Real-time microwave imaging of differential temperature for thermal therapy monitoring

A translational review of hyperthermia biology

This review was written to be included in the Special Collection 'Therapy Ultrasound: Medicine's Swiss Army Knife?' The purpose of this review is to provide basic presentation and interpretation of the fundamentals of hyperthermia biology, as it pertains to uses of therapeutic ultrasound. The fundamentals are presented but in the setting of a translational interpretation and a view toward the future. Subjects that require future research and development are highlighted. The effects of hyperthermia are time and temperature dependent. Because intra-tumoral temperatures are non-uniform in tumors, one has to account for differential biologic effects in different parts of a tumor that occur simultaneously during and after hyperthermia.

Real-Time 3D Microwave Medical Imaging With Enhanced Variational Born Iterative Method

In this paper, we present a new variational Born iterative method (VBIM) for real-time microwave imaging (MWI) applications. The S-parameter volume integral equation and waveport vector Green's function are implemented to utilize the measured signal of the MWI system. Meanwhile, the real and imaginary separation (RIS) approach is used at each iterative step to simultaneously reconstruct the dielectric permittivity and conductivity of unknown objects. Compared with the Born iterative method and distorted Born iterative method, VBIM requires less computational time to reach the convergence threshold. The graphics processing unit based acceleration technique is implemented for real-time imaging. To demonstrate the efficiency and accuracy of this VBIM-RIS method, synthetic analysis of a complex multi-layer spherical phantom is first conducted. Then, the algorithm is tested with measured data using our new MWI system prototype. Finally, a synthetic brain-tumor phantom model under a thermal therapy procedure is monitored to exemplify the real-time imaging with about 5 seconds per reconstruction frame.

Fast multi-source nanophotonic simulations using augmented partial factorization

Numerical solutions of Maxwell's equations are indispensable for nanophotonics and electromagnetics but are constrained when it comes to large systems, especially multi-channel ones such as disordered media, aperiodic metasurfaces and densely packed photonic circuits where the many inputs require many large-scale simulations. Conventionally, before extracting the quantities of interest, Maxwell's equations are first solved on every element of a discretization basis set that contains much more information than is typically needed. Furthermore, such simulations are often performed one input at a time, which can be slow and repetitive. Here we propose to bypass the full-basis solutions and directly compute the quantities of interest while also eliminating the repetition over inputs. We do so by augmenting the Maxwell operator with all the input source profiles and all the output projection profiles, followed by a single partial factorization that yields the entire generalized scattering matrix via the Schur complement, with no approximation beyond discretization. This method applies to any linear partial differential equation. Benchmarks show that this approach is 1,000-30,000,000 times faster than existing methods for two-dimensional systems with about 10,000,000 variables. As examples, we demonstrate simulations of entangled photon backscattering from disorder and high-numerical-aperture metalenses that are thousands of wavelengths wide.

Real-Time Detection and 3D Localization of Coronary Atherosclerosis Using a Microwave Imaging Technique: A Simulation Study

Obtaining the exact position of accumulated calcium on the inner walls of coronary arteries is critical for successful angioplasty procedures. For the first time to our knowledge, in this work, we present a high accuracy imaging of the inner coronary artery using microwaves for precise calcium identification. Specifically, a cylindrical catheter radiating microwave signals is designed. The catheter has multiple dipole-like antennas placed around it to enable a 360° field-of-view around the catheter. In addition, to resolve image ambiguity, a metallic rod is inserted along the axis of the plastic catheter. The reconstructed images using data obtained from simulations show successful detection and 3D localization of the accumulated calcium on the inner walls of the coronary artery in the presence of blood flow. Considering the space and shape limitations, and the highly lossy biological tissue environment, the presented imaging approach is promising and offers a potential solution for accurate localization of coronary atherosclerosis during angioplasty or other related procedures.

A Versatile and Shelf-Stable Dielectric Coupling Medium for Microwave Imaging

OBJECTIVE

To develop a new class of emulsions using a protein-based emulsifier as the coupling fluid for microwave imaging systems.

METHODS

In this paper, we provide a theoretical basis for engineering shelf-stable dielectric fluids, a step-by-step formulation method, and measurements of complex dielectric properties in the frequency range of 0.5-3 GHz, which can be applicable for many of the recent microwave imaging systems.

