a transform domain have been effective for various applications in image and video processing. Transform learning methods involve cheap computations and have been demonstrated to perform well in applications such as image denoising and medical image reconstruction. Recently, we proposed methods for on...

Techniques exploiting the sparsity of images in a transform domain have been effective for various applications in image and video processing. Transform learning methods involve cheap computations and have been demonstrated to perform well in applications such as image denoising and medical image reconstruction. Recently, we proposed methods for on...

Features based on sparse representation, especially using the synthesis dictionary model, have been heavily exploited in signal processing and computer vision. However, synthesis dictionary learning typically involves NP-hard sparse coding and expensive learning steps. Recently, sparsifying transform learning received interest for its cheap computa...

Blind deconvolution (BD) arises in many applications. Without assumptions on the signal and the filter, BD does not admit a unique solution. In practice, subspace or sparsity assumptions have shown the ability to reduce the search space and yield the unique solution. However, existing theoretical analysis on uniqueness in BD is rather limited. In a...

Range-space based identification aims at the recovery of a linear system (e.g multi-FIR channel identification for deblurring) by its output span, and constraints on its structure, often given by explicit parameterization. A key question for this inverse problem is under what conditions the recovered system is unique. When the parametrization is po...

Tremendous efforts have been made to study the theoretical and algorithmic aspects of sparse recovery and low-rank matrix recovery. This paper fills a theoretical gap in matrix recovery: the optimal sample complexity for stable recovery without constants or log factors. We treat sparsity, low-rankness, and potentially other parsimonious structures...

Many variables that we would like to predict depend nonlinearly on two types of attributes. For example, prices are influenced by supply and demand. Movie ratings are determined by demographic attributes and genre attributes. This paper addresses the dimensionality reduction problem in such regression problems with two predictor vectors. In particu...

A dramatic reduction in data required for chemically specific 3-D imaging is achieved through prior constraints on the known constituents of the sample. We solve the inverse scattering problem to determine morphology and composition.

Blind gain and phase calibration (BGPC) is a structured bilinear inverse problem, which arises in many applications, including inverse rendering in computational relighting (albedo estimation with unknown lighting), blind phase and gain calibration in sensor array processing, and multichannel blind deconvolution. The fundamental question of the uni...

Blind gain and phase calibration (BGPC) is a structured bilinear inverse problem, which arises in many applications, including inverse rendering in computational relighting (albedo estimation with unknown lighting), blind phase and gain calibration in sensor array processing, and multichannel blind deconvolution. The fundamental question of the uni...

Subsampled blind deconvolution is the recovery of two unknown signals from samples of their convolution. To overcome the ill-posedness of this problem, solutions based on priors tailored to specific application have been developed in practical applications. In particular, sparsity models have provided promising priors. However, in spite of empirica...

Compressed sensing is a powerful tool in applications such as magnetic resonance imaging (MRI). It enables accurate recovery of images from highly undersampled measurements by exploiting the sparsity of the images or image patches in a transform domain or dictionary. In this work, we focus on blind compressed sensing (BCS), where the underlying spa...

Compressed sensing is a powerful tool in applications such as magnetic resonance imaging (MRI). It enables accurate recovery of images from highly undersampled measurements by exploiting the sparsity of the images or image patches in a transform domain or dictionary. In this work, we focus on blind compressed sensing (BCS), where the underlying spa...

Compressed Sensing has been demonstrated to be a powerful tool for magnetic resonance imaging (MRI), where it enables accurate recovery of images from highly undersampled k-space measurements by exploiting the sparsity of the images or image patches in a transform domain or dictionary. In this work, we focus on blind compressed sensing, where the u...

Recent years have numerous algorithms to learn a sparse synthesis or analysis model from data. Recently, a generalized analysis model called the 'transform model' has been proposed. Data following the transform model is approximately sparsified when acted on by a linear operator called a sparsifying transform. While existing transform learning algo...

Blind deconvolution (BD) arises in many applications. Without assumptions on the signal and the filter, BD is ill-posed. In practice, subspace or sparsity assumptions have shown the ability to reduce the search space and yield the unique solution. However, existing theoretical analysis on uniqueness in BD is rather limited. In an earlier paper of o...

Compressed sensing exploits the sparsity of images or image patches in a transform domain or synthesis dictionary to reconstruct images from undersampled measurements. In this work, we focus on blind compressed sensing, where the underlying sparsifying transform is a priori unknown, and propose a framework to simultaneously reconstruct both the ima...

