Fixes #211: Adjust normalization of density compensation coefficients…

…. Add Cufinufft Pipe function authored by Chaithya G.R.

src/mrinufft/operators/interfaces/cufinufft.py

@@ -39,6 +39,30 @@
 
 DTYPE_R2C = {"float32": "complex64", "float64": "complex128"}
 
+def _next235beven(n, b):
+    """Find the next even integer not less than n.
+
+    This function finds the next even integer not less than n, with prime factors no
+    larger than 5, and is a multiple of b (where b is a number that only
+    has prime factors 2, 3, and 5).
+    It is used in particular with `pipe` density compensation estimation.
+    """
+    if n <= 2:
+        return 2
+    if n % 2 == 1:
+        n += 1  # make it even
+    nplus = n - 2  # to cancel out the +=2 at start of loop
+    numdiv = 2  # a dummy that is >1
+    while numdiv > 1 or nplus % b != 0:
+        nplus += 2  # stays even
+        numdiv = nplus
+        while numdiv % 2 == 0:
+            numdiv //= 2  # remove all factors of 2, 3, 5...
+        while numdiv % 3 == 0:
+            numdiv //= 3
+        while numdiv % 5 == 0:
+            numdiv //= 5
+    return nplus
 
 def _error_check(ier, msg):
     if ier != 0:
@@ -849,3 +873,60 @@ def toggle_grad_traj(self):
         if self.uses_sense:
             self.smaps = self.smaps.conj()
         self.raw_op.toggle_grad_traj()
+
+    @classmethod
+    def pipe(
+        cls,
+        kspace_loc,
+        volume_shape,
+        num_iterations=10,
+        osf=2,
+        normalize=True,
+        **kwargs,
+    ):
+        """Compute the density compensation weights for a given set of kspace locations.
+
+        Parameters
+        ----------
+        kspace_loc: np.ndarray
+            the kspace locations
+        volume_shape: np.ndarray
+            the volume shape
+        num_iterations: int default 10
+            the number of iterations for density estimation
+        osf: float or int
+            The oversampling factor the volume shape
+        normalize: bool
+            Whether to normalize the density compensation.
+        """
+        if CUFINUFFT_AVAILABLE is False:
+            raise ValueError(
+                "gpuNUFFT is not available, cannot " "estimate the density compensation"
+            )
+        original_shape = volume_shape
+        volume_shape = np.array([_next235beven(int(osf * i), 1) for i in volume_shape])
+        grid_op = MRICufiNUFFT(
+            samples=kspace_loc,
+            shape=volume_shape,
+            upsampfac=1,
+            gpu_spreadinterponly=1,
+            gpu_kerevalmeth=0,
+            **kwargs,
+        )
+        density_comp = cp.ones(kspace_loc.shape[0], dtype=grid_op.cpx_dtype)
+        for _ in range(num_iterations):
+            density_comp /= cp.abs(
+                grid_op.op(
+                    grid_op.adj_op(density_comp.astype(grid_op.cpx_dtype))
+                ).squeeze()
+            )
+        if normalize:
+            test_op = MRICufiNUFFT(
+                samples=kspace_loc,
+                shape=original_shape,
+                **kwargs
+            )
+            test_im = cp.ones(original_shape, dtype=test_op.cpx_dtype)
+            test_im_recon = test_op.adj_op(density_comp*test_op.op(test_im))
+            density_comp /= cp.mean(cp.abs(test_im_recon))
+        return density_comp.squeeze()

src/mrinufft/operators/interfaces/gpunufft.py

@@ -590,12 +590,12 @@ def pipe(
             The oversampling factor the volume shape
         normalize: bool
             Whether to normalize the density compensation.
-            We normalize such that the energy of PSF = 1
         """
         if GPUNUFFT_AVAILABLE is False:
             raise ValueError(
                 "gpuNUFFT is not available, cannot " "estimate the density compensation"
             )
+        original_shape = volume_shape
         volume_shape = (np.array(volume_shape) * osf).astype(int)
         grid_op = MRIGpuNUFFT(
             samples=kspace_loc,
@@ -607,11 +607,14 @@ def pipe(
             max_iter=num_iterations
         )
         if normalize:
-            spike = np.zeros(volume_shape)
-            mid_loc = tuple(v // 2 for v in volume_shape)
-            spike[mid_loc] = 1
-            psf = grid_op.adj_op(grid_op.op(spike))
-            density_comp /= np.linalg.norm(psf)
+            test_op = MRIGpuNUFFT(
+                samples=kspace_loc,
+                shape=original_shape,
+                **kwargs
+            )
+            test_im = np.ones(original_shape, dtype=np.complex64)
+            test_im_recon = test_op.adj_op(density_comp*test_op.op(test_im))
+            density_comp /= np.mean(np.abs(test_im_recon))
         return density_comp.squeeze()
 
     def get_lipschitz_cst(self, max_iter=10, tolerance=1e-5, **kwargs):