Single-pixel compressive imaging in shift-invariant spaces via exact wavelet frames

This paper introduces a novel framework for single-pixel imaging via compressive sensing (CS) in shift-invariant (SI) spaces by exploiting the sparsity property of wavelet representation. We reinterpret acquisition procedure camera as filtering observed signal with continuous-domain functions that lie an SI subspace spanned integer shifts box function. The is modeled arbitrary generator whose special case function, which, we show paper, conventionally used imaging. propose to use separable B-spline generators which are intuitively complemented sparsity-inducing spline wavelets. models and underlying lead exact discretization inherently inverse problem finite-dimensional CS type. By solving optimization problem, parametric representation obtained. Such offers many practical advantages image processing applications. efficient matrix-free implementation conduct it on standard test images real-world measurement data. Experimental results proposed achieves significant improvement reconstruction quality relative conventional setups. MATLAB method described this has been made publicly available https://github.com/retiro/compressive_imaging_in_si_spaces.