Abstract

During the past few years, the emergence of spatial light modulators operating at the tens of kHz has enabled new imaging modalities based on single-pixel photodetectors. The nature of single-pixel imaging enforces a reciprocal relationship between frame rate and image size. Compressive imaging methods allow images to be reconstructed from a number of projections that is only a fraction of the number of pixels. In microscopy, single-pixel imaging is capable of producing images with a moderate size of 128 × 128 pixels at frame rates under one Hz. Recently, there has been considerable interest in the development of advanced techniques for high-resolution real-time operation in applications such as biological microscopy. Here, we introduce an adaptive compressive technique based on wavelet trees within this framework. In our adaptive approach, the resolution of the projecting patterns remains deliberately small, which is crucial to avoid the demanding memory requirements of compressive sensing algorithms. At pattern projection rates of 22.7 kHz, our technique would enable to obtain 128 × 128 pixel images at frame rates around 3 Hz. In our experiments, we have demonstrated a cost-effective solution employing a commercial projection display.

Highlights

  • During the past few years, the emergence of spatial light modulators operating at the tens of kHz has enabled new imaging modalities based on single-pixel photodetectors

  • To better understand the Adaptive Compressive Imaging (ACI) algorithm one has to figure out how the 2D wavelet transform technique works

  • Four N/2 × N/2 quadrants are obtained; a low resolution version of the image and three more quadrants with the information of the horizontal, vertical and diagonal edges. This process can be applied again to the low resolution version of the image, giving the tree-structured image shown in the right image of Fig. 1 where the upper left quadrant has been replaced by its wavelet transform. This procedure can be repeated up to N times, when the pixel in the upper left corner contains the total energy of the scene and the rest of the image has the information about the edges of the scene

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Summary

Introduction

During the past few years, the emergence of spatial light modulators operating at the tens of kHz has enabled new imaging modalities based on single-pixel photodetectors. There are several approaches that exploit the simplicity of the detectors in order to acquire multidimensional information, such as 3D, polarization and spectral images[6,7,8,9,10] This complexity reduction in the sensor entails an increase of computational time to recover an image when compared to conventional techniques. In order to solve this problem, compressive sensing (CS) techniques provide a method to recover the images with a number of measurements lower than the total number of pixels This is possible because natural images tend to be sparse (i.e. only a small fraction of these projections have relevant information) in some basis of functions[15]. Some other techniques tackle this problem by using temporal sparsity[16,17]

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