Efficient methods for iterative ultrasound image reconstruction using L1 and L2 norm regularization

Delay-and-sum (DAS) beamformers, when applied to photoacoustic (PA) image reconstruction, produce strong sidelobes due to the absence of transmit focusing. Consequently, DAS PA images are often severely degraded by strong off-axis clutter. For preclinical in vivo cardiac PA imaging, the presence of these noise artifacts hampers the detectability and interpretation of PA signals from the myocardial wall, crucial for studying blood-dominated cardiac pathological information and to complement functional information derived from ultrasound imaging. In this article, we present PA subaperture processing (PSAP), an adaptive beamforming method, to mitigate these image degrading effects. In PSAP, a pair of DAS reconstructed images is formed by splitting the received channel data into two complementary nonoverlapping subapertures. Then, a weighting matrix is derived by analyzing the correlation between subaperture beamformed images and multiplied with the full-aperture DAS PA image to reduce sidelobes and incoherent clutter. We validated PSAP using numerical simulation studies using point target, diffuse inclusion and microvasculature imaging, and in vivo feasibility studies on five healthy murine models. Qualitative and quantitative analysis demonstrate improvements in PAI image quality with PSAP compared to DAS and coherence factor weighted DAS (DAS CF ). PSAP demonstrated improved target detectability with a higher generalized contrast-to-noise (gCNR) ratio in vasculature simulations where PSAP produces 19.61% and 19.53% higher gCNRs than DAS and DAS CF , respectively. Furthermore, PSAP provided higher image contrast quantified using contrast ratio (CR) (e.g., PSAP produces 89.26% and 11.90% higher CR than DAS and DAS CF in vasculature simulations) and improved clutter suppression.

Undoubtedly, photoacoustic tomography (PAT) is a promising technique unveiling physiological information in the biomedical imaging field. However, targeting optically/acoustically non-uniform biological tissues and receiving signals with finite aperture/band-limited ultrasonic transducers have been practical limitations that hinder the clinical application of PAT. This study closely analyzes the effects of four main limiting factors named limited view (LV), limited bandwidth (LB), lossy medium (LM), and heterogeneous medium (HM) and compared the adverse effects given from the four factors. First, radiofrequency (RF) data was generated assuming a realistic situation using k-Wave, a MATLAB-based wave propagation-simulating tool. A single 4 mm-sized circular target was used, and physical parameters of the detector array were designed referring to a commercial linear probe (GE9LD, General Electric). Supposing double-aperture, full-band signal reception from the lossless, homogeneous medium as a baseline, RF data were acquired under a successive accumulation of the limiting factors in order of LV, LB, LM, and HM. Second, the obtained RF datasets were reconstructed with 7 representative beamforming algorithms; delay and sum (DAS), delay multiply and sum, pth root DAS, minimum variance, filtered back-projection, frequency-domain reconstruction, and time reversal. Among obtained images, common graphical features for each limiting factor were specified. Lastly, we quantitatively assessed the similarity between the image and the actual target with peak signal-to-noise ratio and structural similarity as performance indices. As a result, the characteristic features from each limiting factor were commonly identified on the reconstructed image, and the performance indices sequentially degraded following the sequence of practical conditions.

Beamforming is an essential step in the ultrasound image formation pipeline and has recently attracted growing interest. An important goal of beamforming is to increase the image spatial resolution, or in other words to narrow down the system Point Spread Function (PSF). In parallel to beamforming approaches, deconvolution methods have also been explored in ultrasound imaging to mitigate the adverse effects of PSF. Unfortunately, these two steps have only been considered separately in a sequential approach. Herein, a novel framework for unifying beamforming and deconvolution in ultrasound image reconstruction is introduced. More specifically, the proposed formulation is a regularized inverse problem including two linear models for beamforming and deconvolution plus additional sparsity constraint. We take advantage of the alternating direction method of multipliers algorithm to find the solution of the joint optimization problem. The performance evaluation is presented on a set of publicly available simulations, real phantoms, and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in vivo</i> data. As compared to Delay-And-Sum (DAS) beamforming, simulation results indicate improvements of 45% and 44% in terms of axial and lateral resolution, respectively. Moreover, the proposed method improves the contrast of simulation data by 6.7% in comparison to DAS. The superiority of the proposed approach in comparison with the sequential approach as well as the state-of-the-art beamforming and deconvolution approaches is also shown.

