Measuring a detection sensitivity metric for non-shift invariant computational imaging systems (Conference Presentation)

The analysis tools of traditional optical systems, such as modulation transfer functions, point spread functions, resolution test charts etc. are often not sufficient when analyzing computational imaging systems. Computational imaging systems benefit from the combined use of optics and electronics for accomplishing a given imaging or system task. In traditional optical systems the goal is essentially to form images that precisely depict a given object. Electronics are not required to form clear images, but could be required to analyze the images. In computational imaging systems specialized images are formed by generalized aspheric optical elements that are jointly optimized with the electronic processing. The specialized images formed at a detector are not necessarily clear images. Electronic processing is used to remove the image blur or otherwise form a final image. Computational imaging systems offer the advantage of increased performance and decreased size, weight, and cost over traditional optical systems. The Ambiguity Function (AF), traditionally used for the design of radar waveforms, plays an important role in computational imaging systems. The AF provides a concise analysis of the optical transfer functions of imaging systems over defocus. The Wigner Distribution (WD), traditionally used for the design of time-varying systems, is related to the AF and provides a concise analysis of the point spread functions (PSF) of imaging systems over defocus. We will describe the relationships and utility of these functions to computational imaging systems.

Computational imaging is a proven strategy for obtaining high-quality images with fast acquisition rates and simpler hardware. Metasurfaces provide exquisite control over electromagnetic fields, enabling the radiated field to be molded into unique patterns. The fusion of these two concepts can bring about revolutionary advances in the design of imaging systems for security screening. In the context of computational imaging, each field pattern serves as a single measurement of a scene; imaging a scene can then be interpreted as estimating the reflectivity distribution of a target from a set of measurements. As with any computational imaging system, the key challenge is to arrive at a minimal set of measurements from which a diffraction-limited image can be resolved. Here, we show that the information content of a frequency-diverse metasurface aperture can be maximized by design, and used to construct a complete millimeter-wave imaging system spanning a 2 m by 2 m area, consisting of 96 metasurfaces, capable of producing diffraction-limited images of human-scale targets. The metasurfacebased frequency-diverse system presented in this work represents an inexpensive, but tremendously flexible alternative to traditional hardware paradigms, offering the possibility of low-cost, real-time, and ubiquitous screening platforms.

The main goals of research in medical and biomedical imaging are to create €œbetter€ imaging systems, more accurate reconstructions, and develop methods of image processing that utilize the most important information present in an image or set of images, for accurate, timely, and cost-effective diagnosis and treatment of disease. How well desired information can be extracted best serves to define image quality and consequently the performance of imaging systems. Furthermore, as we deepen our understanding of medical images, new systems and new methods of image processing and image display may help optimize performance and assist radiologists in their challenge for accurate diagnostics. Image quality is thus best measured by the performance of an observer on specific tasks [1]. The observer may be human such as a physician making a diagnosis, or a mathematical model such as an ideal observer [2], or a computer algorithm. Specific tasks may be the detection of a lesion in a chest x ray [3], the estimation of the percent stenosis of a detected aneurysm [4], or the registration of images such as the superimposition of anatomical atlases on patient data [5]. Regardless of the task considered, however, methods to assess image quality based on task performance are most important. Traditionally, the conception of improved imaging systems in medical imaging has been accomplished by designing and constructing proposed systems and characterizing them from an engineering point of view, by reporting parameters such as resolution, modulation transfer function, and pixel signal-to-noise ratio. Naturally, such evaluation is not sufficient to predict the performance that the system will have in the clinic, given that it does not take into account either information about the types of objects being imaged or the tasks being carried out. To fully assess the system, clinical trials based on specific tasks must be conducted. While clinical trials are required for final system assessment, the reliance on clinical trials for system design and optimization has severe limitations. First, the construction of proposed systems is costly and time consuming. In addition, if the system requires further optimization, it may take multiple trials and errors to find the best set of parameters and tradeoff to satisfy required task-based image-quality criteria. Finally, it is nearly impossible to know the anatomical underlying structures of the acquired clinical images unless the diagnosis is verified by physical examination. Instead, disease states are most often estimated by interpreting the images and looking for correlation with previous cases established statistically as well. The approach of building systems and conducting trial-and-error changes based on clinical images thus constitutes a highly impractical means of optimizing imaging systems.

