Patent Publication Number: US-2023139382-A1

Title: Filtering Pulse-Width Modulated (PWM) Noise from a Fingerprint Image Captured with an Optical Under-Display Fingerprint Sensor (UDFPS)

Description:
BACKGROUND 
     To preserve space on a display side of an electronic device, a manufacturer may embed sensors under the display. These sensors can include an optical under-display fingerprint sensor (UDFPS), an ambient light sensor, a camera, and so forth. For the optical UDFPS, as a user places a finger on the display and over the optical UDFPS, the electronic device uses the brightness of the display to illuminate the finger. Example illumination systems use a pulse-width modulation circuit to enable the electronic device to generate a pulse-width modulated (PWM) signal to control a brightness, a refresh rate, and so forth, by which to illuminate the finger. Unfortunately, the optical UDFPS may capture a fingerprint image that includes PWM noise. The PWM noise increases a temporal noise and may reduce a signal-to-noise ratio of the captured fingerprint image. The reduced signal-to-noise ratio of the captured fingerprint image lowers the fingerprint image&#39;s quality. A fingerprint with a lower image quality may increase a false acceptance rate, consequently compromising a biometric security of the electronic device. The fingerprint with a lower image quality may also increase a false rejection rate, thereby providing a poor user experience. 
     SUMMARY 
     This disclosure describes methods, apparatuses, and techniques for capturing a fingerprint image using an electronic device with an under-display fingerprint sensor (UDFPS) embedded under a display screen of a display system. The display system utilizes a pulse-width modulation circuit to generate a pulse-width modulated (PWM) signal to control light emitted by the display screen. As the display screen illuminates a user&#39;s touch, the UDFPS captures light reflected off the user&#39;s touch, therefore, capturing the fingerprint image. The captured fingerprint image, however, includes a PWM noise. The electronic device uses a noise-filtering algorithm to filter out and/or reduce the PWM noise in the captured fingerprint image. In one aspect, the noise-filtering algorithm estimates and/or determines the PWM noise in the captured fingerprint image. The noise-filtering algorithm then reduces, extracts, and/or filters out the PWM noise from the captured fingerprint image. The noise-filtering algorithm can use limited hardware and/or memory resources and may utilize relatively-few computational resources. 
     In one aspect, a computer-implemented method is described that performs a principal component analysis on background images associated with a sensor embedded under a display screen of a display system, the principal component analysis providing an artifact on the background images. The method then extracts principal component vectors from the artifact and, responsive to the extracting and based on the principal component vectors, determines at least one pulse-width modulated (PWM) noise. Responsive to determination of the PWM noise, the method vectorizes the PWM noise to create a PWM noise vector and illuminates, with light from the display screen, a user touch. Illuminating the user touch causes the light to reflect off a user&#39;s skin. The method then captures the reflected light at the sensor to provide a user-associated image and projects the user-associated image onto a vector space, the vector space being associated with the PWM noise vector to provide the user-associated image on the vector space. Based on the user-associated image on the vector space, the method filters out the PWM noise from the user-associated image to provide a reduced-noise image. 
     In another aspect, an electronic device includes a display screen of a display system, a pulse-width modulation circuit of the display system, a sensor, one or more processors, and one or more computer-readable media having instructions thereon that, responsive to execution by the one or more processors, perform the operations of the method mentioned above. In yet other aspects, a system, a software, or means includes performing the operations of the method mentioned above. 
     This summary introduces simplified concepts for capturing a fingerprint with fingerprint sensors, which is further described below in the Detailed Description and Drawings. For ease of description, the disclosure focuses on optical UDFPSs embedded under a display screen (e.g., an organic light-emitting diode (OLED) display) of an electronic device. The described concepts, however, may be utilized in numerous software, systems, and/or apparatuses to filter out, extract, and/or reduce noise associated with a pulse-width modulated signal. Optional features of one aspect, such as the method described above, may be combined with other aspects. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The details of one or more aspects of user devices with fingerprint identification systems that increase a quality of a fingerprint image by extracting a pulse-width modulated noise from the fingerprint image are illustrated in the following figures: 
         FIG.  1    illustrates an example electronic device with a fingerprint identification system having a fingerprint sensor embedded under a display screen of a display system; 
         FIG.  2    illustrates example causes of a pulse-width modulated (PWM) noise in a captured fingerprint image; 
         FIG.  3    illustrates examples artifacts that include variations in a phase and a frequency of the PWM noise; 
         FIG.  4    illustrates various example artifacts due to the PWM noise; 
         FIG.  5    illustrates an example computer-implemented method for filtering out PWM noise from a captured fingerprint image to provide a filtered fingerprint image with reduced PWM noise; and 
         FIG.  6    illustrates examples of patterns and minutiae used in fingerprint authentication. 
