Compressed imaging by sparse random convolution

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. 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 contrastto-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.

From modeling to hardware: an experimental evaluation of image plane and Fourier plane coded compressive optical imaging

“…1(b)). Here, the SLM modulates the spatial frequencies present in the object [21]. This configuration allows for amplitude and/or phase modulation and provides the opportunity for superresolution from only a single measurement, therefore maintaining the possibility of high-speed imaging [22].…”

“…Willett et al have previously noted that phase modulation in the imaging path, as is done in DRPE architectures, is more appropriate for coherent imaging [5]. While in theory phase modulation in the imaging path with incoherent light is feasible [39], and hardware implementation has been demonstrated [21], masks with low light throughput are required in order to achieve sufficient diversity of observations for compressive imaging [21]. Therefore, we have chosen to investigate amplitude-only SLM since phase modulation is impractical in many biomedical applications, especially those in low light settings and/or requiring short sensor integration times.…”

“…For random binary mask, the magnitude of their Fourier transform is effectively a two-dimensional delta function because the central DC component is several orders-of-magnitude larger than all other components. This, combined with the non-negativity constraint intrinsic to an incoherent setting causes observational diversity to decrease as the number of non-zero elements in the mask increases [21]. However, in practice, a minimum number of non-zero elements must be included in the mask to achieve sufficient light throughput and signal-tonoise ratio at the sensor [21].…”

“…This, combined with the non-negativity constraint intrinsic to an incoherent setting causes observational diversity to decrease as the number of non-zero elements in the mask increases [21]. However, in practice, a minimum number of non-zero elements must be included in the mask to achieve sufficient light throughput and signal-tonoise ratio at the sensor [21]. This dictates that the masks suitable for FPC with incoherent light should have some notion of sparsity in order to achieve the observational diversity necessary for CS, but not so much that the light throughput is insufficient to produce enough signal at the detector.…”

Interferometry-based modal analysis with finite aperture effects

“…Moreover, since such masks block a large portion of the light field through sampling, they tend to reduce the effective signal-to-noise ratio (SNR) [24], [25].…”