Origami is the art of paper folding that allows a single flat piece of paper to assume different 3D shapes depending on the fold patterns and the sequence of folding. Using the principles of origami along with computation imaging technique the authors demonstrate a versatile shape‐morphing microwave imaging array with reconfigurable field‐of‐view and scene‐adaptive imaging capability. Microwave/millimeter‐wave based array imaging systems are expected to be the workhorse for sensory perception of future autonomous intelligent systems. The imaging capability of a planar array‐based systems operating in complex scattering conditions have limited field‐of‐view and lack the ability to adaptively reconfigure resolution. To overcome this, here, deviations from planarity and isometry are allowed, and a shape‐morphing computational imaging system is demonstrated. Implemented on a reconfigurable Waterbomb origami surface with 22 active metasurface panels that radiate near‐orthogonal modes across 17–27 GHz, capability to image complex 3D objects in full details minimizing the effects of specular reflections in diffraction‐limited sparse imaging with scene adaptability, reconfigurable cross‐range resolution, and field‐of‐view is demonstrated. Such electromagnetic origami surfaces, through simultaneous surface shape‐morphing ability (potentially with shape‐shifting electronic materials) and electromagnetic field programmability, opens up new avenues for intelligent and robust sensing and imaging systems for a wide range of applications.

Wavefront coding technique can extend the depth of filed (DOF) of the incoherent imaging system. Several rectangular separable phase masks (such as cubic type, exponential type, logarithmic type, sinusoidal type, rational type, et al) have been proposed and discussed, because they can extend the DOF up to ten times of the DOF of ordinary imaging system. But according to the research on them, researchers have pointed out that the images are damaged by the artifacts, which usually come from the non-linear phase transfer function (PTF) differences between the PTF used in the image restoration filter and the PTF related to real imaging condition. In order to alleviate the image artifacts in imaging systems with wavefront coding, an optimization model based on the PTF was proposed to make the PTF invariance with the defocus. Thereafter, an image restoration filter based on the average PTF in the designed depth of field was introduced along with the PTF-based optimization. The combination of the optimization and the image restoration proposed can alleviate the artifacts, which was confirmed by the imaging simulation of spoke target. The cubic phase mask (CPM) and exponential phase mask (EPM) were discussed as example.

One practical way to characterize the spatial performance of an in-flight satellite optical imaging system is to determine the modulation transfer function (MTF) from its remotely sensed images on the ground. Currently, there are many MTF measurement techniques designed to provide accurate measurements for high-resolution imaging systems. However, these existing techniques usually rely on the presence and manual identification of a well-separated characteristics target. We introduce an insight to effectively estimate a degradation function based on the MTF by analyzing the nonlocal self-similarity characteristics, namely the structural component, in the observed image. To this end, this paper presents several strategies to realize the aim of this work. First, we propose a segmentation method to select the ideal candidates for MTF estimation. Second, we develop an adaptive structure selection method that removes detrimental structures and selects useful information for point spread function (PSF) estimation. Finally, we put forward a robust estimation method by introducing a spatial prior that is able to simultaneously suppress noises while preserving the sparsity and continuity of the PSF kernels. For the experiments, datasets used in the analyses are synthetically blurred images simulated from level 2A product of IKONOS and real remotely sensed images from level 0 product of RazakSAT. The experimental results demonstrate that the proposed method is practical and effective, with <2.3 % of relative error at the Nyquist frequency as compared to the well-established edge method. This indicates that the proposed method can warrant a reliable result for on-orbit spatial characterization.

Medical images are acquired for the purpose of gathering information regarding the disease state of a patient. The quality of the image should be a measure of how a specified task may be performed given the resulting image. Image quality is task dependent; one imaging system may provide images that allow better task performance than another system's for one task, but worse for another task. Determining the quality of an imaging system involves specifying the task of interest, the range of objects that will be imaged, and the observer (human or machine reader) who will perform the task. In radiography it has become common to use Fourier measures to describe image quality through a combination of Fourier‐based measures of system resolution and noise. The Line Spread Function, when Fourier transformed, yields the Modulation Transfer Function (MTF) as a measure of system resolution. Use of the MTF to describe a system's resolution is appropriate when the imaging system is shift‐invariant, that is, the line spread function is independent of position. Image noise is described in the Fourier domain by the Noise Power Spectrum (NPS). We can use the NPS to describe the noise in an imaging system whenever the noise properties are stationary, meaning that the variance and correlations between fluctuations in different locations are not dependent on their absolute location. These Fourier measures of system resolution and noise are commonly combined to give an overall figure of merit known as the Detective Quantum Efficiency (DQE). The DQE describes the signal‐to‐noise transfer characteristics of an imaging system as long as those assumptions of shift‐invariance and noise stationarity are valid. In digital systems the image of an object is affected by the location of the object with respect to the pixel grid. In other words, the detector pixels cause the system to be shift‐variant. In this case the MTF does not describe the resolution properties completely. This is particularly the case for tomographic systems, where the point‐response function is quite position‐dependent. Moreover, in real imaging systems the noise properties will depend on position, most notably because real patients always have structure. So, the Fourier‐domain noise concept of Noise Power Spectrum does not capture all the properties of noise for real imaging systems and tasks. In this talk we will consider a general treatment of the imaging system as a mapping of information from the patient to the data, without the assumptions inherent in Fourier analysis. We will discuss approaches to the characterization of system resolution and noise in terms of position‐dependent parameters. Once such position‐dependent imaging properties of a system are determined, we can use them to calculate measures of image quality that summarize the usefulness of the images for the performance of various visual tasks.