RESULTS

This medium was primarily designed for long-term stability while providing a controllable range of complex dielectric permittivities given different fractions of its constituents. Consequently, this emulsion shows dielectric stability in open air throughout a 7-day experiment and temperature insensitivity over the range of 0 to 60 Celsius degree.

CONCLUSIONS

This control over dielectric permittivity enables formulations that tune the background-to-target contrast to the linearizable regime of iterative inverse scattering algorithms. Accordingly, the emulsion conductivity can also be controlled and reduced to maintain the required signal-to-noise ratio within the dynamic range of the imaging system. The new formulation overcomes the practical challenges of engineering coupling fluids for microwave imaging systems, e.g., temporal stability, non-toxic, low sensitivity to temperature variation, and easy formulation from readily available and inexpensive materials.

SIGNIFICANCE

The achieved properties associated with this new fluid are of particular benefit to microwave imaging systems used in thermal therapy monitoring.

Quantitative Interpretation of UWB Radar Images for Non-Invasive Tissue Temperature Estimation during Hyperthermia

The knowledge of temperature distribution inside the tissue to be treated is essential for patient safety, workflow and clinical outcomes of thermal therapies. Microwave imaging represents a promising approach for non-invasive tissue temperature monitoring during hyperthermia treatment. In the present paper, a methodology for quantitative non-invasive tissue temperature estimation based on ultra-wideband (UWB) radar imaging in the microwave frequency range is described. The capabilities of the proposed method are demonstrated by experiments with liquid phantoms and three-dimensional (3D) Delay-and-Sum beamforming algorithms. The results of our investigation show that the methodology can be applied for detection and estimation of the temperature induced dielectric properties change.

A feasibility study on microwave imaging of bone for osteoporosis monitoring

The dielectric properties of bones are found to be influenced by the demineralisation of bones. Therefore, microwave imaging (MWI) can be used to monitor in vivo dielectric properties of human bones and hence aid in the monitoring of osteoporosis. This paper presents the feasibility analysis of the MWI device for monitoring osteoporosis. Firstly, the dielectric properties of tissues present in the human heel are analysed. Secondly, a transmission line (TL) formalism approach is adopted to examine the feasible frequency band and the matching medium for MWI of trabecular bone. Finally, simplified numerical modelling of the human heel was set to monitor the penetration of E-field, the received signal strength, and the power loss in a numerical model of the human heel. Based on the TL formalism approach, 0.6-1.9-GHz frequency band is found to feasible for bone imaging purpose. The relative permittivity of the matching medium can be chosen between 15 and 40. The average percentage difference between the received signal for feasible and inconvenient frequency band was found to be 82%. The findings based on the dielectric contrast of tissues in the heel, the feasible frequency band, and the finite difference time domain simulations support the development of an MWI prototype for monitoring osteoporosis.

A Novel Approach on Microwave Hyperthermia

Microwave hyperthermia (MH) requires the selective focusing of microwave energy on the targeted region while minimally affecting the healthy tissue. Emerging from the simple nature of the linear antenna arrays, this work demonstrates focusing maps as an application guide for MH focusing by adjusting the antenna phase values. The focusing of the heating potential (HP) on different density breast models is performed via the proposed method using Vivaldi antennas. The effect of the tumor conductivity on the focusing is discussed. As a straightforward approach and utilizing the Vivaldi antennas, the system can be further combined with MH monitoring application.

Expansion of the Nodal-Adjoint Method for Simple and Efficient Computation of the 2D Tomographic Imaging Jacobian Matrix

This paper focuses on the construction of the Jacobian matrix required in tomographic reconstruction algorithms. In microwave tomography, computing the forward solutions during the iterative reconstruction process impacts the accuracy and computational efficiency. Towards this end, we have applied the discrete dipole approximation for the forward solutions with significant time savings. However, while we have discovered that the imaging problem configuration can dramatically impact the computation time required for the forward solver, it can be equally beneficial in constructing the Jacobian matrix calculated in iterative image reconstruction algorithms. Key to this implementation, we propose to use the same simulation grid for both the forward and imaging domain discretizations for the discrete dipole approximation solutions and report in detail the theoretical aspects for this localization. In this way, the computational cost of the nodal adjoint method decreases by several orders of magnitude. Our investigations show that this expansion is a significant enhancement compared to previous implementations and results in a rapid calculation of the Jacobian matrix with a high level of accuracy. The discrete dipole approximation and the newly efficient Jacobian matrices are effectively implemented to produce quantitative images of the simplified breast phantom from the microwave imaging system.

