in this paper, by considering a squint angle for synthetic aperture radar in the strip-map mode, a method is proposed for estimating parameters of a fixed acceleration moving target. non-zero doppler centroid and range-azimuth coupling in the squint mode add complexity to estimation equations of moving target parameters and cause doppler ambiguity. this, in turn, causes to lose the efficiency o...

In this paper we develop an algorithm to reconstruct the wavelet coefficients of an image from the Radon transform data. The proposed method uses the properties of wavelets to localize the Radon transform and can be used to reconstruct a local region of the cross-section of a body using almost completely local data which significantly reduces the amount of exposure and computations in X-ray tom...

We present a novel approach to parameterised curve detection. The method is based on the generalised Radon transform, which is traditionally applied to a 2D edge/line map. The novelty of our method is the mapping of the original 2D image to a 3D orientation space, which then forms the input for the Radon transform. The orientation space representation offers important advantages. It can represe...

We develop an algorithm to reconstruct the wavelet coee-cients of an image from the Radon transform data. The proposed method uses the properties of wavelets to localize the Radon transform and can be used to reconstruct a local region of the cross section of a body, using almost completely local data which signiicantly reduces the amount of exposure and computations in X-ray tomography. For ex...

This thesis contains three articles. The first two concern inversion and local injectivity of the weighted Radon transform in the plane. The third paper concerns two of the key results from compressive sensing. In Paper A we prove an identity involving three singular double integrals. This is then used to prove an inversion formula for the weighted Radon transform, allowing all weight functions...

Two theorems are presented for wavelet decompositions of the two-dimensional Radon transform. The first theorem establishes an upper error bound in L-norm between the Radon transform and its wavelet approximation whose coefficients at different scales are estimated from Radon data acquired at corresponding sampling rates. The second theorem gives an estimate of the accuracy of a local image rec...

We use the theory of the continuous wavelet transform to derive inversion formulas for the Radon transform on L 1 \L 2 (R d). These inversion formulas turn out to be local in even dimensions in the following sense. In order to recover a function f from its Radon transform in a ball of radius R > 0 about a point x to within error , we can nd () > 0 such that this can be accomplished by knowing t...

The generalised Radon transform is a well-known tool for detecting parameterised shapes in an image. Applying the Radon transform to an image results in a parameter response function (PRF). Curves in the image become peaks in the PRF. The location of a peak corresponds to the parameters of a shape, and the amplitude to the amount of evidence for that shape. In this paper we discuss two importan...

reflection seismic data consist of primary reflections, coherent and incoherent noises. one of the objectives of seismic data processing is to enhance the quality of the real signals by attenuating different kinds of noises. multiples constitute one of the most troublesome forms of coherent noises in exploration seismology. multiple reflections often destructively interfere with the desired pri...

In shape reconstruction, the celebrated Fourier slice theorem plays an essential role. By virtue of the relation between the Radon transform, the Fourier transform and the 2-dimensional inverse Fourier transform, the shape of an object can be reconstructed from the knowledge of the object’s Radon transform. Unfortunately, a discrete implementation requires the use of interpolation techniques, s...