     
    
    
     DETAILED DESCRIPTION 
     Example Environments 
       FIG.  1    illustrates an example environment  100  of an electronic device  102 . The electronic device  102  enables a user to biometrically secure their device using a fingerprint identification system  120  (FIS  120 ) with at least one optical under-display fingerprint sensor  122  (UDFPS  122 ). The electronic device  102  can provide biometric security by comparing a verify image to an enrolled image of the user&#39;s thumb, fingertip, or plurality of fingertips. For example, the electronic device  102  can utilize the UDFPS  122  to capture a “verify image” and match patterns and/or minutiae of the verify image to an “enrolled image,” where examples of patterns and minutiae are illustrated in  FIG.  6   . 
     As described herein, a “verify image” is a fingerprint image used for authentication. An “enrolled image” is an image that the user device captures during enrollment, such as when the user first sets up the electronic device  102  or an application  104 . Further, an “enrolled image template” (an enrolled template) can be a mathematical representation of the enrolled image. The enrolled template can be a vectorized representation of the enrolled image and, among other advantages noted below, take less memory space in the user device. While beneficial in some respects, the use of a vectorized representation for an enrolled image template is not required for matching a verify image to the enrolled image template. The described apparatuses, methods, and techniques can perform image-to-image (rather than vector-to-vector) comparisons, as well as other representations, to compare each verify image to the enrolled image. 
     The electronic device  102  may be a smartphone, a tablet, a laptop, a desktop computer, a computing watch, computing eyeglasses, a gaming system or controller, a smart speaker system, an appliance, a television, an entertainment system, an audio system, an automobile, an unmanned vehicles (in-air, on the ground, or submersible “drones”), a trackpad, a drawing pad, a netbook, an e-reader, a home security system, a doorbell, a refrigerator, and other devices with a fingerprint identification system  120 . 
     The electronic device  102  may include additional or fewer components than what is illustrated in  FIG.  1   . The electronic device  102  includes one or more application processor(s)  106  and one or more computer-readable storage media (CRM  108 ). The application processor  106  may include any combination of one or more controllers, microcontrollers, processors, microprocessors, hardware processors, hardware processing units, digital signal processors, graphics processors, graphics processing units, and the like. The application processor  106  processes computer-executable instructions (e.g., code, MATLAB® code) stored by the CRM  108 . The CRM  108  may include any suitable memory media and storage media, for example, volatile memory (e.g., random-access memory (RAM)), non-volatile memory (e.g., Flash memory), optical media, magnetic media (e.g., disk or tape), and so forth. Also, the CRM  108  may store instructions, data (e.g., biometric data), and/or other information, and the CRM  108  excludes propagating signals. 
     The electronic device  102  may also include an application  104 . The application  104  may be a software, applet, peripheral, or other entity that requires or favors authentication of a verified user. For example, the application  104  can be a secured component of the electronic device  102  or an access entity to secure information accessible from the electronic device  102 . The application  104  can be an online banking application software or webpage that requires fingerprint identification before logging in to an account. Alternatively, the application  104  may be part of an operating system (OS) that prevents access (generally) to the electronic device  102  until the user&#39;s fingerprint is authenticated as the verified user&#39;s fingerprint. The verified user may execute the application  104  partially or wholly on the electronic device  102  or in “the cloud” (e.g., on a remote device accessed through the Internet). For example, the application  104  may provide an interface to an online account using an internet browser and/or an application programming interface (API). 
     Further, the electronic device  102  may also include one or more input/output (I/O) ports (not illustrated) and a display system  110 . The display system  110  includes at least one display screen  112 , for example, an organic light-emitting diode (OLED) display screen. The display system also includes a pulse-width modulation circuit  114 , which may be part of a driver (not illustrated in  FIG.  1   ) associated with the display screen  112 . The pulse-width modulation circuit  114  can generate a pulse-width modulated (PWM) signal that enables the electronic device  102  to control a brightness, a refresh rate, and so forth, of the display screen  112 . 
     To preserve space on a display side of an electronic device  102 , a manufacturer may embed sensor(s)  116  (e.g., an ambient light sensor, a camera) and the UDFPS  122  under the display screen  112 . The sensor  116  and the UDFPS  122 , however, may favor different brightness of the display screen  112  and/or different duty cycles of the PWM signal. For example, an ambient light sensor may operate better when the PWM signal has a higher pixel off-time, or as may be referred herein, a “blanking time.” On the other hand, the UDFPS  122  may operate better when the PWM signal has a lower blanking time. To accommodate these different requirements, the PWM signal has a duty cycle of less than one hundred percent (100%). In addition, a user may favor a display screen  112  that has a high refresh rate (e.g., 360 Hertz (Hz)). Often, a higher refresh rate can support a higher image quality (e.g., text, still picture, video) on the display screen  112 . In aspects, the UDFPS  122  may be calibrated to accommodate multiple modes of operation encompassing varying duty cycles or varying frequency of a PWM noise  132  (e.g., see  FIGS.  2  and  3   ). 
