Joseph Shtok

A Wide-Angle View at Iterated Shrinkage Algorithms

Sparse and redundant representations − an emerging and powerful model for signals − suggests that a data source could be described as a linear combination of few atoms from a pre-specified and over-complete dictionary. This model has drawn a considerable attention in the past decade, due to its appealing theoretical foundations, and promising practical results it leads to. Many of the applications that use this model are formulated as a mixture of l2-lp (p ≤ 1) optimization expressions. Iterated Shrinkage algorithms are a new family of highly effective numerical techniques for handling these optimization tasks, surpassing traditional optimization techniques. In this paper we aim to give a broad view of this group of methods, motivate their need, present their derivation, show their comparative performance, and most important of all, discuss their potential in various applications.

Sparsity-based Sinogram Denoising for low-dose Computed Tomography

We propose a sinogram restoration method which consists of a patch-wise non-linear processing, based on a sparsity prior in terms of a learned dictionary. An off-line learning process uses a statistical model of the sinogram noise and minimizes an error measure in the image domain over the training set. The error measure is designed to preserve low-contrast edges for visibility of soft tissues. Our numerical study shows that the algorithm improves on the performance of the standard Filtered Back-Projection algorithm and effectively allows to halve the radiation dose for the same image quality.

Spatially-Adaptive Reconstruction in Computed Tomography Using Neural Networks

We propose a supervised machine learning approach for boosting existing signal and image recovery methods and demonstrate its efficacy on example of image reconstruction in computed tomography. Our technique is based on a local nonlinear fusion of several image estimates, all obtained by applying a chosen reconstruction algorithm with different values of its control parameters. Usually such output images have different bias/variance trade-off. The fusion of the images is performed by feed-forward neural network trained on a set of known examples. Numerical experiments show an improvement in reconstruction quality relatively to existing direct and iterative reconstruction methods.

Adaptive filtered-back-projection for computed tomography

We propose an extension of the Filtered Back-Projection (FBP) algorithm for reconstruction of attenuation images in Computed Tomography (CT). In our scheme, the standard filtering of projections with windowed ramp kernel is replaced by an adaptive, spatially-variant linear filter, based on a structured bank of 2D convolution kernels. In addition, the proposed scheme includes a post-processing step of image filtering by convolution with a 2D adaptive filter. Both filters are trained for specified reconstruction task via an optimization of corresponding objective function. The reconstruction task is defined through (i) a representative set of specific family of images; (ii) data acquisition conditions (partial set of projections, noise level); and (iii) a Region-Of-Interest (ROI) to be recovered. The resulting adaptive scheme absorbs various imperfections of reconstruction algorithm and specializes to given task, effectively improving the reconstruction quality.

Fine-Grained Recognition of Thousands of Object Categories with Single-Example Training

We approach the problem of fast detection and recognition of a large number (thousands) of object categories while training on a very limited amount of examples, usually one per category. Examples of this task include: (i) detection of retail products, where we have only one studio image of each product available for training, (ii) detection of brand logos, and (iii) detection of 3D objects and their respective poses within a static 2D image, where only a sparse subset of (partial) object views is available for training, with a single example for each view. Building a detector based on so few examples presents a significant challenge for the current top-performing (deep) learning based techniques, which require large amounts of data to train. Our approach for this task is based on a non-parametric probabilistic model for initial detection, CNN-based refinement and temporal integration where applicable. We successfully demonstrate its usefulness in a variety of experiments on both existing and our own benchmarks achieving state-of-the-art performance.

Learned shrinkage approach for low-dose reconstruction in computed tomography

We propose a direct nonlinear reconstruction algorithm for Computed Tomography (CT), designed to handle low-dose measurements. It involves the filtered back-projection and adaptive nonlinear filtering in both the projection and the image domains. The filter is an extension of the learned shrinkage method by Hel-Or and Shaked to the case of indirect observations. The shrinkage functions are learned using a training set of reference CT images. The optimization is performed with respect to an error functional in the image domain that combines the mean square error with a gradient-based penalty, promoting image sharpness. Our numerical simulations indicate that the proposed algorithm can manage well with noisy measurements, allowing a dose reduction by a factor of 4, while reducing noise and streak artifacts in the FBP reconstruction, comparable to the performance of a statistically based iterative algorithm.

Direct adaptive algorithms for CT reconstruction

This work concerns with linear and spatially-adaptive direct reconstruction algorithms for 2-D parallel-beam transmission tomography, extending the Filtered Back-Projection (FBP). The standard apodized Ram-Lak filter kernel is replaced with a bank of statistically trained 2-D convolution kernels, leading to improved reconstruction results. Two types of filter training procedures are considered. The first deals with reconstruction from noisy and truncated projections in a predefined region of interest, for images from a known family. In the second algorithm, termed SPADES, the training aims at improving the impulse response properties of the overall projection-reconstruction scheme. In this algorithm, the degree of smoothing applied to the reconstructed image is spatially controlled by a switch rule. Both methods are shown by simulations to operate well and lead to substantially improved reconstruction results.

Analysis of Basis Pursuit via Capacity Sets

Finding the sparsest solution α for an under-determined linear system of equations Dα=s is of interest in many applications. This problem is known to be NP-hard. Recent work studied conditions on the support size of α that allow its recovery using ℓ1-minimization, via the Basis Pursuit algorithm. These conditions are often relying on a scalar property of D called the mutual-coherence. In this work we introduce an alternative set of features of an arbitrarily given D, called the capacity sets. We show how those could be used to analyze the performance of the basis pursuit, leading to improved bounds and predictions of performance. Both theoretical and numerical methods are presented, all using the capacity values, and shown to lead to improved assessments of the basis pursuit success in finding the sparest solution of Dα=s.