Superposition frames for adaptive time-frequency analysis and fast reconstruction

In this article we introduce a broad family of adaptive, linear time-frequency representations termed superposition frames, and show that they admit desirable fast overlap-add reconstruction properties akin to standard short-time Fourier techniques. This approach stands in contrast to many adaptive time-frequency representations in the extant literature, which, while more flexible than standard fixed-resolution approaches, typically fail to provide efficient reconstruction and often lack the regular structure necessary for precise frame-theoretic analysis. Our main technical contributions come through the development of properties which ensure that this construction provides for a numerically stable, invertible signal representation. Our primary algorithmic contributions come via the introduction and discussion of specific signal adaptation criteria in deterministic and stochastic settings, based respectively on time-frequency concentration and nonstationarity detection. We conclude with a short speech enhancement example that serves to highlight potential applications of our approach.Comment: 16 pages, 6 figures; revised versio

GPU-based Iterative Cone Beam CT Reconstruction Using Tight Frame Regularization

X-ray imaging dose from serial cone-beam CT (CBCT) scans raises a clinical concern in most image guided radiation therapy procedures. It is the goal of this paper to develop a fast GPU-based algorithm to reconstruct high quality CBCT images from undersampled and noisy projection data so as to lower the imaging dose. For this purpose, we have developed an iterative tight frame (TF) based CBCT reconstruction algorithm. A condition that a real CBCT image has a sparse representation under a TF basis is imposed in the iteration process as regularization to the solution. To speed up the computation, a multi-grid method is employed. Our GPU implementation has achieved high computational efficiency and a CBCT image of resolution 512\times512\times70 can be reconstructed in ~5 min. We have tested our algorithm on a digital NCAT phantom and a physical Catphan phantom. It is found that our TF-based algorithm is able to reconstrct CBCT in the context of undersampling and low mAs levels. We have also quantitatively analyzed the reconstructed CBCT image quality in terms of modulation-transfer-function and contrast-to-noise ratio under various scanning conditions. The results confirm the high CBCT image quality obtained from our TF algorithm. Moreover, our algorithm has also been validated in a real clinical context using a head-and-neck patient case. Comparisons of the developed TF algorithm and the current state-of-the-art TV algorithm have also been made in various cases studied in terms of reconstructed image quality and computation efficiency.Comment: 24 pages, 8 figures, accepted by Phys. Med. Bio

On the performance of superposition window

Superposition window is often used in the digital signal processing and other fields of signal processing such as power spectral estimation and adaptive time-frequency analysis. Different overlap and windows used in superposition system may affect the final results. The main contribution of this paper is in providing the insight into the properties of the overlap-add technique with different window or overlap ratio, which is very helpful in selecting these parameters for a practical application

Holographic Imaging of Crowded Fields: High Angular Resolution Imaging with Excellent Quality at Very Low Cost

We present a method for speckle holography that is optimised for crowded fields. Its two key features are an iterativ improvement of the instantaneous Point Spread Functions (PSFs) extracted from each speckle frame and the (optional) simultaneous use of multiple reference stars. In this way, high signal-to-noise and accuracy can be achieved on the PSF for each short exposure, which results in sensitive, high-Strehl re- constructed images. We have tested our method with different instruments, on a range of targets, and from the N- to the I-band. In terms of PSF cosmetics, stability and Strehl ratio, holographic imaging can be equal, and even superior, to the capabilities of currently available Adaptive Optics (AO) systems, particularly at short near-infrared to optical wavelengths. It outperforms lucky imaging because it makes use of the entire PSF and reduces the need for frame selection, thus leading to higher Strehl and improved sensitivity. Image reconstruction a posteriori, the possibility to use multiple reference stars and the fact that these reference stars can be rather faint means that holographic imaging offers a simple way to image large, dense stellar fields near the diffraction limit of large telescopes, similar to, but much less technologically demanding than, the capabilities of a multi-conjugate adaptive optics system. The method can be used with a large range of already existing imaging instruments and can also be combined with AO imaging when the corrected PSF is unstable.Comment: Accepted for publication in MNRAS on 15 Nov 201