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Lensless Imaging with Compressive Sense 时间:2017-05-23 09:10 来源:未知作者:admin 点击: 次 Abstract—Lensless imaging is an important and challenging problem. One notable solution to lensless imaging is a single pixel camera which benefits from ideas central to compressive sampling. However, traditional single pixel cameras require many illumination patterns which result in a long acquisition process. Here we present a method for lensless imaging based on compressive ultrafast sensing. Each sensor acquisition is encoded with a different illumination pattern and produces a time series where time is a function of the photon’s origin in the scene. Currently available hardware with picosecond time resolution enables time tagging photons as they arrive to an omnidirectional sensor. This allows lensless imaging with significantly fewer patterns compared to regular single pixel imaging. To that end, we develop a framework for designing lensless imaging systems that use ultrafast detectors. We provide an algorithm for ideal sensor placement and an algorithm for optimized active illumination patterns. We show that efficient lensless imaging is possible with ultrafast measurement and compressive sensing. This paves the way for novel imaging architectures and remote sensing in extreme situations where imaging with a lens is not possible.
I.INTRODUCTION
Traditional imaging is based on lenses that map the scene plane to the sensor plane. In this physics-based approach the imaging quality depends on parameters such as lens quality, numerical aperture, density of the sensor array and pixel size. Recently it has been challenged by modern signal processing techniques. Fundamentally the goal is to transfer most of the burden of imaging from high quality hardware to computation. This is known as computational imaging, in which the measurement encodes the target features; these are later computationally decoded to produce the desired image.Furthermore, the end goal is to completely eliminate the need for high quality lenses, which are heavy, bulky, and expensive. One of the key workhorses in omputational imaging is compressive sensing (CS) [1], [2]. For example, CS enabled the single pixel camera [3], which demonstrated imaging with a single pixel that captured scene information encoded with a spatial light modulator (SLM). The pixel measurement is a set of consecutive readings, with different SLM patterns. The scene is then recovered using compressive deconvolution.
Broadly, the traditional imaging and single pixel camera demonstrate two extremes: traditional cameras use a pure hardware approach whereas single pixel cameras minimize the requirement for high quality hardware using modern signal processing. There are many trade-offs between the two approaches. One notable difference is the overall acquisition time: the physics-based approach is done in one shot (i.e. all the sensing is done in parallel). The single pixel camera and its variants require hundreds of consecutive acquisitions, which translates into a substantially longer overall acquisition time. Recently, time-resolved sensors enabled new imaging capabilities. Here we consider a time-resolved system with pulsed active illumination combined with a sensor with a time resolution on the order of picoseconds. Picosecond time resolution allows distinguishing between photons that arrive from different parts of the target with mm resolution. The sensor provides more information per acquisition (compared to regular pixel), and so fewer masks are needed. Moreover, the
time-resolved sensor is characterized by a measurement matrix that enables us to optimize the active illumination patterns and reduce the required number of masks even further. Currently available time-resolved sensors allow a wide range of potential implementations. For example, Streak cameras provide picosecond or even sub-picosecond time resolution [4], however they suffer from poor sensitivity. Alternatively, Single Photon Avalanche Photodiode (SPAD) are compatible with standard CMOS technology [5] and allow time
tagging with resolutions on the order of tens of picoseconds. These devices are available as a single pixel or in pixel arrays.
In this paper we present a method that leverages both timeresolved sensing and compressive sensing. The method enables lensless imaging for reflectance recovery with fewer illumination patterns compared to traditional single pixel cameras. This relaxed requirement translates to a shorter overall acquisition time. The presented framework provides guidelines and decision tools for designing time-resolved lensless imaging systems. In this framework the traditional single pixel camera is one extreme design point which minimizes the cost with simple hardware, but requires many illumination patterns (long acquisition time). Better hardware reduces the acquisition time with fewer illumination patterns at the cost of complexity. We provide sensitivity analysis of reconstruction quality to changes in various system parameters. Simulations with system parameters chosen based on currently available hardware indicate potential savings of up to 50 fewer illumination patterns compared to traditional single pixel cameras.