Compressive Optical Imaging: Architectures and Algorithms

Abstract

Many traditional optical sensors are designed to collect directly interpretable and intuitive measurements. For instance, a standard digital camera directly measures the intensity of a scene at different spatial locations to form a pixel array. Recent advances in the fields of image reconstruction, inverse problems, and compressive sensing (CS) [1,2] indicate, however, that substantial performance gains may be possible in many contexts via less direct measurements combined with computational methods. In particular, CS allows for the extraction of high-resolution images from relatively small focal plane arrays (FPAs). CS is described in detail in Chapter 23. The basic idea of CS theory is that when the image of interest is very sparse or highly compressible in some basis (i.e., most basis coefficients are small or zero valued), relatively few well-chosen observations suffice to reconstruct the most significant nonzero components. In particular, judicious selection of the type of image transformation introduced by measurement systems may significantly improve our ability to extract high-quality images from a limited number of measurements. By designing optical sensors to collect measurements of a scene according to CS theory, we can use sophisticated computational methods to infer critical scene structure and content.These ideas are particularly relevant to imaging applications in which it is useful or even crucial to keep the FPA of an optical system relatively small. For example, in low-light settings where sensitive detectors are costly, smaller FPAs translate directly to less expensive systems. Smaller FPAs also make systems lighter and, thus, more portable. In addition, imaging systems with fewer photodetectors consume less power and, therefore, require fewer battery charges. Finally, smaller cameras can fit into tighter spaces for unobtrusive surveillance. An important goal in the design of many imaging systems, then, is to extract as much information as possible from a small number of detector array measurements.While recent progress in the exploitation of CS theory is highly encouraging, there are several key issues in the context of optical systems that must be addressed:Optical and Digital Image Processing: Fundamentals and Applications, First Edition. Edited

Do log factors matter? On optimal wavelet approximation and the foundations of compressed sensing

“…In the realm of optical imaging, the single-pixel camera [33] was one of the first empirical demonstrations of compressed sensing principles, and its various progenitors such as lensless imaging [16,43] continue to be active areas of investigation [39]. Other modalities, including X-ray CT [40], infrared imaging [52], spectral imaging [11], light-field imaging [53], ghost imaging [44], STORM [69], holography [18], fluorescence microscopy [61], NMR [42,45], radio interferometry [67], to name but a few, have all benefitted from compressed sensing approaches.…”

Fourier Single-Pixel Imaging Based on Lateral Inhibition for Low-Contrast Scenes

“…CS has proved to be an excellent theoretical framework for SPI because of the natural image's sparse priors [19], [20]. Especially, the CS-based total variation regularization method (TV) has been widely applied to various applications [21], [22]. Although CS recovers higher quality image with lower sampling ratio compared to the optical correlation method, it cannot be applied for real-time high-resolution applications because of high computational cost associated with 1-minimization.…”

Adaptive Basis Scan by Wavelet Prediction for Single-Pixel Imaging

“…The compressive sensing (CS) paradigm [30] has been widely applied to optical systems [31], [32]. In particular, since the pioneering work of Duarte and coauthors [1], [2], SPC has been mainly associated to the CS that provides an excellent theoretical framework for recovering an image from SPC measurements.…”