Ultrasound images are contaminated with both additive and multiplicative noise, which is modeled by Gaussian and speckle noise respectively. Distinguishing small features such as fallopian tubes in the female genital tract in the noisy environment is problematic. A new method for noise reduction, Wavelet Median Denoising, is presented. Wavelet Median Denoising consists of performing a standard noise reduction technique, median filtering, in the wavelet domain. The new method is tested on 126 images, comprised of 9 original images each with 14 levels of Gaussian or speckle noise. Results for both separable and non-separable wavelets are evaluated, relative to soft-thresholding in the wavelet domain, using the signal-to-noise ratio and subjective assessment. The performance of Wavelet Median Denoising is comparable to that of soft-thresholding. Both methods are more successful in removing Gaussian noise than speckle noise. Wavelet Median Denoising outperforms soft-thresholding for a larger number of cases of speckle noise reduction than of Gaussian noise reduction. Noise reduction is more successful using non-separable wavelets than separable wavelets. When both methods are applied to ultrasound images obtained from a phantom of the female genital tract a small improvement is seen; however, a substantial improvement is required prior to clinical use.

The main inherent property of medical ultrasound imaging is speckle noise which generally obscures and reduces the diagnostic image resolution and contrast. Consequently, the substantial improvement of ultrasound images is an important prerequisite, whenever ultrasound is used as one of the most utilized diagnostic modalities. The problem of reconstruction of ultrasound images by means of blind deconvolution has long been recognized as a prerequisite in ultrasound imaging processing in the recent decades. Recently, the Total Variation (TV) regularization method has become extremely effective approach for image reconstruction, especially for restoring edges of the blurring image. In this paper, we present a new blind iterative TV deconvolution algorithm for reconstructing ultrasound images from blurry and noisy observations. First, it proposes the initial estimation of the point-spread function (PSF) based on a generalization of two-dimensional homomorphic filtering in cepstrum domain. It is demonstrated that the initial PSF can be effectively estimated by applying a proper smoothing low-pass filtering in cepstrum domain. Second, it introduces a novel blind iterative TV deconvolution which is derived from an alternating minimization algorithm. Fast Fourier Transform (FFT) is used in the pre-iteration computation. The innovative blind deconvolution is based on either concurrent or successive estimation of the PSF function and the image of interest. The iterative scheme is devised to recover the image and simultaneously identify the PSF function. The estimated PSF and restored image will be close to real values in the subsequent iterative deconvolution. Final, tests on phantom and clinical images have proven our novel blind iterative TV deconvolution gives more positive results of higher spatial resolution and better defined tissue structures than other deconvolution methods.

The visual quality of ultrasound (US) images is crucial for clinical diagnosis and treatment. The main source of image quality degradation is the inherent speckle noise generated during US image acquisition. Current deep learning-based methods cannot preserve the maximum boundary contrast when removing noise and speckle. In this paper, we address the issue by proposing a novel wavelet-based generative adversarial network (GAN) for real-time high-quality US image reconstruction, viz. WGAN-DUS. First, we propose a batch normalization module (BNM) to balance the importance of each sub-band image and fuse sub-band features simultaneously. Then, a wavelet reconstruction module (WRM) integrated with a cascade of wavelet residual channel attention block (WRCAB) is proposed to extract distinctive sub-band features used to reconstruct denoised images. A gradual tuning strategy is proposed to fine-tune our generator for better despeckling performance. We further propose a wavelet-based discriminator and a comprehensive loss function to effectively suppress speckle noise and preserve the image features. Besides, we have designed an algorithm to estimate the noise levels during despeckling of real US images. The performance of our network was then evaluated on natural, synthetic, simulated and clinical US images and compared against various despeckling methods. To verify the feasibility of WGAN-DUS, we further extend our work to uterine fibroid segmentation with the denoised US image of the proposed approach. Experimental result demonstrates that our proposed method is feasible and can be generalized to clinical applications for despeckling of US images in real-time without losing its fine details.