     In one aspect, the blanking time of the PWM signal and the refresh rate of the display screen  112  may cause the UDFPS  122  to capture a fingerprint image  130  that includes a PWM noise  132 , as is further described below. The PWM noise  132  increases a temporal noise and reduces a signal-to-noise ratio (SNR) of the captured fingerprint image  130 . The reduced SNR and a presence of the PWM noise  132  on the captured fingerprint image  130  lower a quality of the fingerprint image, adversely affecting biometric security. In biometric security, a success rate is often characterized using a receiver operating curve (ROC), which can be represented as a graphical plot illustrating the diagnostic ability of a binary classifier system as its discrimination threshold is varied. More specifically, biometric security measurements may include a false acceptance rate (FAR) for a proportion of times a fingerprint identification system grants access to an unauthorized person and a false rejection rate (FRR) for a proportion of times a fingerprint identification system fails to grant access to an authorized person. Qualitatively speaking, a fingerprint identification system with a high success rate has a low false acceptance rate and a low false rejection rate. 
     To increase the success rate of the fingerprint identification system  120 , the electronic device  102  can remove and/or filter out the PWM noise  132  from the captured fingerprint image  130  to generate, store, and use a filtered fingerprint image  134 . The filtered fingerprint image  134  has an increased SNR, less PWM noise  132 , a lower FAR, a lower FRR, and offers better biometric security than the captured fingerprint image  130 . Therefore, the filtered fingerprint image  134  enables the user to better secure the electronic device  102 , the application  104 , a function, or peripheral thereof. 
     It is to be understood that the user has control over their biometric data (e.g., fingerprints) because the electronic device  102  may capture, collect, store, analyze, filter, and/or process the information associated with the user after the electronic device  102  receives explicit permission from the user. In fact, throughout the disclosure, examples are described where the electronic device  102  analyzes information (e.g., captured fingerprint image) associated with the user. In situations discussed below in which the electronic device  102  authenticates a user based on fingerprints, the user can be provided with an opportunity to control whether programs or features of the user device or a remote system can collect and make use of the fingerprint for a current or subsequent authentication procedure. Individual users, therefore, have control over what the electronic device  102  can or cannot do with fingerprint images and other information associated with the user. Information associated with the user (e.g., an enrolled image, a verify image, a captured fingerprint image), if ever stored, is pre-treated in one or more ways so that personally identifiable information is removed before being transferred, stored, or otherwise used. For example, before a user device stores an enrolled image, the user device may encrypt the enrolled image. Pre-treating the data this way ensures the information cannot be traced back to the user, thereby removing any personally identifiable information that would otherwise be inferable from the fingerprint of the user. Alternatively, the user may elect to forgo securing the electronic device  102  using biometric data. Instead, the user may employ a username, a password, a personal identification number (PIN), and/or a combination thereof to secure their electronic device  102  and/or the application  104 . 
     PWM Noise 
       FIG.  2    illustrates an environment  200  of a display side of an electronic device  102  (e.g., a smartphone).  FIG.  2    helps describe some example causes of the PWM noise  132  in a captured fingerprint image  130 . As is illustrated, the electronic device  102  may include a speaker  202  and a display screen  112 . To preserve space on a display side of the electronic device  102 , a manufacturer may embed the sensor  116  and the UDFPS  122  under the display screen  112 . In  FIG.  2   , electronic components that are embedded under the display screen  112  are illustrated with dashed lines. 
     In one aspect, the driver and/or the pulse-width modulation circuit  114  drives pixels of the display screen  112  using a display “rolling shutter” scheme, where consecutive rows of the pixels  204  (display rows  204 ) are refreshed at a certain frequency (e.g., 60 Hz, 90 Hz, 360 Hz). As described herein, a “rolling shutter” scheme is a method to capture and/or display an image in which a still picture or each frame of a video is captured and/or displayed by scanning across the image rapidly, vertically (as illustrated in  FIG.  2   ) or horizontally (not illustrated). The “rolling shutter” scheme differs from a “global shutter” scheme (not illustrated); in the “global shutter” scheme, an entire still picture or frame of the video is captured and/or displayed at a same instant. As is illustrated by a direction of an arrow of the display rows  204 , the display rolling shutter scheme may be a vertical scheme. Although not illustrated, the display rolling shutter scheme may be a vertical scheme with an opposite direction than what is illustrated in  FIG.  2   . Alternatively, the display rolling shutter scheme may be a horizontal scheme, where the horizontal scheme may have a left-to-right or right-to-left direction. 