Imaging systems using aspheric imaging lenses with complementary computation can deliver performance unobtainable in conventional imaging systems. These new imaging systems, termed Wavefront coded imaging systems, use specialized optics to capture a coded image of the scene. Decoding the intermediate image provides the "human-usable" image expected of an imaging system. Computation for the decoding step can be made completely transparent to the user with today's technology. Real-time Wavefront coded systems are feasible and cost-effective. This "computational imaging" technology can be adapted to solve a wide range of imaging problems. Solutions include the ability to provide focus-free imaging, to increase the field of view, to increase the depth of read, to correct for aberrations (even in single lens systems), and to account for assembly and temperature induced misalignment. Wavefront coded imaging has been demonstrated across a wide range of applications, including microscopy, miniature cameras, machine vision systems, infrared imaging systems and telescopes.

A number of complementary metrics are available to assess the performance of digital X-ray imaging systems. However, the sensitivity of these metrics to changes in the electro-optical imaging chain is poorly understood. Some of the commonly used metrics include Contrast to Noise ratio (CNR), limiting spatial resolution, Modulation Transfer Function (MTF), Noise Power Spectrum (NPS) and the Detective Quantum Efficiency (DQE). We evaluated the utility of these metrics in characterizing the imaging plate, imaging system optics and electronic components of computed radiography (CR) systems. We developed practical and easy to use test objects (phantoms) and implemented software to aid in calculating each metric. The results of this research will facilitate the characterization of differences in CR systems using the appropriate metrics.

Computational imaging techniques that rely on a compressed set of measurements and exploit prior information such as target size, scene sparsity, transceiver radiation pattern, etc are rapidly gaining popularity in areas such as medical and security imaging, remote sensing, and automotive radar as they can significantly reduce SWAP-C (Size, Weight, Power, and Cost) of hardware modules, especially at millimeter-wave frequencies. In this article, we propose using the covariance matrix of a large ensemble of representative targets to form a diagonalizing basis in which the transformed scene voxels are uncorrelated. In this basis, we introduce a method of image reconstruction, Covariance Likelihood based Regularization (CLR), where transformed voxels, with low likelihood according to the ensemble statistics, are penalized. We also discuss another method, Thresholded Eigenbasis (TE), which involves thresholding the eigenvalues of the covariance matrix and reconstructing the transformed scene voxels in a lower dimensional approximate basis. We use these techniques to reconstruct images from simulations of measurements made using a W-band (75 - 110 GHz) imaging system, where the linear imaging matrix is carefully designed based on vector electromagnetics and realistic hardware. Based on these reconstruction results, we discuss the opportunities and challenges for these methods, including scenarios where TE provides improved reconstruction speed and CLR provides improved accuracy.

This paper demonstrates a convenient experimental tech- nique for measuring the resolution of a digital imaging system. The spa- tial frequency response of the system is obtained by deriving the modu- lation transfer function (MTF) from the measured contrast transfer function (CTF). Basic signal-processing techniques are used to establish a relationship between the MTF and the CTF. Experimental methodology is discussed with respect to avoidance of shift variation in the CTF. Dis- crete Fourier transformation is applied for a power-spectrum analysis of the MTF. Using the CTF as a measure of performance, a series of ex- periments were carried out to characterize an imaging system based on an integrated CMOS camera. The experimental results showed that this approach can be applied in general, for the assessment of spatial reso- lution for digital imaging systems. © 1998 Society of Photo-Optical Instrumenta- tion Engineers. (S0091-3286(98)00609-6)

The line spread function (LSF) is a classical figure of merit used to derive the modulation transfer function (MTF) of an imaging system. However this test cannot be directly applied to cameras based on an infrared focal plane array (IRFPA), as these sampled systems exhibit aliasing effects. ONERA has proposed a new technique called generalized line spread function allowing MTF assessment for sampled imaging systems. A testing of spatial frequency filtering becomes possible until at least twice the Nyquist frequency. The purpose of this paper is to show that this method is well-adapted to IRFPA cameras. In particular, the effects of bad a priori estimation of the characteristics of the camera are discussed. Secondly, we have carried on a laboratory experiment with a widespread infrared imaging system. The purpose is to demonstrate experimentally the advantages of this new method, not only in terms of performances but also in terms of simplicity of implementation and robustness. The infrared imaging system tested is a 512 by 512 Si:Pt IR5120C Mitsubishi camera equipped with a F/1.2 Angenieux lens.