Medical ultrasound images are usually degraded by a specific type of noise, called speckle. The presence of speckle noise in medical ultrasound images will reduce the image quality and affect the effective information, which can potentially cause a misdiagnosis. Therefore, medical image enhancement processing has been extensively studied and several denoising approaches have been introduced and developed. In the current work, a robust fractional partial differential equation (FPDE) model based on the anomalous diffusion theory is proposed and used for medical ultrasound image enhancement. An efficient computational approach based on a combination of a time integration scheme and localized meshless method in a domain decomposition framework is performed to deal with the model. {In order to evaluate the performance of the proposed de-speckling approach, it is used for speckle noise reduction of a synthetic ultrasound image degraded by different levels of speckle noise. The results indicate the superiority of the proposed approach in comparison with classical anisotropic diffusion denoising model (Catt$acute{e}$'s pde model).}

Compared to traditional focused transmissions, plane wave (PW) ultrasound imaging has the potential to enable higher frame rates, which is clinically relevant to real-time applications and ultrafast imaging. However, when reducing the number of PW transmissions to reduce image formation times, PW imaging is confounded by image quality degradation, acoustic clutter, and speckle noise. To tackle this challenge, we present a deep learning-based method to analyze raw radiofrequency (RF) channel data acquired by the ultrasound probe and convert this signal to the final B-mode image, bypassing the traditional beamforming procedure. The deep learning architecture for this approach relies on a conditional generative adversarial network (cGAN), in which the generative model and classifying model work simultaneously to produce an indistinguishable output from a ground truth. The cGAN was trained to predict B-mode images that look like beamformed PW results after multiple insonifications. This network was trained and tested utilizing a publicly accessible PICMUS database composed of in vivo and ex vivo ultrasound inclusions with randomly distributed scatterers in various combinations. The proposed method produces signal-to-noise ratio (SNR) enhancements from 1.112 to 1.540 when compared with conventional delay-and-sum (DAS) beamforming of a single PW insonification. The cross-correlation coefficient between a 75 PW image and cGAN-predicted data was 0.976, an improvement over the 0.641 obtained when the 75 PW image was cross-correlated with a DAS PW image created after a single insonification. These results demonstrate the potential of generative adversarial networks to substitute traditional DAS beamforming in future applications.

Deep reconstruction of high-quality ultrasound images from raw plane-wave data: A simulation and in vivo study

Independence of Synthetic Aperture Radar (SAR) images from weather and sun illumination helps us in maritime surveillance like an oil spill, to identify the illegal fishery activity and unauthorized marine vessels. Detection of marine vessels is like a point target detection in coarse to moderate resolution images. Detection of point targets is adversely affects by speckle noise. Object detection in SAR images, without explicitly reducing the speckle noise is one of the challenging task. In this paper two algorithms are presented, which show how improvement in the power of point target lead us to reduced number of false alarms. The first algorithm has three parts. First part uses Grave matrix, which is a ( $2\times 2$ ) Hermitian power matrix, generated by the multiplication of Sinclair matrix and conjugate of Sinclair matrix. Second part uses discrimination criteria to discriminate between clutter and vessels based on eigenvalue of the Grave matrix (G). The third part, fill the gaps by using morphological dilation. The only difference between the first and the second algorithms is that, in the second algorithm we uses Sinclair matrix (S2) instead of Grave matrix. Both the algorithms tested on two full-polarization (HH, HV, VH, VV) datasets and the results show the importance of scattering power matrix (G) as compared to scattering matrix (S2) for point target detection. The first data set is of size $498^{\ast}498$ captured by AlOS-1 PALSAR L-band data, covering the coastal region of Singapore. The second data set is of size $472^{\ast}472$ , covering the coast of Vancouver acquired in C-band by Radarsat-2.