     In  FIG.  2   , the PWM signal drives the pixels of the display rows  204  with a duty cycle of less than 100%. As described herein, a “duty cycle” is a fraction of one “period” in which the PWM signal turns on pixels of the display row(s)  204 . The period is a time it takes the PWM signal to complete an on-and-off cycle. The duty cycle of the PWM signal may be expressed as a percentage or a ratio. For example, an 80% duty cycle describes a PWM signal that is on 80% of the time and off 20% of the time during each period. Diagrams  204 - 10  and  204 - 20  help illustrate a first ( 204 - 10 ) and a second ( 204 - 20 ) PWM signal with respective duty cycles that are less than 100%. For consistency, brevity, and the sake of clarity of this illustration, the PWM signals  204 - 10  and  204 - 20  have a same frequency (e.g., 360 Hz)—therefore, a period  204 - 12  of the first PWM signal  204 - 10  equals a period  204 - 22  of the second PWM signal  204 - 20 . Utilizing the display “rolling shutter” scheme, during each period (e.g.,  204 - 12 ), the first PWM signal  204 - 10  may turn on pixels of the display row(s)  204  during approximately 80% (e.g.,  204 - 14 , on time) of the time, and may turn off pixels of the display row(s)  204  during approximately 20% (e.g.,  204 - 16 , blanking time, off time) of the time. Similarly, during each period (e.g.,  204 - 22 ), the second PWM signal  204 - 20  may turn on pixels of the display row(s)  204  during approximately 95% (e.g.,  204 - 24 ) of the time and may turn off pixels of the display row(s)  204  during approximately 5% (e.g.,  204 - 26 ) of the time. In this illustration, the first PWM signal  204 - 10  has an 80% duty cycle, and the second PWM signal  204 - 20  has a 95% duty cycle. 
     Modulating the duty cycle of the PWM signal (e.g.,  204 - 12 ,  204 - 22 ) modulates and/or controls a brightness output of the pixels of the display screen  112 . A shorter blanking time (e.g.,  204 - 26 ) and a higher refresh rate (e.g., 360 Hz) enable the display screen  112  to display a higher-quality image and with less “flicker.” The shorter blanking time (e.g.,  204 - 26 ), however, impedes the sensor  116  (e.g., the ambient light sensor) from functioning properly because the ambient light sensor benefits from a longer blanking time. Therefore, the display screen  112  and the UDFPS  122  favor a PWM signal with a higher duty cycle (e.g.,  204 - 20 ), while the sensor  116  favors a PWM signal with a lower duty cycle (e.g.,  204 - 10 ). Engineers, designers, and scientists strive to design and build an electronic device  102  that can successfully utilize all components, applications, and peripheral thereof. To enable the ambient light sensor to work properly, the electronic device  102  operates with a longer blanking time (e.g.,  204 - 16 ) of the duty cycle of the PWM signal. 
     To further describe and illustrate what may cause the PWM noise  132 , consider some operation principles of the fingerprint identification system  120  with the UDFPS  122 . As the user places their thumb somewhere inside (e.g., touch area  122 - 1 ) a UDFPS active area  122 - 2 , the UDFPS  122  captures the fingerprint image  130 . In more detail, the display screen  112  illuminates the user&#39;s skin touching the display screen  112  (e.g., with visible light). The illumination of the user&#39;s touch causes light to reflect off the user&#39;s skin (e.g., thumb). The UDFPS  122  captures the reflected light. The UDFPS  122  may utilize various image sensor technologies, such as a complementary metal-oxide-semiconductor (CMOS) image sensor, a charge-coupled device (CCD) image sensor, a thin film transistor (TFT) image sensor, or any image sensor that utilizes light. Assume that the UDFPS  122  includes a CMOS image sensor having some number of pixels (e.g., 2 to 10 megapixels) that are arranged in rows and columns. The UDFPS also uses a UDFPS “rolling shutter” scheme to capture the fingerprint image  130 , where consecutive rows of the pixels of the CMOS image sensor (UDFPS rows  206 ) capture the fingerprint image  130 . A time to capture the fingerprint image  130  using the UDFPS “rolling shutter” scheme may be referred to as an “integration time.” 
     The integration time of the fingerprint identification system  120  with the UDFPS  122 , however, is appreciatively slower than a refresh time of the display screen  112 . The refresh time of the display screen  112  is inversely proportional to the refresh rate of the display screen  112 . An illumination of the display screen  112  with a 360-Hz fresh rate may be driven by a PWM signal having a frequency of 360 Hz with an 80% duty cycle. In such a scenario, the PWM signal that controls the illumination of the display screen  112  may include 35 or 36 blanking times during the integration time for capturing the fingerprint image  130 . 