Bilinear inverse problems (BIPs), the resolution of two vectors given their image under a bilinear mapping, arise in many applications, such as blind deconvolution and dictionary learning. However, there are few results on the uniqueness of solutions to BIPs. For example, blind gain and phase calibration (BGPC) is a structured bilinear inverse prob...

Blind deconvolution is the recovery of two unknown signals from their convolution. To overcome the ill-posedness of this problem, solutions based on priors tailored to specific application have been developed in practical applications. In particular, sparsity models have provided promising priors. In spite of empirical success in many applications,...

Sparsity-based techniques have been widely popular in signal processing applications such as compression, denoising, and compressed sensing. Recently, the learning of sparsifying transforms for data has received interest. The advantage of the transform model is that it enables cheap and exact computations. In Part I of this work, efficient methods...

Techniques exploiting the sparsity of signals in a transform domain or dictionary have been popular in signal processing. Adaptive synthesis dictionaries have been shown to be useful in applications such as signal denoising, and medical image reconstruction. More recently, the learning of sparsifying transforms for data has received interest. The s...

Blind deconvolution (BD), the resolution of a signal and a filter given their convolution, arises in many applications. Without further constraints, BD is ill-posed. In practice, subspace or sparsity constraints have been imposed to reduce the search space, and have shown some empirical success. However, existing theoretical analysis on uniqueness...

The multiple measurement vector problem (MMV) is a generalization of the compressed sensing problem that addresses the recovery of a set of jointly sparse signal vectors. One of the important contributions of this paper is to reveal that the seemingly least related state-of-art MMV joint sparse recovery algorithms - M-SBL (multiple sparse Bayesian...

Dynamic positron emission tomography (PET) is widely used to measure changes in the bio-distribution of radiopharmaceuticals within particular organs of interest over time. However, to retain sufficient temporal resolution, the number of photon counts in each time frame must be limited. Therefore, conventional reconstruction algorithms such as the...

The sparsity of images in a transform domain or dictionary has been widely exploited in image processing. Compared to the synthesis dictionary model, sparse coding in the (single) transform model is cheap. However, natural images typically contain diverse textures that cannot be sparsified well by a single transform. Hence, we propose a union of sp...

Bilinear inverse problems (BIPs), the resolution of two vectors given their image under a bilinear mapping, arise in many applications. Without further constraints, BIPs are usually ill-posed. In practice, properties of natural signals are exploited to solve BIPs. For example, subspace constraints or sparsity constraints are imposed to reduce the s...

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 exploits the sparsity of images or image patches in a transform domain or synthesis dictionary to reconstruct...

Many applications in signal processing benefit from the sparsity of signals in a certain transform domain or dictionary. Synthesis sparsifying dictionaries that are directly adapted to data have been popular in applications such as image denoising, inpainting, and medical image reconstruction. In this work, we focus instead on the sparsifying trans...

Many techniques in signal and image processing exploit the sparsity of natural signals in a transform domain or dictionary. Adaptive synthesis dictionaries have been shown to be useful in applications such as signal denoising, and compressed sensing. More recently, the data-driven adaptation of sparsifying transforms has received some interest. The...

In recent years, sparse signal modeling, especially using the synthesis model has been popular. Sparse coding in the synthesis model is however, NP-hard. Recently, interest has turned to the sparsifying transform model, for which sparse coding is cheap. However, natural images typically contain diverse textures that cannot be sparsified well by a s...

One of the technical challenges in cine MRI is to reduce the acquisition time to enable the high spatio-temporal resolution imaging of a cardiac volume within a short scan time. Recently, compressed sensing approaches have been investigated extensively for highly accelerated cine MRI by exploiting transform domain sparsity using linear transforms s...

The sparsity of natural signals in transform domains such as the DCT has been heavily exploited in various applications. Recently, we introduced the idea of learning sparsifying transforms from data, and demonstrated the usefulness of learnt transforms in image representation, and denoising. However, the learning formulations therein were non-conve...

A central problem in computed tomography (CT) imaging is to obtain useful, high-quality images from low-dose measurements. Methods that exploit the sparse representations of tomographic images have long been known to improve the quality of reconstructions from low-dose data. Recent work has shown that sparse representations learned directly from th...

Model based iterative reconstruction algorithms are capable of reconstructing high-quality images from lowdose CT measurements. The performance of these algorithms is dependent on the ability of a signal model to characterize signals of interest. Recent work has shown the promise of signal models that are learned directly from data. We propose a ne...

Compressed sensing of simultaneously sparse and rank-one matrices enables recovery of sparse signals from a few linear measurements of their bilinear form. One important question is how many measurements are needed for a stable reconstruction in the presence of measurement noise. Unlike the conventional compressed sensing for sparse vectors, where...