Detection and estimating the blood accumulation volume of brain hemorrhage in a human anatomical skull using a RF single coil

OBJECTIVE

An experimental study for testing a simple robust algorithm on data derived from an electromagnetic radiation device that can detect small changes in the tissue/fluid ratio in a realistic head configuration.

METHODS

Changes in the scattering parameters (S21) of an inductive coil resulting from injections of chicken blood in the 0-18 ml range into calf brain tissue in a human anatomical skull were measured over a 100-1,000 MHz frequency range.

RESULTS

An algorithm that combines amplitude and phase results was found to detect changes in the tissue/fluid ratio with 90% accuracy. An algorithm that estimated the injected blood volume was found to have a 1-4 ml average error. This demonstrates the possibility of the inductive coil-based device to possess a practical ability to detect a change in the tissue/fluid ratio in the head.

SIGNIFICANCE

This study is an important step towards the goal of building an inexpensive and safe device that can detect an early brain hemorrhagic stroke.

Low Cost, High Performance, 16-Channel Microwave Measurement System for Tomographic Applications

We have developed a multichannel software defined radio-based transceiver measurement system for use in general microwave tomographic applications. The unit is compact enough to fit conveniently underneath the current illumination tank of the Dartmouth microwave breast imaging system. The system includes 16 channels that can both transmit and receive and it operates from 500 MHz to 2.5 GHz while measuring signals down to −140 dBm. As is the case with multichannel systems, cross-channel leakage is an important specification and must be lower than the noise floors for each receiver. This design exploits the isolation inherent when the individual receivers for each channel are physically separate; however, these challenging specifications require more involved signal isolation techniques at both the system design level and the individual, shielded component level. We describe the isolation design techniques for the critical system elements and demonstrate specification compliance at both the component and system level.

Localization of Small Anomalies via the Orthogonality Sampling Method from Scattering Parameters

We investigate the application of the orthogonality sampling method (OSM) in microwave imaging for a fast localization of small anomalies from measured scattering parameters. For this purpose, we design an indicator function of OSM defined on a Lebesgue space to test the orthogonality relation between the Hankel function and the scattering parameters. This is based on an application of the Born approximation and the integral equation formula for scattering parameters in the presence of a small anomaly. We then prove that the indicator function consists of a combination of an infinite series of Bessel functions of integer order, an antenna configuration, and material properties. Simulation results with synthetic data are presented to show the feasibility and limitations of designed OSM.

Imaging-based internal body temperature measurements: The journal Temperature toolbox

Noninvasive imaging methods of internal body temperature are in high demand in both clinical medicine and physiological research. Thermography and thermometry can be used to assess tissue temperature during thermal therapies: ablative and hyperthermia treatments to ensure adequate temperature rise in target tissues but also to avoid collateral damage by heating healthy tissues. In research use, measurement of internal body temperature enables us the production of thermal maps on muscles, internal organs, and other tissues of interest. The most used methods for noninvasive imaging of internal body temperature are based on different parameters acquired with magnetic resonance imaging, ultrasound, computed tomography, microwave radiometry, photoacoustic imaging, and near-infrared spectroscopy. In the current review, we examine the aforementioned imaging methods, their use in estimating internal body temperature in vivo with their advantages and disadvantages, and the physical phenomena the thermography or thermometry modalities are based on.

Advances in Microwave Near-Field Imaging: Prototypes, Systems, and Applications

Microwave imaging employs detection techniques to evaluate hidden or embedded objects in a structure or media using electro-magnetic (EM) waves in the microwave range, 300 MHz-300 GHz. Microwave imaging is often associated with radar detection such as target location and tracking, weather-pattern recognition, and underground surveillance, which are far-field applications. In recent years, due to microwaves' ability to penetrate optically opaque media, short-range applications, including medical imaging, nondestructive testing (NDT) and quality evaluation, through-the-wall imaging, and security screening, have been developed. Microwave near-field imaging most often occurs when detecting the profile of an object within the short range (when the distance from the sensor to the object is less than one wavelength to several wave-lengths) and depends on the electrical size of the antenna(s) and target.

