Abstract
The theory of compressed sensing (CS) shows that signals can be acquired at sub-Nyquist rates if they are sufficiently sparse or compressible. Since many images bear this property, several acquisition models have been proposed for optical CS. An interesting approach is random convolution (RC). In contrast with single-pixel CS approaches, RC allows for the parallel capture of visual information on a sensor array as in conventional imaging approaches. Unfortunately, the RC strategy is difficult to implement as is in practical settings due to important contrast-to-noise-ratio (CNR) limitations. In this paper, we introduce a modified RC model circumventing such difficulties by considering measurement matrices involving sparse non-negative entries. We then implement this model based on a slightly modified microscopy setup using incoherent light. Our experiments demonstrate the suitability of this approach for dealing with distinct CS scenarii, including 1-bit CS.
Highlights
Since the 1970s, the redundant nature of real-world signals has been widely exploited in distinct applications such as seismology, computed tomography, magnetic resonance imaging, and radar imaging
We proposed a novel strategy and implementation for the parallel acquisition of optical compressed sensing (CS)-type measurements under spatially-incoherent illumination
Based on an adaptation of the initial random-convolution paradigm, our approach consisted in the modeling and design of tailored phase masks ensuring satisfactory contrast-to-noise ratios in practical settings
Summary
Since the 1970s, the redundant nature of real-world signals has been widely exploited in distinct applications such as seismology, computed tomography, magnetic resonance imaging, and radar imaging. We understand that, when expressed in some appropriate basis Ψ, the signal x consists of few non-zero entries. This is mathematically expressed as kΨxk0 ⌧ N, where k · k0 is the l0 pseudo-norm. Algorithmic tools exploiting the (conditional) equivalence between the l0 and l1-norm have been developed. This equivalence is the key to computational tractability because it allows one to cast CS reconstruction—which initially corresponds to an NP-hard l0norm-minimization problem—into a convex l1-norm minimization problem for which several efficient resolution techniques are readily available in the literature
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