Multi-Dimensional Signal Alignment

This paper deals with the estimation of a deformation that describes the geometric transformation between two images. To solve this problem, we propose a novel framework that relies upon the brightness consistency hypothesis-a pixel’s intensity is maintained throughout the transformation. Instead of assuming small distortion and linearizing the problem (e.g. via Taylor Series expansion), we propose to interpret the brightness hypothesis as an all-pass filtering relation between the two images. The key advantages of this new interpretation are that no restrictions are placed on the amplitude of the deformation or on the spatial variations of the images. Moreover, by converting the all-pass filtering to a linear forward-backward filtering relation, our solution to the estimation problem equates to solving a linear system of equations, which leads to a highly efficient implementation. Using this framework, we develop a fast algorithm that relates one image to another, on a local level, using an all-pass filter and then extracts the deformation from the filter-hence the name ’Local All-Pass’ (LAP) algorithm. The effectiveness of this algorithm is demonstrated on a variety of synthetic and real deformations that are found in applications, such as image registration and motion estimation. In particular, when compared with a selection of image registration algorithms, the LAP obtains very accurate results for significantly reduced computation time and is very robust to noise corruption.

The optical flow is a velocity field that describes the motion of pixels within a sequence (or set) of images. Its estimation plays an important role in areas such as motion compensation, object tracking and image registration. In this paper, we present a novel framework to estimate the optical flow using local all-pass filters. Instead of using the optical flow equation, the framework is based on relating one image to another, on a local level, using an all-pass filter and then extracting the optical flow from the filter. Using this framework, we present a fast novel algorithm for estimating a smoothly varying optical flow, which we term the Local All-Pass (LAP) algorithm. We demonstrate that this algorithm is consistent and accurate, and that it outperforms three state-of-the-art algorithms when estimating constant and smoothly varying flows. We also show initial competitive results for real images.

Image registration is a required step in many practical applications that involve the acquisition of multiple related images. In this paper, we propose a methodology to deal with both the geometric and intensity transformations in the image registration problem. The main idea is to modify an accurate and fast elastic registration algorithm (Local All-Pass - LAP) so that it returns a parametric displacement field, and to estimate the intensity changes by fitting another parametric expression. Although we demonstrate the methodology using a low-order parametric model, our approach is highly flexible and easily allows substantially richer parametrisations, while requiring only limited extra computation cost. In addition, we propose two novel quantitative criteria to evaluate the accuracy of the alignment of two images (’salience correlation’) and the number of degrees of freedom (’parsimony’) of a displacement field, respectively. Experimental results on both synthetic and real images demonstrate the high accuracy and computational efficiency of our methodology. Furthermore, we demonstrate that the resulting displacement fields are more parsimonious than the ones obtained in other state-of-the-art image registration approaches.

Purpose: To develop a motion correction for Positron-Emission-Tomography (PET) using simultaneously acquired magnetic-resonance (MR) images within 90. Methods: A 90s MR acquisition allows the generation of a cardiac and respiratory motion model of the body trunk. Thereafter, further diagnostic MR sequences can be recorded during the PET examination without any limitation. To provide full PET scan time coverage, a sensor fusion approach maps external motion signals (respiratory belt, ECG-derived respiration signal) to a complete surrogate signal on which the retrospective data binning is performed. A joint Compressed Sensing reconstruction and motion estimation of the subsampled data provides motion-resolved MR images (respiratory + cardiac). A 1-POINT DIXON method is applied to these MR images to derive a motion-resolved attenuation map. The motion model and the attenuation map are fed to the Customizable and Advanced Software for Tomographic Reconstruction (CASToR) PET reconstruction system in which the motion correction is incorporated. All reconstruction steps are performed online on the scanner via Gadgetron to provide a clinically feasible setup for improved general applicability. The method was evaluated on 36 patients with suspected liver or lung metastasis in terms of lesion quantification (SUVmax, SNR, contrast), delineation (FWHM, slope steepness) and diagnostic confidence level (3-point Likert-scale). Results: A motion correction could be conducted for all patients, however, only in 30 patients moving lesions could be observed. For the examined 134 malignant lesions, an average improvement in lesion quantification of 22%, delineation of 64% and diagnostic confidence level of 23% was achieved. Conclusion: The proposed method provides a clinically feasible setup for respiratory and cardiac motion correction of PET data by simultaneous short-term MRI. The acquisition sequence and all reconstruction steps are publicly available to foster multi-center studies and various motion correction scenarios.