A Novel Method to Mitigate Real-Imaginary Image Imbalance in Microwave Tomography

Typical microwave tomographic techniques reconstruct the real part of the permittivity with much greater accuracy as compared to the imaginary part. In this paper, we propose a method to mitigate the imbalance between the reconstructed complex permittivity components and increase the accuracy of the overall image recovery. To do so, the complex permittivity in the imaging domain is expressed as a weighted sum of a few preselected permittivities, close to the range of the expected values. To obtain the permittivity weights, a Gauss-Newton algorithm is employed. Image reconstructions from simulated and experimental data for different biomedical phantoms are presented. Results show that the proposed method leads to excellent reconstruction with balanced real and imaginary parts, across different scenarios.

Multifrequency Analysis of Single Inductive Coil Measurements Across a Gel Phantom Simulation of Internal Bleeding in the Brain

The present study is part of an ongoing effort to develop a simple diagnostic technology for detecting internal bleeding in the brain, which can be used in lieu or in support of medical imaging and thereby reduce the cost of diagnostics in general, and in particular, would make diagnostics accessible to economically disadvantaged populations. The study deals with a single coil inductive device to be used for detecting cerebral hemorrhage. It presents a first-order experimental study that examines the predictions of our recently published theoretical study. The experimental model employs a homogeneous cylindrical phantom in which internal head bleeding was simulated by way of a fluid inclusion. We measured the changes in amplitude and phase across the coil with a network vector analyzer as a function of frequency (100-1,000 MHz), volume of blood simulating fluid, and the site of the fluid injection. We have developed a new mathematical model to statistically analyze the complex data produced in this experiment. We determined that the resolution for the fluid volume increase following fluid injection is strongly dependent on frequency as well as the location of liquid accumulation. The experimental data obtained in this study supports the predictions of our previous theoretical study, and the statistical analysis shows that the simple single coil device is sensitive enough to detect changes due to fluid volume alteration of two milliliters. Bioelectromagnetics. 2020;41:21-33 © 2019 Bioelectromagnetics Society.

Preliminary Investigations for Non-invasive Temperature Change Detection in Thermotherapy by Means of UWB Microwave Radar

Non-invasive differential temperature monitoring by means of ultra-wideband sensing is a promising approach concerning temperature controlling during thermotherapy. In this paper the principal of temperature difference detection by UWB radar is explained and appropriate phantom measurements are discussed. In a first step, temperature dependent dielectric properties of the phantom materials (sunflower oil and distilled water) are analyzed. Subsequently, temperature dependent phantom measurements are conducted where the temperature dependent signal changes of the received UWB signals are investigated. Results show a linear behavior between the received differential radar signals and the temperature differences of the target in the considered temperature range. Furthermore, investigations show that temperature changes of the target, which are common in thermal therapy (e.g., hyperthermia), are detectable by means of UWB radar.

Kirchhoff Migration for Identifying Unknown Targets Surrounded by Random Scatterers

In this paper, we take into account a two-dimensional inverse scattering problem for localizing small electromagnetic anomalies when they are surrounded by small, randomly distributed electromagnetic scatterers. Generally, subspace migration is considered to be an improved version of Kirchhoff migration; however, for the problem considered here, simulation results have confirmed that Kirchhoff migration is better than subspace migration, though the reasons for this have not been investigated theoretically. In order to explain theoretical reason, we explored that the imaging function of Kirchhoff migration can be expressed by the size, permittivity, permeability of anomalies and random scatterers, and the Bessel function of the first kind of order zero and one. Considered approach is based on the fact that the far-field pattern can be represented using an asymptotic expansion formula in the presence of such anomalies and random scatterers. We also present results of numerical simulations to validate the discovered imaging function structures.

