Single pixel imaging at high pixel resolutions

The usually reported pixel resolution of single pixel imaging (SPI) varies between $32 \times 32$ and $256 \times 256$ pixels falling far below imaging standards with classical methods. Low resolution results from the trade-off between the acceptable compression ratio, the limited DMD modulation frequency, and reasonable reconstruction time, and has not improved significantly during the decade of intensive research on SPI. In this paper we show that image measurement at the full resolution of the DMD, which lasts only a fraction of a second, is possible for sparse images or in a situation when the field of view is limited but is a priori unknown. We propose the sampling and reconstruction strategies that enable us to reconstruct sparse images at the resolution of $1024 \times 768$ within the time of $0.3~$s. Non-sparse images are reconstructed with less details. The compression ratio is on the order of $0.4 \%$ which corresponds to an acquisition frequency of $7~$Hz. Sampling is differential, binary, and non-adaptive, and includes information on multiple partitioning of the image which later allows us to determine the actual field of view. Reconstruction is based on the differential Fourier domain regularized inversion (D-FDRI). The proposed SPI framework is an alternative to both adaptive SPI, which is challenging to implement in real time, and to classical compressive sensing image recovery methods, which are very slow at high resolutions.

Differential real-time single-pixel imaging with Fourier domain regularization -- applications to VIS-IR imaging and polarization imaging

The speed and quality of single-pixel imaging (SPI) are fundamentally limited by image modulation frequency and by the levels of optical noise and compression noise. In an approach to come close to these limits, we introduce a SPI technique, which is inherently differential, and comprises a novel way of measuring the zeroth spatial frequency of images and makes use of varied thresholding of sampling patterns. With the proposed sampling, the entropy of the detection signal is increased in comparison to standard SPI protocols. Image reconstruction is obtained with a single matrix-vector product so the cost of the reconstruction method scales proportionally with the number of measured samples. A differential operator is included in the reconstruction and following the method is based on finding the generalized inversion of the modified measurement matrix with regularization in the Fourier domain. We demonstrate $256 \times 256$ SPI at up to $17~$Hz at visible and near-infrared wavelength ranges using two polarization or spectral channels. A low bit-resolution data acquisition device with alternating-current-coupling can be used in the measurement indicating that the proposed method combines improved noise robustness with a differential removal of the direct current component of the signal.

Single-pixel imaging with Morlet wavelet correlated random patterns

Single-pixel imaging is an indirect imaging technique which utilizes simplified optical hardware and advanced computational methods. It offers novel solutions for hyper-spectral imaging, polarimetric imaging, three-dimensional imaging, holographic imaging, optical encryption and imaging through scattering media. The main limitations for its use come from relatively high measurement and reconstruction times. In this paper we propose to reduce the required signal acquisition time by using a novel sampling scheme based on a random selection of Morlet wavelets convolved with white noise. While such functions exhibit random properties, they are locally determined by Morlet wavelet parameters. The proposed method is equivalent to random sampling of the properly selected part of the feature space, which maps the measured images accurately both in the spatial and spatial frequency domains. We compare both numerically and experimentally the image quality obtained with our sampling protocol against widely-used sampling with Walsh-Hadamard or noiselet functions. The results show considerable improvement over the former methods, enabling single-pixel imaging at low compression rates on the order of a few percent.

Compressive phase-only filtering at extreme compression rates

We introduce an efficient method for the reconstruction of the correlation between a compressively measured image and a phase-only filter. The proposed method is based on two properties of phase-only filtering: such filtering is a unitary circulant transform, and the correlation plane it produces is usually sparse. Thanks to these properties, phase-only filters are perfectly compatible with the framework of compressive sensing. Moreover, the lasso-based recovery algorithm is very fast when phase-only filtering is used as the compression matrix. The proposed method can be seen as a generalisation of the correlation-based pattern recognition technique, which is hereby applied directly to non-adaptively acquired compressed data. At the time of measurement, any prior knowledge of the target object for which the data will be scanned is not required. We show that images measured at extremely high compression rates may still contain sufficient information for target classification and localization, even if the compression rate is high enough, that visual recognition of the target in the reconstructed image is no longer possible. The method has been applied by us to highly undersampled measurements obtained from a single-pixel camera, with sampling based on randomly chosen Walsh-Hadamard patterns.

Efficient adaptation of complex-valued noiselet sensing matrices for compressed single-pixel imaging

Minimal mutual coherence of discrete noiselets and Haar wavelets makes this pair of bases an essential choice for the measurement and compression matrices in compressed-sensing-based single-pixel detectors. In this paper we propose an efficient way of using complex-valued and non-binary noiselet functions for object sampling in single-pixel cameras with binary spatial light modulators and incoherent illumination. The proposed method allows to determine m complex noiselet coefficients from m+1 binary sampling measurements. Further, we introduce a modification to the complex fast noiselet transform, which enables computationally-efficient real-time generation of the binary noiselet-based patterns using efficient integer calculations on bundled patterns. The proposed method is verified experimentally with a single-pixel camera system using a binary spatial light modulator.