Many applications in signal processing benefit from the sparsity of signals in a certain transform domain or dictionary. Synthesis sparsifying dictionaries that are directly adapted to data have been popular in applications such as image denoising, and medical image reconstruction. In this work, we focus specifically on the learning of orthonormal...

The multiple measurement vector problem (MMV) is a generalization of the compressed sensing problem that addresses the recovery of a set of jointly sparse signal vectors. One of the important contributions of this paper is to reveal that the seemingly least related state-of-art MMV joint sparse recovery algorithms - M-SBL (multiple sparse Bayesian...

Adaptive sparse representations have been very popular in numerous applications in recent years. The learning of synthesis sparsifying dictionaries has particularly received much attention, and such adaptive dictionaries have been shown to be useful in applications such as image denoising, and magnetic resonance image reconstruction. In this work,...

The sparsity of images in a transform domain or dictionary has been exploited in many applications in image processing. For example, analytical sparsifying transforms such as Wavelets and DCT have been extensively used in compression standards. Recently, synthesis sparsifying dictionaries that are directly adapted to the data have become popular es...

In this correspondence, a corrected version of the convergence analysis given by Lee and Bresler in the above titled paper (ibid., vol. 56, no. 9, pp. 4402-4416, Sep. 2010) is presented.

Compressed sensing enables universal, simple, and reduced-cost acquisition by exploiting a sparse signal model. Most notably, recovery of the signal by computationally efficient algorithms is guaranteed for certain random measurement models, which satisfy the so-called isotropy property. However, in real-world applications, this property is often n...

Compressed Sensing (CS) enables magnetic resonance imaging (MRI) at high undersampling by exploiting the sparsity of MR images in a certain transform domain or dictionary. Recent approaches adapt such dictionaries to data. While adaptive synthesis dictionaries have shown promise in CS based MRI, the idea of learning sparsifying transforms has not r...

The sparsity of signals and images in a certain transform domain or dictionary has been exploited in many applications in signal and image processing. Analytical sparsifying transforms such as Wavelets and DCT have been widely used in compression standards. Recently, synthesis sparsifying dictionaries that are directly adapted to the data have beco...

We introduce a fast algorithm to backproject fan-beam tomographic projections. For typical configurations of computed tomography scanners, the algorithm reduces the number of computations and actual runtimes by an order of magnitude. Similar to fast algorithms for the parallel-beam geometry, this algorithm is a divide-and-conquer method that aggreg...

The sparsity of signals and images in a certain analytically defined transform domain or dictionary such as discrete cosine transform or wavelets has been exploited in many applications in signal and image processing. Recently, the idea of learning a dictionary for sparse representation of data has become popular. However, while there has been exte...

Compressed sensing is a new data acquisition paradigm enabling universal, simple, and reduced-cost acquisition, by exploiting a sparse signal model. Most notably, recovery of the signal by computationally efficient algorithms is guaranteed for certain randomized acquisition systems. However, there is a discrepancy between the theoretical guarantees...

We study the feasibility of short finite impulse re- sponse (FIR) synthesis for perfect reconstruction (PR) in generic FIR filter banks. Among all PR synthesis banks, we focus on the one with the minimum filter length. For filter banks with over- sampling factors of at least two, we provide prescriptions for the shortest filter length of the synthe...

Compressed Sensing (CS) takes advantage of the sparsity of MR images in certain bases or dictionaries to obtain accurate reconstructions from undersampled k-space data. The (pseudo) random sampling schemes used most often for CS may have good theoretical asymptotic properties; however, with limited data they may be far from optimal. In this paper,...

Compressive sensing (CS) has seen impressive successes and fast growth over the past ten years, including applications in medical imaging. Applications of CS to magnetic resonance imaging (MRI) have been the earliest, most numerous, and most diverse, owing to the tremendous flexibility in designing the acquisition process and the pressing need that...

Self-calibrating k-space-based image reconstruction in parallel MRI interpolates the subsampled multi-channel data to a fully sampled Nyquist grid in k-space. Adopting a filter bank interpolation framework, we provide a new formulation of the associated inverse problem and develop the theory for blind identification of the interpolant filters. The...

Compressed sensing (CS) exploits the sparsity of MR images to enable accurate reconstruction from undersampled k-space data. Recent CS methods have employed analytical sparsifying transforms such as wavelets and finite differences. In this paper, we propose a novel framework for adaptively learning the sparsifying transform (dictionary), and recons...