Design of Cavity-Backed Bow-Tie Antenna with Matching Layer for Human Body Application

This paper presents the broadband antenna for the microwave radiometric sensing of internal body temperature. For broadband operation, the bow-tie antenna was designed and backed with a cylindrical cavity, which decreased environmental electromagnetic interference and also improved the directivity of the antenna. The broadband impedance-transforming balun in microstrip form was also designed to feed the bow-tie antenna, and was located inside the cavity. An impedance-matching dielectric layer (IMDL) was introduced on top of the bow-tie antenna, for impedance match with the human body with high permittivity. The fabricated antenna was measured in free space with the IMDL removed, showing an input reflection coefficient lower than -10 dB from 2.64 to > 3.60 GHz with antenna gain over 6.0 dBi and radiation efficiency over 74.7% from 2.7 to 3.5 GHz. The IMDL was re-installed on the cavity-backed bow-tie antenna to measure the antenna performance for the human head with relative permittivity of about 40. The measured reflection coefficient was as low as -28.9 dB at 2.95 GHz and lower than -10 dB from 2.65 to > 3.5 GHz. It was also shown that the designed antenna recovered a good impedance match by adjusting the permittivity and thickness of the IMDL for the different parts of the human body with different permittivities.

Ultra-Wideband Temperature Dependent Dielectric Spectroscopy of Porcine Tissue and Blood in the Microwave Frequency Range

The knowledge of frequency and temperature dependent dielectric properties of tissue is essential to develop ultra-wideband diagnostic technologies, such as a non-invasive temperature monitoring system during hyperthermia treatment. To this end, we characterized the dielectric properties of animal liver, muscle, fat and blood in the microwave frequency range from 0.5 GHz to 7 GHz and in the temperature range between 30 °C and 50 °C. The measured data were modeled to a two-pole Cole-Cole model and a second-order polynomial was introduced to fit the Cole-Cole parameters as a function of temperature. The parametric model provides access to the dielectric properties of tissue at any frequency and temperature in the specified range.

A 4-channel, vector network analyzer microwave imaging prototype based on software defined radio technology

We have implemented a prototype 4-channel transmission-based, microwave measurement system built on innovative software defined radio (SDR) technology. The system utilizes the B210 USRP SDR developed by Ettus Research that operates over a 70 MHz-6 GHz bandwidth. While B210 units are capable of being synchronized with each other via coherent reference signals, they are somewhat unreliable in this configuration and the manufacturer recommends using N200 or N210 models instead. For our system, N-series SDRs were less suitable because they are not amenable to RF shielding required for the cross-channel isolation necessary for an integrated microwave imaging system. Consequently, we have configured an external reference that overcame these limitations in a compact and robust package. Our design exploits the rapidly evolving technology being developed for the telecommunications environment for test and measurement tasks with the higher performance specifications required in medical microwave imaging applications. In a larger channel configuration, the approach is expected to provide performance comparable to commercial vector network analyzers at a fraction of the cost and in a more compact footprint.

Full-Vectorial 3D Microwave Imaging of Sparse Scatterers through a Multi-Task Bayesian Compressive Sensing Approach

In this paper, the full-vectorial three-dimensional (3D) microwave imaging (MI) of sparse scatterers is dealt with. Towards this end, the inverse scattering (IS) problem is formulated within the contrast source inversion (CSI) framework and it is aimed at retrieving the sparsest and most probable distribution of the contrast source within the imaged volume. A customized multi-task Bayesian compressive sensing (MT-BCS) method is used to yield regularized solutions of the 3D-IS problem with a remarkable computational efficiency. Selected numerical results on representative benchmarks are presented and discussed to assess the effectiveness and the reliability of the proposed MT-BCS strategy in comparison with other competitive state-of-the-art approaches, as well.

Differential Ultra-Wideband Microwave Imaging: Principle Application Challenges

Wideband microwave imaging is of interest wherever optical opaque scenarios need to be analyzed, as these waves can penetrate biological tissues, many building materials, or industrial materials. One of the challenges of microwave imaging is the computation of the image from the measurement data because of the need to solve extensive inverse scattering problems due to the sometimes complicated wave propagation. The inversion problem simplifies if only spatially limited objects—point objects, in the simplest case—with temporally variable scattering properties are of interest. Differential imaging uses this time variance by observing the scenario under test over a certain time interval. Such problems exist in medical diagnostics, in the search for surviving earthquake victims, monitoring of the vitality of persons, detection of wood pests, control of industrial processes, and much more. This paper gives an overview of imaging methods for point-like targets and discusses the impact of target variations onto the radar data. Because the target variations are very weak in many applications, a major issue of differential imaging concerns the suppression of random effects by appropriate data processing and concepts of radar hardware. The paper introduces related methods and approaches, and some applications illustrate their performance.