     Engineers, designers, and scientists strive to synchronize a clock (not illustrated) of the fingerprint identification system  120  and a clock (not illustrated) of the display screen  112 . In more detail, engineers strive to design a fingerprint identification system  120  with an integration time that is an integer (e.g., a whole number) multiple of the period (e.g.,  204 - 12 ) and the duty cycle (e.g.,  204 - 14 ) of the PWM signal. For example, the integration time may be 35 times the period and the duty cycle of the PWM signal. Unfortunately, the respective clocks of the display screen  112  and the fingerprint identification system  120  include respective jitters (e.g., 1%, 2%, 3%) due to process, voltage, and temperate (PVT) variations. In one aspect, the PWM signal may struggle to maintain a constant duty cycle, and/or the fingerprint identification system  120  may struggle to maintain a constant integration time. Consequently, a combination of the shorter duty cycle (longer blanking time) of the PWM signal, the higher refresh rate of the display screen  112 , and the jitters of the clocks of the display screen  112  and the fingerprint identification system  120  may cause PWM noise (e.g.,  132  of  FIG.  1   ) to appear at a captured fingerprint image (e.g.,  130  of  FIG.  1   ). Next,  FIG.  3    illustrates an example aspect of the PWM noise  132 . 
       FIG.  3    illustrates an environment  300  of examples of PWM noise  132 . In one aspect, to determine the PWM noise  132 , the electronic device  102  may capture multiple (e.g., four) consecutive images of a same non-transparent (e.g., white) flat surface that does not include example patterns and/or minutiae of  FIG.  6   . If the integration time of the fingerprint identification system  120  equals an integer (e.g., 35) multiple of the period (e.g.,  204 - 12 ) and the duty cycle (e.g.,  204 - 14 ) of the PWM signal  204 - 10 , the electronic device  102  captures consecutive images that are also flat.  FIG.  3   , however, illustrates basis  301  to  304  of four consecutively captured images of the flat surface that include dark stripes. These dark stripes are artifacts of the PWM noise  132  because the flat surface does not include stripes. 
     In addition, a count of dark stripes in the captured images  301  to  304  differs. In one aspect, the different count of the dark stripes in the captured images  301  to  304  may be due to a variation in frequency of the PWM noise  132 . To further examine the PWM noise  132 ,  FIG.  3    illustrates enlarged images  301 - 2  to  304 - 2  of areas  301 - 1  to  304 - 1  of the basis  301  to  304  of the captured images, respectively. The images  301 - 2 ,  302 - 2 ,  303 - 2 , and  304 - 2  illustrate variations in a phase of the PWM noise  132 . In one aspect, the variations in the phase of the PWM noise may appear as a location shift of the dark stripes in the captured images (e.g., with basis  301  to  304 ,  301 - 1  to  304 - 1 ,  301 - 2  to  304 - 1 ). Therefore,  FIG.  3    helps illustrate that even after a synchronization of clocks of the fingerprint identification system  120  (with the UDFPS  122 ) and the display system  110  (with the display screen  112 ), the captured images include PWM noise  132  with variations in phase and in frequency. The variations in phase and frequency of the PWM noise  132  increase an unpredictability of the PWM noise  132 . The electronic device  102 , however, uses a noise-filtering algorithm to remove and/or filter out the PWM noise  132  from the captured fingerprint image  130  to generate, store, and use the filtered fingerprint image  134 . Next,  FIG.  4    illustrates how the noise-filtering algorithm may use a principal component analysis (PCA) technique to identify, model, estimate, extract, and/or determine the PWM noise  132 . 
     PWM Noise Estimation 
       FIG.  4    is an example environment  400  that illustrates basis  401  to  410  of respective captured images of a non-transparent (e.g., white) flat (e.g., smooth) surface.  FIG.  4    is described in the context of  FIGS.  1  to  3   , the electronic device  102 , the display system  110  with the display screen  112 , and the fingerprint identification system  120  with the UDFPS  122 . The captured images of the non-transparent flat surface may be considered and/or referred to as “background images” of the fingerprint identification system  120 . Thus, artifacts (e.g., of  401  to  410 , patterns, variations in brightness/darkness) that are captured in the background images are due to the PWM noise  132 . 
     The PCA technique can model the PWM noise  132 , where the PWM noise  132  may include variations in phase, frequency, and/or amplitude (e.g., brightness or darkness). In mathematics, image processing, signal processing, mechanics, neuroscience, and/or other engineering and science disciplines, the PCA is a technique for computing principal components and/or principal component vectors. As described herein, the PCA technique may be used to identify, model, estimate, extract, and/or determine the artifacts in the background images, as is illustrated in  401  to  410  in  FIG.  4   . The basis  401 - 410 , identify, model, estimate, extract, and/or determine the PWM noise  132 . To reduce the PWM noise  132 , the electronic device  102  may synchronize start cycles between the PWM signal used to control light emitted by the display screen  112  and the integration time used to capture the fingerprint image  130  with the UDFPS  122 . 