Synthetic aperture radar (SAR) images are corrupted by speckle noise due to random interference of electromagnetic waves. In this paper, we proposed a speckle reduction technique based on sparse representation and dictionary learning. Firstly, an adaptive dictionary was learned by performing KSVD algorithm through a large amount of training patches extracted from the noisy SAR image. Considering the inaccurate recovery of point targets which is brought by the inadequate number of training samples, we employed a point target enhancing scheme to highlight the important point targets in the SAR image. Some experiments were conducted on real SAR images, and the results shows that our proposed algorithm can effectively reduce the speckle noise as well as preserve details. Some comparisons are made to prove its superiority to the available algorithms.

We are interested in examining how our model-based beamforming algorithm, referred to as aperture-domain model image reconstruction (ADMIRE), performs on plane wave sequences in conjunction with synthetic aperture beamforming. We also aim to identify the impact of ADMIRE applied before and after synthetic focusing. We employed simulated phantoms using Field II and tissue-mimicking phantoms to evaluate ADMIRE as applied to synthetic sequencing. We generated plane wave images with and without synthetic aperture focusing (SAF) and measured contrast and contrast-to-noise ratio (CNR). For simulated cyst images formed from single plane waves, the contrast for delay-and-sum (DAS) and ADMIRE are 15.64 and 28.34dB, respectively, whereas the CNR are 1.76 and 3.90dB, respectively. We also applied ADMIRE to simulated resolution phantoms having a point target at 3cm depth on-axis. We simulated the point spread functions from data obtained from 1 plane wave and 75 steered plane waves, along with linear scans with 3 and 4cm- focal depths. We then compared the outcome of applying ADMIRE before and after SAF using 3 and 11 steered plane waves. Finally, we applied this to an in vivo carotid artery. Based on the findings in this study, ADMIRE can be adapted to full field insonification sequences to improve image quality in plane wave imaging. Additionally, we investigated how robustly ADMIRE performs in the presence of random noise. We then address identified limitations using a conventional envelope detection method with decluttered signals.

We discuss physical and information theoretical limits of optical 3D metrology. Based on these principal considerations we introduce a novel single-shot 3D movie camera that almost reaches these limits. The camera is designed for the 3D acquisition of macroscopic live scenes. Like a hologram, each movie-frame encompasses the full 3D information about the object surface and the observation perspective can be varied while watching the 3D movie. The camera combines single-shot ability with a point cloud density close to the theoretical limit. No space-bandwidth is wasted by pattern codification. With 1-megapixel sensors, the 3D camera delivers nearly 300,000 independent 3D points within each frame. The 3D data display a lateral resolution and a depth precision only limited by physics. The approach is based on multi-line triangulation. The requisite low-cost technology is simple. Only two properly positioned synchronized cameras solve the profound ambiguity problem omnipresent in 3D metrology.

This paper presents a new semantic sparse recoding method to generate more descriptive and robust representation of visual content for image applications. Although the visual bag-of-words (BOW) representation has been reported to achieve promising results in different image applications, its visual codebook is completely learnt from low-level visual features using quantization techniques and thus the so-called semantic gap remains unbridgeable. To handle such challenging issue, we utilize the annotations (predicted by algorithms or shared by users) of all the images to improve the original visual BOW representation. This is further formulated as a sparse coding problem so that the noise issue induced by the inaccurate quantization of visual features can also be handled to some extent. By developing an efficient sparse coding algorithm, we successfully generate a new visual BOW representation for image applications. Since such sparse coding has actually incorporated the high-level semantic information into the original visual codebook, we thus consider it as semantic sparse recoding of the visual content. Finally, we apply our semantic sparse recoding method to automatic image annotation and social image classification. The experimental results on several benchmark datasets show the promising performance of our semantic sparse recoding method in these two image applications.

Noise-robust semi-supervised learning via fast sparse coding