Review of breast screening: Toward clinical realization of microwave imaging

Microwave imaging (MI) technology has come a long way to introduce a noninvasive, inexpensive, fast, convenient, and safe screening tool for clinical breast monitoring. However, there is a niche between the existing understanding of MI by engineers versus clinicians. Our manuscript targets that niche and highlights the state of the art in MI technology compared to the existing breast cancer detection modalities (mammography, ultrasound, molecular imaging, and magnetic resonance). The significance of our review article is in consolidation of up-to-date breast clinician views with the practical needs and engineering challenges of a novel breast screening modality. We summarize breast tissue abnormalities and highlight the benefits as well as potential drawbacks of the MI as a cancer detection methodology. Our goal is to present an article that MI researchers as well as practitioners in the field can use to assess the viability of the MI technology as a competing or complementary modality to the existing means of breast cancer screening.

Laser Ablation for Cancer: Past, Present and Future

Laser ablation (LA) is gaining acceptance for the treatment of tumors as an alternative to surgical resection. This paper reviews the use of lasers for ablative and surgical applications. Also reviewed are solutions aimed at improving LA outcomes: hyperthermal treatment planning tools and thermometric techniques during LA, used to guide the surgeon in the choice and adjustment of the optimal laser settings, and the potential use of nanoparticles to allow biologic selectivity of ablative treatments. Promising technical solutions and a better knowledge of laser-tissue interaction should allow LA to be used in a safe and effective manner as a cancer treatment.

Two-step inversion with a logarithmic transformation for microwave breast imaging

PURPOSE

The authors have developed a new two-step microwave tomographic image reconstruction process specifically designed to incorporate logarithmic transformed microwave imaging algorithms as a means of significantly improving spatial resolution and target property recovery. Log transform eliminates the need for a priori information, but spatial filtering often integrated as part of the regularization required to stabilize image recovery, generally smooths image features and reduces object definition. The new implementation begins with this smoothed image as the first step, but then utilizes it as the starting estimate for a second step which continues the iterative process with a standard weighted Euclidean distance regularization. The penalty term of the latter restricts the new image to a multi-dimensional location close to the original but allows the algorithm to optimize the image without excessive smoothing.

METHODS

The overall approach is based on a Gauss-Newton iterative scheme which incorporates a log transformation as a way of making the reconstruction more linear. It has been shown to be robust and not require a priori information as a condition for convergence, but does produce somewhat smoothed images as a result of associated regularization. The new two-step process utilizes the previous technique to generate a smoothed initial estimate and then uses the same reconstruction process with a weighted Euclidean distance penalty term. A simple and repeatable method has been implemented to determine the weighting factor without significant computational burden. The reconstructions are assessed according to conventional parameter estimation metrics.

RESULTS

We apply the approach to phantom experiments using large, high contrast canonical shapes followed by a set of images recovered from an actual patient exam. The image improvements are substantial in regards to improved property recovery and feature delineation without inducing unwanted artifacts. Analysis of the residual vector after the reconstruction process further emphasizes that the minimization criterion is efficient with minimal biases.

CONCLUSIONS

The outcome is a novel synergism of an established stable reconstruction algorithm with a conventional regularization technique. It maintains the ability to recover high quality microwave tomographic images without the bias of a priori information while substantially improving image quality. The results are confirmed on both phantom experiments and patient exams.

Real-Time Three-Dimensional Microwave Monitoring of Interstitial Thermal Therapy

We report a method for real-time three-dimensional monitoring of thermal therapy through the use of noncontact microwave imaging. This method is predicated on using microwaves to image changes in the dielectric properties of tissue with changing temperature. Instead of the precomputed linear Born approximation that was used in prior work to speed up the frame-to-frame inversions, here we use the nonlinear distorted Born iterative method (DBIM) to solve the electric volume integral equation (VIE) to image the temperature change. This is made possible by using a recently developed graphic processing unit accelerated conformal finite difference time domain method to solve the forward problem and update the electric field in the monitored region in each DBIM iteration. Compared to our previous work, this approach provides a far superior approximation of the electric field within the VIE, and thus yields a more accurate reconstruction of tissue temperature change. The proposed method is validated using a realistic numerical model of interstitial thermal therapy for a deep-seated brain lesion. With the new DBIM, we reduced the average estimation error of the mean temperature within the region of interest from 2.5 to 1.0 for the noise-free case, and from 2.9 to 1.7 for the 2% background noise case.