     In one aspect, to identify, model, estimate, extract, and/or determine the PWM noise  132 , the electronic device  102  can capture background images (e.g., with basis  401  to  410 ) by varying and/or simulating clock jitter, frequency shifts, amplitude variations, and/or other parameters that can induce the PWM noise  132 . By so doing, the noise-filtering algorithm may identify, model, estimate, extract, and/or determine the PWM noise  132  in the captured fingerprint image  130  due to respective clock jitters (e.g., 1%, 2%, 3%) of the clock of the FIS  120  and/or the clock of the display system  110 . The noise-filtering algorithm can also identify, model, estimate, extract, and/or determine frequency shifts in the PWM noise  132  (e.g.,  301 - 2 ,  302 - 2 ,  303 - 2 ,  304 - 2 ). The frequency shifts in the PWM noise  132  may occur due to variations of the refresh rate (e.g., 359.6 Hz to 360.4 Hz) of the display screen  112  and/or variations in the integration time (e.g., 97.6 milliseconds to 98.4 milliseconds) using the UDFPS  122 . Further, the noise-filtering algorithm can identify, model, estimate, extract, and/or determine amplitude variations due to variations on an amount of light captured by the UDFPS  122  (e.g., UDFPS rows  206 ). The amplitude variations may occur due to variations of the duty cycle (e.g.,  204 - 14 ) of the PWM signal (e.g.,  204 - 10 ) of the display system  110 , a mis-synchronization of clocks of the FIS  120  and the display system  110 , and/or other factors. The noise-filtering algorithm can use limited hardware and/or memory resources and may utilize relatively-few computational resources to ensure minimal disruption to the user experience. 
     Alternatively, or additionally, instead of capturing artifacts on the background images, a manufacturer may use datasheets, specifications, and/or models of the FIS  120  and the display system  110  to calculate potential and/or anticipated artifacts. By so doing, the noise-filtering algorithm may develop a database that includes the PWM noise  132 . Thus, the noise-filtering algorithm can identify, model, estimate, extract, and/or determine the PWM noise  132  on an individual electronic device  102 , on electronic devices of a same make and model, and/or on a variety of makes and models that share a same display system  110  and a same fingerprint identification system  120 . A vectorized form of the background images that include the artifacts (e.g.,  401  to  410 ) may be encrypted and stored on the database. Note that the database that includes the background images with the artifacts does not contain any user biometric data (e.g., fingerprint data). Therefore, the noise-filtering algorithm further protects a user&#39;s privacy. Next,  FIG.  5    illustrates how the noise-filtering algorithm uses the vectorized form of the background images (e.g., with basis  401  to  410 ) to filter out the PWM noise  132  from a captured fingerprint image  130  to obtain a filtered fingerprint image  134 . 
     Example Method(s) 
       FIG.  5    illustrates an example method  500  used to filter out the PWM noise  132  from a captured fingerprint image  130  to obtain a filtered fingerprint image  134 .  FIG.  5    is described in the context of  FIGS.  1  to  4   , the electronic device  102 , the display system  110  with the display screen  112 , and the fingerprint identification system  120  with the UDFPS  122 . The operations performed in the example method  500  may be performed in a different order or with additional or fewer steps than what is shown in  FIG.  5   . The PCA technique of example method  500  can model the PWM noise  132 , where the PWM noise  132  includes variations in phase, frequency, and/or amplitude (e.g., brightness or darkness). The PCA is a technique for extracting principal components and/or principal component vectors. In aspects, the PCA technique analyzes data (e.g., biometric data) in order to identify, model, estimate, extract, and/or determine the artifacts in the background images. 
     At stage  502 , the method  500  performs a principal component analysis (PCA) on background images (e.g., with basis  401  to  410 ) using the PCA technique described in  FIG.  4   . As is illustrated in  FIGS.  3 ,  4 , and  5   , the background images may include artifacts (e.g., dark stripes). The PCA technique enables the method  500  to identify the artifacts (e.g.,  132  of  FIG.  5   ). The method  500  then extracts principal component vectors of the background images at stage  504 . As is illustrated in the background images with basis  401  to  410  of  FIG.  4   , a first plurality of principal components (e.g.,  402 ,  403 ) may include more artifacts than a second plurality of principal components (e.g.,  409 ). Therefore, at stage  506 , the method  500  determines which artifacts are due to the PWM noise  132 . The method  500  may ignore some artifacts because they may include an appreciable Gaussian noise. For example, the method  500  may ignore the background image  401  due to a reduced number of artifacts (e.g., few measurable and/or detectable dark stripes). After the method  500  determines which artifacts are due to the PWM noise  132 , at stage  508 , the method  500  creates a PWM noise vector for each artifact (e.g.,  401 - 410 ). As is illustrated in  FIGS.  3  to  5   , since the artifacts of the background images are striped, a horizontal portion of the PWM noise  132  is constant. As such, the method  500  may utilize one-dimensional (instead of two-dimensional) PWM noise vectors. The use of the one-dimensional vectors enables the noise-filtering algorithm to use limited hardware and/or memory resources (e.g., CRM  108 ) and utilize relatively few computational resources (e.g., application processor  106 ). Mathematically, the method  500  may express the PWM noise vector as a matrix denoted herein [PCA_PWM]. These principal component vectors may be stored and accessed in the future. 