Fast and accurate motion estimation is an important tool in biomedical imaging applications such as motion compensation and image registration. In this paper, we present a novel algorithm to estimate motion in volumetric images based on the recently developed Local All-Pass (LAP) optical flow framework. The framework is built upon the idea that any motion can be regarded as a local rigid displacement and is hence equivalent to all-pass filtering. Accordingly, our algorithm aims to relate two images, on a local level, using a 3D all-pass filter and then extract the local motion flow from the filter. As this process is based on filtering, it can be efficiently repeated over the whole image volume allowing fast estimation of a dense 3D motion. We demonstrate the effectiveness of this algorithm on both synthetic motion flows and in-vivo MRI data involving respiratory motion. In particular, the algorithm obtains greater accuracy for significantly reduced computation time when compared to competing approaches.

Estimation of conduction velocity (CV) is an important task in the analysis of surface electromyography (sEMG). The problem can be framed as estimation of a time-varying delay (TVD) between electrode recordings. In this paper we present an algorithm which incorporates information from multiple electrodes into a single TVD estimation. The algorithm uses a common all-pass filter to relate two groups of signals at a local level. We also address a current limitation of CV estimators by providing an automated way of identifying the innervation zone from a set of electrode recordings, thus allowing incorporation of the entire array into the estimation. We validate the algorithm on both synthetic and real sEMG data with results showing the proposed algorithm is both robust and accurate.

Estimating the displacements between two images is often addressed using a small displacement assumption, which leads to what is known as the optical flow equation. We study the quality of the underlying approximation for the recently developed Local All-Pass (LAP) optical flow algorithm, which is based on another approach–displacements result from filtering. While the simplest version of LAP computes only first-order differences, we show that the order of LAP approximation is quadratic, unlike standard optical flow equation based algorithms for which this approximation is only linear. More generally, the order of approximation of the LAP algorithm is twice larger than the differentiation order involved. The key step in the derivation is the use of Padé approximants.

We propose an efficient method for image registration based on iteratively fitting a parametric model to the output of an elastic registration. It combines the flexibility of elastic registration - able to estimate complex deformations - with the robustness of parametric registration - able to estimate very large displacement. Our approach is made feasible by using the recent Local All-Pass (LAP) algorithm; a fast and accurate filter-based method for estimating the local deformation between two images. Moreover, at each iteration we fit a linear parametric model to the local deformation which is equivalent to solving a linear system of equations (very fast and efficient). We use a quadratic polynomial model however the framework can easily be extended to more complicated models. The significant advantage of the proposed method is its robustness to model mis-match (e.g. noise and blurring). Experimental results on synthetic images and real images demonstrate that the proposed algorithm is highly accurate and outperforms a selection of image registration approaches.

Image registration is a significant step in a wide range of practical applications and it is a fundamental problem in various computer vision tasks. In this paper, we propose a highly accurate and fast parametric registration method for mobile phone photos. The proposed algorithm is based on a fast and accurate elastic registration algorithm, the Local All-Pass (LAP) algorithm, which performs in a coarse-to-fine manner. At each iteration, the LAP displacement field is fitted by a parametric model. Thus the image registration problem is equivalent to finding a few parameters to describe the displacement field. The fitting step can be performed very efficiently by solving a linear system of equations. In terms of the fitting model, it is easy to change the type of models to do the parametric fitting for specific applications. Experimental results on both synthetic and real images demonstrate the high accuracy and computational efficiency of the proposed algorithm.

Recently, sampling theory has been broadened to include a class of non-bandlimited signals that possess finite rate of innovation (FRI). In this paper, we consider the problem of determining the minimum rate of innovation (RI) in a noisy setting. First, we adapt a recent model-fitting algorithm for FRI recovery and demonstrate that it achieves the Cramér-Rao bounds. Using this algorithm, we then present a framework to estimate the minimum RI based on fitting the sparsest model to the noisy samples whilst satisfying a mean squared error (MSE) criterion - a signal is recovered if the output MSE is less than the input MSE. Specifically, given a RI, we use the MSE criterion to judge whether our model-fitting has been a success or a failure. Using this output, we present a Dichotomic algorithm that performs a binary search for the minimum RI and demonstrate that it obtains a sparser RI estimate than an existing information criterion approach.

