Learned SVD: solving inverse problems via hybrid autoencoding

Our world is full of physics-driven data where effective mappings between data manifolds are desired. There is an increasing demand for understanding combined model-based and data-driven methods. We propose a nonlinear, learned singular value decomposition (L-SVD), which combines autoencoders that simultaneously learn and connect latent codes for desired signals and given measurements. We provide a convergence analysis for a specifically structured L-SVD that acts as a regularisation method. In a more general setting, we investigate the topic of model reduction via data dimensionality reduction to obtain a regularised inversion. We present a promising direction for solving inverse problems in cases where the underlying physics are not fully understood or have very complex behaviour. We show that the building blocks of learned inversion maps can be obtained automatically, with improved performance upon classical methods and better interpretability than black-box methods

A Partially Learned Algorithm for Joint Photoacoustic Reconstruction and Segmentation

In an inhomogeneously illuminated photoacoustic image, important information like vascular geometry is not readily available when only the initial pressure is reconstructed. To obtain the desired information, algorithms for image segmentation are often applied as a post-processing step. In this work, we propose to jointly acquire the photoacoustic reconstruction and segmentation, by modifying a recently developed partially learned algorithm based on a convolutional neural network. We investigate the stability of the algorithm against changes in initial pressures and photoacoustic system settings. These insights are used to develop an algorithm that is robust to input and system settings. Our approach can easily be applied to other imaging modalities and can be modified to perform other high-level tasks different from segmentation. The method is validated on challenging synthetic and experimental photoacoustic tomography data in limited angle and limited view scenarios. It is computationally less expensive than classical iterative methods and enables higher quality reconstructions and segmentations than state-of-the-art learned and non-learned methods.Comment: "copyright 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

A Framework for Directional and Higher-Order Reconstruction in Photoacoustic Tomography

Photoacoustic tomography is a hybrid imaging technique that combines high optical tissue contrast with high ultrasound resolution. Direct reconstruction methods such as filtered backprojection, time reversal and least squares suffer from curved line artefacts and blurring, especially in case of limited angles or strong noise. In recent years, there has been great interest in regularised iterative methods. These methods employ prior knowledge on the image to provide higher quality reconstructions. However, easy comparisons between regularisers and their properties are limited, since many tomography implementations heavily rely on the specific regulariser chosen. To overcome this bottleneck, we present a modular reconstruction framework for photoacoustic tomography. It enables easy comparisons between regularisers with different properties, e.g. nonlinear, higher-order or directional. We solve the underlying minimisation problem with an efficient first-order primal-dual algorithm. Convergence rates are optimised by choosing an operator dependent preconditioning strategy. Our reconstruction methods are tested on challenging 2D synthetic and experimental data sets. They outperform direct reconstruction approaches for strong noise levels and limited angle measurements, offering immediate benefits in terms of acquisition time and quality. This work provides a basic platform for the investigation of future advanced regularisation methods in photoacoustic tomography.Comment: submitted to "Physics in Medicine and Biology". Changes from v1 to v2: regularisation with directional wavelet has been added; new experimental tests have been include

A Partially-Learned Algorithm for Joint Photo-acoustic Reconstruction and Segmentation

In an inhomogeneously illuminated photoacoustic image, important information like vascular geometry is not readily available, when only the initial pressure is reconstructed. To obtain the desired information, algorithms for image segmentation are often applied as a post-processing step. In this article, we propose to jointly acquire the photoacoustic reconstruction and segmentation, by modifying a recently developed partially learned algorithm based on a convolutional neural network. We investigate the stability of the algorithm against changes in initial pressures and photoacoustic system settings. These insights are used to develop an algorithm that is robust to input and system settings. Our approach can easily be applied to other imaging modalities and can be modified to perform other high-level tasks different from segmentation. The method is validated on challenging synthetic and experimental photoacoustic tomography data in limited angle and limited view scenarios. It is computationally less expensive than classical iterative methods and enables higher quality reconstructions and segmentations than the state-of-the-art learned and non-learned methods

Sensitivity of a partially learned model‐based reconstruction algorithm

We replace part of a model-based iterative algorithm with a convolutional neural network in order to improve the quality of tomography reconstructions. We analyse its robustness against uncertainties in the image and uncertainties in system settings. Results are presented for the application of photoacoustic tomography in a limited angle setup

Robustness of a partially learned photoacoustic reconstruction algorithm

Classical non-learned algorithms for photoacoustic tomography (PAT) reconstructions are mathematically proven to converge, but they can be very slow and inadequate with respect to model and data assumptions. Recently, learned neural networks have shown to surpass the reconstruction quality of non-learned algorithms, but since analysis is challenging, convergence and stability are not guaranteed. To bridge this gap, we investigate the stability of algorithms in which we combine the structure of model-based algorithms with the efficiency of data-driven neural networks. In the last decade, primal-dual algorithms have become popular due to their ability to employ non-smooth regularisation, which is used to overcome the limited sampling problem in photoacoustic tomography. The algorithm performs updates in both the image domain (primal) and the data domain (dual). These are connected by the photoacoustic operator, which modelling is based on the laws of physics and system settings. In our approach, we replace the updates with shallow neural networks, while maintaining the primal-dual structure and the information from the photoacoustic operator. This greatly improves reconstruction quality, especially in cases of strong noise and limited sampling. This has the additional benefit that a hand-crafted regularisation does not have to be chosen, but is learned in a data-driven manner. We show its robustness in simulation and experiment against uncertainty and changes in PAT system settings. This includes the number, placement and calibration of detectors, but also changes in the tissue type that is imaged. The method is stable, computationally efficient and applicable to a generic photoacoustic system with universal applications

Handheld versus mounted laser speckle contrast perfusion imaging demonstrated in psoriasis lesions

Enabling handheld perfusion imaging would drastically improve the feasibility of perfusion imaging in clinical practice. Therefore, we examine the performance of handheld laser speckle contrast imaging (LSCI) measurements compared to mounted measurements, demonstrated in psoriatic skin. A pipeline is introduced to process, analyze and compare data of 11 measurement pairs (mounted-handheld LSCI modes) operated on 5 patients and various skin locations. The on-surface speeds (i.e. speed of light beam movements on the surface) are quantified employing mean separation (MS) segmentation and enhanced correlation coefficient maximization (ECC). The average on-surface speeds are found to be 8.5 times greater in handheld mode compared to mounted mode. Frame alignment sharpens temporally averaged perfusion maps, especially in the handheld case. The results show that after proper post-processing, the handheld measurements are in agreement with the corresponding mounted measurements on a visual basis. The absolute movement-induced difference between mounted-handheld pairs after the background correction is 16.4±9.3% (mean ± std, n= 11), with an absolute median difference of 23.8 %. Realization of handheld LSCI facilitates measurements on a wide range of skin areas bringing more convenience for both patients and medical staff

Tomographic imaging with an ultrasound and LED-based photoacoustic system

Pulsed lasers in photoacoustic tomography systems are expensive, which limit their use to a few clinics and small animal labs. We present a method to realize tomographic ultrasound and photoacoustic imaging using a commercial LED-based photoacoustic and ultrasound system. We present two illumination configurations using LED array units and an optimal number of angular views for tomographic reconstruction. The proposed method can be a cost-effective solution for applications demanding tomographic imaging and can be easily integrated into conventional linear array-based ultrasound systems. We present a potential application for finger joint imaging in vivo, which can be used for point-of-care rheumatoid arthritis diagnosis and monitoring