     At stage  510 , the method  500  illuminates, with light from the display screen  112 , a user touch (e.g., touch area  122 - 1 ). The illumination causes the light to reflect off a user&#39;s skin. At stage  512 , then, the method  500  captures the reflected light at the UDFPS  122  to provide a user-associated image (e.g., captured fingerprint image  130 ). At the stage  512 , however, the captured fingerprint image  130  is an unfiltered fingerprint image and includes the PWM noise  132 . In addition to the artifacts (e.g., dark stripes) of the PWM noise  132 , the captured fingerprint image  130  has a reduced signal-to-noise ratio (SNR), further reducing a quality of the captured fingerprint image  130 . In  FIG.  5   , the reduced SNR in the captured fingerprint image  130  is illustrated as a lighter shade of grey of the patterns and/or minutiae compared to the filtered fingerprint image  134 . 
     At stage  514 , the method  500  projects the user-associated image (e.g., captured fingerprint image  130 ) onto a vector space, where the vector space is associated with the PWM noise vector (e.g.,  132 , [PCA_PWM]). Projecting the user-associated image may include multiplying the PWM noise vector, a transpose of the PWM noise vector matrix, and a vectorized form of the captured fingerprint image  130 . Mathematically, the stage  514  of the method  500  may be expressed using Equation 1: 
       [ I   PCA_PWM ]=[PCA_PWM]·[PCA_PWM] T ·[ I   Captured ]  Equation 1
 
     where a [PCA_PWM] matrix denotes the PWM noise vector, a [PCA_PWM] T  denotes a transpose of the [PCA_PWM] matrix, an [I Captured ] matrix denotes a vectorized form of the captured fingerprint image  130 , and a [I PCA_PWM ] matrix denotes the user-associated image (e.g., the captured fingerprint image  130 ) projected onto the vector space of the PWM noise. 
     At stage  516 , based on the user-associated image projected onto the vector space of the PWM noise, the method  500  filters out the PWM noise  132  from the user-associated image (e.g., captured fingerprint image  130 ) to provide a reduced-noise image (e.g., filtered fingerprint image  134 ). Filtering out the PWM noise  132  may subtract the user-associated image on the vector space from the PWM noise vector. Mathematically, the stage  516  of the method  500  may be expressed using Equation 2: 
       [ I   Filtered ]=[ I   Captured ]−[ I   PCA_PWM ]  Equation 2
 
     where an [I Filtered ]matrix denotes a vectorized form of the filtered fingerprint image  134 . 
     Patterns and Minutiae 
       FIG.  6    illustrates examples of patterns ( 602 ,  604 , and  606 ) and minutiae ( 610  through  626 ) used in matching fingerprints. The analysis of fingerprints for matching purposes generally requires the comparison of patterns and/or minutiae. The method  500  lowers the false acceptance rate, consequently improving the biometric security of the electronic device  102 . The method  500  also lowers the false rejection rate, thereby providing a better user experience. 
     The three main patterns of fingerprint ridges are an arch  602 , a loop  604 , and a whorl  606 . The arch  602  is a fingerprint ridge that enters from one side of the finger, rises in the center, forming an arc, and then exits the other side of the finger. The loop  604  is a fingerprint ridge that enters from one side of the finger, forms a curve, and then exits on that same side of the finger. The whorl  606  is a fingerprint ridge that is circular around a central point. The minutiae  610  through  626  are features of fingerprint ridges, such as ridge ending  610 , bifurcation  612 , short ridge  614 , dot  616 , bridge  618 , break  620 , spur  622 , island  624 , double bifurcation  626 , delta  628 , trifurcation  630 , lake or ridge enclosure (not illustrated), core (not illustrated), and so forth. 
     For example, presence of artifacts in the captured fingerprint image  130  (e.g., verify image), due to the PWM noise  132 , may appear as “valleys” in the verify image. Therefore, an electronic device may falsely reject a user when comparing the verify image to the enrolled image. The electronic device  102 , however, uses the method  500  and the techniques described in  FIGS.  1  to  5    to filter out the artifacts that may erroneously appear as “valleys” in a fingerprint image. 
     Generally, any of the components, modules, methods, and operations described herein can be implemented using software, firmware, hardware (e.g., fixed logic circuitry), manual processing, or any combination thereof. Some operations of the example methods may be described in the general context of executable instructions stored on computer-readable storage memory that is local and/or remote to a computer processing system, and implementations can include software applications, programs, functions, and the like. Alternatively or in addition, any of the functionality described herein can be performed, at least in part, by one or more hardware logic components, including, and without limitation, Field-programmable Gate Arrays (FPGAs), Application-specific Integrated Circuits (ASICs), Application-specific Standard Products (ASSPs), System-on-a-chip systems (SoCs), Complex Programmable Logic Devices (CPLDs), and the like. 