In this paper, a preliminary study related to the detection of breast cancer based on a computational microwave imaging system is presented at K-band frequencies. In comparison to normal tissues, the different dielectric properties (permittivity and conductivity) of the malignant tissues can be exploited in order to detect the presence of tumour through a microwave imaging system. This work demonstrates the detection of breast tumour as an application of a computational imaging technique by leveraging the concept of the dynamic metasurface antenna (DMA) aperture as a transmitter. In this framework, the computational imaging aperture can provide a compact system design with a low-cost deployment for detecting tumours in early-stage, and this can speed up the screening process of the population at risk. Particularly, early detection of Stage 1 can help with the determination of the best treatment method and enhance a patient's prognosis.

Purpose: To demonstrate a method of measuring the modulation transfer function (MTF) of digital imaging systems using the common star pattern test tool. The goal of this research is to develop a technique that brings precise and objective evaluation of spatial resolution to routine quality control in radiography and fluoroscopy. Method and Materials: Images of a 2‐degree star pattern were obtained on a variety of digital radiographic imaging systems, spanning a range of spatial resolution performance levels. One‐dimensional profiles from concentric circles around the center of the star were obtained from each star image. The circular profiles were unwrapped to produce a series of square waves, which were analyzed to produce the square wave response function (SWRF). Droege's method was used to compute the MTF from the SWRF. The MTF determined using the star pattern method was compared to published and quality control measurements of the MTF for several digital mammography and digital radiography systems. In implementing this method, important parameters that must be considered include the radial and angular sampling rates, the method for determining the zero‐frequency normalization and correction for beam nonuniformity. Results: The MTF computed from star pattern profile measurements closely matched the MTF obtained using other methods over the range of spatial frequencies between the Nyquist frequency and 1/3 of the Nyquist frequency. The star pattern MTF, which is a system measurement and includes the effects of detector and geometric unsharpness, was within 6–8% of reference values obtained from the scientific literature for two models digital mammography equipment. Conclusion: Images of a 2‐degree star pattern can produce estimates of the two‐dimensional system MTF. This method may offer a convenient means of assessing the spatial resolution of digital imaging systems for acceptance testing and quality control.

엑스선 의료영상이 디지털 시스템으로 발전함에 따라 의료영상의 평가 방법 또한 디지털 시스템에 맞춰 새롭게 개선되었으며 그 중 MTF(Modulation Transfer Function) 측정법은 Fujita이론에 기초한 에지법으로 ISO에 규정되었다. 에지법의 기초인 Fujita이론은 MTF 측정을 위해 슬릿의 각도를 디지털 검출기의 픽셀 열에 대하여 <TEX>$1^{\circ}{\sim}2^{\circ}$</TEX> 기울여 영상을 획득한 후 LSF를 합성하는 것으로 샘플링 간격은 각도에 따라 크게는 1/54배, 작게는 1/28배 감소하게 된다. 본 연구에서 사용된 장비는 Simens사의 MAMMOMAT Inspiration으로 비정질 셀레늄(amorphous selenium) 기반의 <TEX>$0.085{\times}0.085mm^2$</TEX> 의 픽셀 사이즈를 갖는 검출기를 이용하여 presampling MTF를 측정하였다. 측정 방법은 Fujita의 슬릿법와 동일한 방법인 와이어법를 이용하였으며 측정된 영상에서 얻은 픽셀값을 이용하여 엑셀에서 이산 푸리에 변환을 시행하였다. 실험 결과 Fujita이론 대비 약 3배 이상의 샘플링 간격(sampling interval)의 경우 해상도 평가 지수인 10% MTF에서 약 85% 이하의 정확도를 보였으며 선예도 평가 지수인 50% MTF에서 약 93% 이하의 정확도를 나타내었다. 하지만 샘플링 간격이 Fujita 이론 대비 2배 정도 늘어난 경우는 50%와 10% MTF 모두 96% 이상의 정확도를 가진다는 것을 알 수 있었다. Assessments of medical image was improved in accordance with development of medical imaging systems. One of them is edge method to determining MTF(Modulation Transfer Function) based on the Fujita method. Fujita was reduced sampling interval used slightly angulated slit to the direction of pixel array and composited finely sampled LSF to determine presampling MTF. In this study, we investigate the effect of sampling interval on the MTF under a digital imaging system by changing wire angle. The wire method was equivalent to the slit method except signal appearance. A Simens's MAMMOMAT Inspiration with <TEX>$0.085{\times}0.085mm^2$</TEX> pixel size made by amorphous selenium was used and 96% accuracy on MTF in twice sampling interval compared with Fujita was obtained. However, three times of sampling interval showed 93% accuracy on 50% of MTF and 85% accuracy on 10% of MTF.