Physiological motion, such as cardiac and respiratory motion, during Magnetic Resonance (MR) image acquisition can cause image artifacts. Motion correction techniques have been proposed to compensate for these types of motion during thoracic scans, relying on accurate motion estimation from undersampled motion-resolved reconstruction. A particular interest and challenge lie in the derivation of reliable non-rigid motion fields from the undersampled motion-resolved data. Motion estimation is usually formulated in image space via diffusion, parametric-spline, or optical flow methods. However, image-based registration can be impaired by remaining aliasing artifacts due to the undersampled motion-resolved reconstruction. In this work, we describe a formalism to perform non-rigid registration directly in the sampled Fourier space, i.e. k-space. We propose a deep-learning based approach to perform fast and accurate non-rigid registration from the undersampled k-space data. The basic working principle originates from the Local All-Pass (LAP) technique, a recently introduced optical flow-based registration. The proposed LAPNet is compared against traditional and deep learning image-based registrations and tested on fully-sampled and highly-accelerated (with two undersampling strategies) 3D respiratory motion-resolved MR images in a cohort of 40 patients with suspected liver or lung metastases and 25 healthy subjects. The proposed LAPNet provided consistent and superior performance to image-based approaches throughout different sampling trajectories and acceleration factors.

Respiratory and cardiac motion can cause artifacts in magnetic resonance imaging of the body trunk if patients cannot hold their breath or triggered acquisitions are not practical. Retrospective correction strategies usually cope with motion by fast imaging sequences with integrated motion tracking under free-movement conditions. These acquisitions perform sub-Nyquist sampling and retrospectively bin the data into the respective motion states, yielding subsampled and motion-resolved k-space data. The motion-resolved k-spaces are linked to each other by non-rigid deformation fields. The accurate estimation of such motion is thus an important task in the successful correction of respiratory and cardiac motion. Usually this problem is formulated in image space via diffusion, parametric-spline or optical flow methods. Image-based registration can be however impaired by aliasing artifacts or by estimation from low-resolution images. Subsequently, any motion-corrected reconstruction can be biased by errors in the deformation fields. In this work, we propose a novel deep-learning based motion-corrected 4D (3D spatial + time) image reconstruction which combines a non-rigid registration network and a(3+1)D reconstruction network. Non-rigid motion is estimated directly in k-space based on an optical flow idea and incorporated into the reconstruction network. The proposed method is evaluated on in-vivo 4D motion-resolved magnetic resonance images of patients with suspected liver or lung metastases and healthy subjects.

Respiratory motion can cause artifacts in magnetic resonance imaging of the body trunk if patients cannot hold their breath or triggered acquisitions are not practical. Retrospective correction strategies usually cope with motion by fast imaging sequences under free-movement conditions followed by motion binning based on motion traces. These acquisitions yield sub-Nyquist sampled and motion-resolved k-space data. Motion states are linked to each other by non-rigid deformation fields. Usually, motion registration is formulated in image space which can however be impaired by aliasing artifacts or by estimation from low-resolution images. Subsequently, any motion-corrected reconstruction can be biased by errors in the deformation fields. In this work, we propose a deep-learning based motion-corrected 4D (3D spatial + time) image reconstruction which combines a non-rigid registration network and a 4D reconstruction network. Non-rigid motion is estimated in k-space and incorporated into the reconstruction network. The proposed method is evaluated on in-vivo 4D motion-resolved magnetic resonance images of patients with suspected liver or lung metastases and healthy subjects. The proposed approach provides 4D motion-corrected images and deformation fields. It enables a ∼14× accelerated acquisition with a 25-fold faster reconstruction than comparable approaches under consistent preservation of image quality for changing patients and motion patterns.

Surface electromyography (sEMG) has the potential to provide valuable information regarding the status and health of a muscle. In particular, recent developments in high density sEMG (HD-sEMG), which allow simultaneous recordings from a greater number of electrodes, enable the calculation of muscle attributes such as the conduction velocity of motor unit action potentials. However, as with standard recording montages, HD-sEMG requires careful placement of the electrodes to align with the direction of the muscle fibres, thus limiting practical applications. In this paper we demonstrate an algorithm for calculating muscle fibre conduction velocity which is independent of the alignment of the array. The algorithm automatically corrects for the misalignment of the array whilst estimating the conduction velocity using common local all-pass (CLAP) filters. Specifically, the misalignment is modelled as a rotation of the array relative to the fibre and this rotation is estimated by iteratively fitting the model to the output of the CLAP filters. We validate the proposed algorithm on simulated HD-sEMG data generated from a realistic biological model, demonstrating that the algorithm obtains an accurate estimate of the conduction velocity even when the array is misaligned.