     Some examples are described below: 
     EXAMPLE 1 
     A computer-implemented method comprising: performing a principal component analysis on background images associated with a sensor embedded under a display screen of a display system, the principal component analysis providing an artifact on the background images; extracting principal component vectors from the artifact; responsive to the extracting and based on the principal component vectors, determining at least one pulse-width modulated, PWM, noise; responsive to determining the PWM noise, vectorizing the PWM noise to create a PWM noise vector; illuminating, with light from the display screen, a user touch, the illumination to cause the light to reflect off a user&#39;s skin; capturing reflected light at the sensor to provide a user-associated image; projecting the user-associated image onto a vector space, the vector space being associated with the PWM noise vector to provide the user-associated image on the vector space; and based on the user-associated image on the vector space, filtering out the PWM noise from the user-associated image to provide a reduced-noise image. 
     EXAMPLE 2 
     The computer-implemented method of example 1, further comprising, based on the PWM noise vector, creating a first matrix of the PWM noise, and creating, based on the user-associated image, a second matrix, and wherein projecting the user-associated image multiplies the first matrix, a transpose of the first matrix, and the second matrix. 
     EXAMPLE 3 
     The computer-implemented method of example 2, wherein filtering out the PWM noise subtracts, from the second matrix, the user-associated image on the vector space. 
     EXAMPLE 4 
     The computer-implemented method of at least one of the examples 1 to 3, further comprising authenticating the user based on the reduced-noise image. 
     EXAMPLE 5 
     The computer-implemented method of example 4, further comprising, responsive to authenticating the user, enabling use of a function, account, or peripheral. 
     EXAMPLE 6 
     The computer-implemented method of at least one of the examples 1 to 5, wherein the vectorizing the PWM noise ( 132 ) to create a PWM noise vector is based on variable frequency in PWM noise; and a quantity of PWM noise vectors corresponds to a quantity of frequencies in PWM noise. 
     EXAMPLE 7 
     The computer-implemented method of at least one of the examples 1 to 6, wherein the vectorizing the PWM noise ( 132 ) to create a PWM noise vector is based on variations in one or more duty cycles of the display system ( 110 ); and a quantity of PWM noise vectors corresponds to a quantity of duty cycles of the display system ( 110 ). 
     EXAMPLE 8 
     The computer-implemented method of at least one of the examples 1 to 7, wherein the sensor may capture multiple images of a non-transparent, flat surface without the user-associated image. 
     EXAMPLE 9 
     The computer-implemented method of example 8, wherein the non-transparent flat surface is white. 
     EXAMPLE 10 
     The computer-implemented method of at least one of the examples 1 to 9, wherein determining the PWM noise further comprises capturing multiple background images by simulating clock jitter to induce the PWM noise. 
     EXAMPLE 11 
     The computer-implemented method of at least one of the examples 1 to 10, wherein the PWM noise is identified, modeled and/or estimated by the electronic device to capture the at least one background image by varying and/or simulating clock jitter, frequency shifts, amplitude variations, and/or other parameters inducing the PWM noise. 
     EXAMPLE 12 
     The computer-implemented method of example 10 or 11, further comprising determining amplitude variations in the PWM noise. 
     EXAMPLE 13 
     The computer-implemented method of at least one of the examples 1 to 12, wherein the artifact comprises a fingerprint image generated from a thumb, fingertip, or plurality of fingertips. 
     EXAMPLE 14 
     The computer-implemented method of at least one of the examples 1 to 13, wherein the background image is a captured image of a non-transparent flat surface of a fingerprint identification system. 
     EXAMPLE 15 
     The computer-implemented method of at least one of the examples 1 to 14, wherein capturing reflected light at the sensor to provide a user-associated image comprises a vertical display rolling shutter scheme. 
     EXAMPLE 16 
     The computer-implemented method of at least one of the examples 1 to 14, wherein capturing reflected light at the sensor to provide a user-associated image comprises a horizontal display rolling shutter scheme. 
     EXAMPLE 17 
     The computer-implemented method of example 15 or 16, wherein a first PWM signal turns on pixels of the display row(s) during more than 70%, in particular more than 80% of the time, and turns off pixels of the display row(s) during less than 30%, in particular less than 20% and a second PWM signal turns on pixels of the display row(s) during more than 90%, in particular more than 95% of the time, and turns off pixels of the display row(s) during less than 10%, in particular less than 5%. 
     EXAMPLE 18 
     A user device comprising: a display system comprising: a display screen; and a pulse-width modulation circuit; a sensor; one or more processors; and one or more computer-readable media having instructions thereon that, responsive to execution by the one or more processors, perform operations of the computer-implemented method of any of examples 1 to 17. 
     Conclusion 
     While various embodiments of the disclosure are described in the foregoing description and shown in the drawings, it is to be understood that this disclosure is not limited thereto but may be variously embodied to practice within the scope of the following claims. From the foregoing description, it will be apparent that various changes may be made without departing from the spirit and scope of the disclosure as defined by the following claims.