[hal-00453288, v1] On the incoherence of noiselet and Haar bases
نویسندگان
چکیده
Noiselets are a family of functions completely uncompressible using Haar wavelet analysis. The resultant perfect incoherence to the Haar transform, coupled with the existence of a fast transform has resulted in their interest and use as a sampling basis in compressive sampling. We derive a recursive construction of noiselet matrices and give a short matrix-based proof of the incoherence.
منابع مشابه
On the incoherence of noiselet and Haar bases
Noiselets are a family of functions completely uncompressible using Haar wavelet analysis. The resultant perfect incoherence to the Haar transform, coupled with the existence of a fast transform has resulted in their interest and use as a sampling basis in compressive sampling. We derive a recursive construction of noiselet matrices and give a short matrix-based proof of the incoherence.
متن کاملEfficient 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 nonbinary noiselet functions for object sampling in single-pixel cameras with binary spatial light modulators and incoh...
متن کاملMultichannel Compressive Sensing MRI Using Noiselet Encoding
The incoherence between measurement and sparsifying transform matrices and the restricted isometry property (RIP) of measurement matrix are two of the key factors in determining the performance of compressive sensing (CS). In CS-MRI, the randomly under-sampled Fourier matrix is used as the measurement matrix and the wavelet transform is usually used as sparsifying transform matrix. However, the...
متن کاملCompressed Sensing Based Computed Tomography Image Reconstruction
In computed tomography (CT), an important objective is to reduce radiation dose without degrading image quality. The radiation exposure from CT scan will make severe problem in humans. This has high risk in the case of children and female. The higher exposure will lead to leukemia, cancer etc. So that low dose CT image reconstruction is the main concern now days. We have to reconstruct the imag...
متن کاملBlock Based Compressive Sensing for GPR Images by Using Noiselet and Haar Wavelet
ompressive sensing (CS) is a new method for image sampling in contrast with well-known Nyquist sampling theorem. In addition to the sampling and sparse domain which play an important role in perfect signal recovery on CS framework, the recovery algorithm which has been used also has effects on the reconstructed image. In this paper, the performance of four recovery algorithms are compared accor...
متن کامل